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Dirac points are found to emerge due to the crossing of bands in the electronic structure of so-called sliding bilayer graphene. Group representation theory analysis corroborated with a tight-binding model for the ${p}_{z}$ orbitals is employed to demonstrate that the band crossings of energy dispersion curves at generic $\mathbf{k}$ points are guaranteed by the compatibility relations between the symmetries of eigenstates at the high-symmetry $\mathbf{k}$ points in the Brillouin zone. The Lifshitz transition picture and the transport properties of the systems are shown as consequences of the presence of Dirac points in governing the geometrical and topological properties of the Fermi energy surfaces.

We study the emergence of non-Hermitian band topology in a two-dimensional metal with planar spiral magnetism due to a momentum-dependent relaxation rate. A sufficiently strong momentum dependence of the relaxation rate leads to exceptional points in the Brillouin zone, where the Hamiltonian is nondiagonalizable. The exceptional points appear in pairs with opposite topological charges and are connected by arc-shaped branch cuts. We show that exceptional points inside hole and electron pockets, which are generally present in a spiral magnetic state with a small magnetic gap, can cause a drastic change of the Fermi surface topology by merging those pockets at isolated points in the Brillouin zone. We derive simple rules for the evolution of the eigenstates under semiclassical motion through these crossing points, which yield geometric phases depending only on the Fermi surface topology. The spectral function observed in photoemission exhibits Fermi arcs. Its momentum dependence is smooth -- despite of the nonanalyticities in the complex quasiparticle band structure., 7+10 pages, 5+3 figures, Supplemental Material included

Monolayer transition metal dichalcogenides (TMDs) with spin-valley coupling are a well-studied class of two-dimensional materials with potential for novel optoelectronics applications. Breaking time-reversal symmetry via an external magnetic field or supporting magnetic substrate can lift the degeneracy of the band gaps at the inequivalent $K$ and ${K}^{\ensuremath{'}}$ high symmetry points, or valleys, in the monolayer TMD Brillouin zone, a phenomenon known as valley splitting. However, reported valley splittings thus far are modest, and a detailed structural and chemical understanding of valley splitting via magnetic substrates is lacking. Here we probe the underlying physical mechanism with a series of density functional theory (DFT) calculations of magnetic atoms with varying coverage on the surface of prototypical monolayer ${\mathrm{WSe}}_{2}$ and ${\mathrm{MoS}}_{2}$ TMDs. Near-valence band edge energies for variable magnetic atom height, lateral registry, and magnetic moment are calculated with DFT, and trends are rationalized with a model Hamiltonian with second-order spin-dependent exchange coupling. From our analysis, we demonstrate how large valley splittings may be achieved and that the valley splitting can be understood with a superexchange mechanism, which strongly depends on overlaps of TMD Bloch states at the valley extrema with the localized $d$ states of the magnetic atom, as well as the out-of-plane component of the magnetic moment of the magnetic atom. Our calculations provide a basis for understanding prior measurements of valley splitting and suggest routes for enhancing valley splitting in future systems of interest.

The electronic properties of $\ensuremath{\pi}$-conjugated two-dimensional (2D) polymers near the Fermi level are determined by structural topology and chemical composition. Thus tight-binding (TB) calculations of the corresponding fundamental network can be used to explore the parameter space to find configurations with intriguing properties before designing the atomistic 2D polymer network. The vertex-transitive fes lattice, which is also called a square-octagon, 4-8, or 4.8${}^{2}$ lattice, is rich in interesting topological features including Dirac points and flat bands. Herein, we study its electronic and topological properties within the TB framework using representative parameters for chemical systems. Secondly, we demonstrate that the rational implementation of band structure features obtained from TB calculations in 2D polymers is feasible with a family of 2D polymers possessing fes structure. A one-to-one band structure correspondence between the fundamental network and 2D polymers is found. Moreover, changing the relative length of linkers connecting the triangulene units in the 2D polymers reflects tuning of hopping parameters in the TB model. These perturbations allow sizable local band gaps to open at various positions in the Brillouin zone. From analysis of the Berry curvature flux, none of the polymers exhibits a large topologically nontrivial band gap. However, we find a particular configuration of semimetallic characteristics with separate electron and hole pockets, which possess very low effective masses both for electrons (as small as ${m}_{\mathrm{e}}^{*}=0.05$) and for holes (as small as ${m}_{\mathrm{h}}^{*}=0.01$).

We develop a microscopic and atomistic theory of electron-spin-based qubits in gated quantum dots in a single layer of transition metal dichalcogenides. The qubits are identified with two degenerate locked spin and valley states in a gated quantum dot. The two qubit states are accurately described using a multimillion atom tight-binding model solved in wave-vector space. The spin-valley locking and strong spin-orbit coupling result in two degenerate states, one of the qubit states being spin down located at the $+K$ valley of the Brillouin zone, and the other state located at the $\ensuremath{-}K$ valley with spin up. We describe the qubit operations necessary to rotate the spin-valley qubit as a combination of the applied vertical electric field, enabling spin-orbit coupling in a single valley, with a lateral strongly localized valley-mixing gate.

High pressure synthesis of rhenium nitride pernitride ReN$_2$ with crystal structure unusual for transition metal dinitrides and high values of hardness and bulk modulus attracted significant attention to this system. We investigate the thermodynamic and electronic properties of the P2$_1$/c phase of ReN$_2$ and compare them with two other polytypes, C2/m and P4/mbm phases suggested in the literature. Our calculations of the formation enthalpy at zero temperature show that the former phase is the most stable of the three up to pressure p=170 GPa, followed by the stabilization of the P4/mbm phase at higher pressure. The theoretical prediction is confirmed by diamond anvil cell synthesis of the P4/mbm ReN$_2$ at $\approx$175 GPa. Considering the effects of finite temperature in the quasi-harmonic approximation at p=100 GPa we demonstrate that the P2$_1$/c phase has the lowest free energy of formation at least up to 1000 K. Our analysis of the pressure dependence of the electronic structure of the rhenium nitride pernitride shows a presence of two electronic topological transitions around 18 GPa, when the Fermi surface changes its topology due to an appearance of a new electron pocket at the high-symmetry Y$_2$ point of the Brillouin zone while the disruption of a neck takes place slightly off from the $\Gamma$-A line., Comment: 15 pages, 7 figures, 3 tables

Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently-reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\alpha$-RuCl$_3$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed., Comment: 19 pages, 7 figures, 1 table; v2: added several minor improvements and references

$\mathrm{Ta}{\mathrm{Se}}_{3}$ is a layered van der Waals semimetal with several inverted band gaps throughout the entire Brillouin zone and nontrivial ${Z}_{2}$ topological indices, which place it at the boundary between a strong and a weak topological phase. Our transport experiments reveal a quadratic nonsaturating magnetoresistance (MR) with values reaching ${10}^{4}$% at 1.8 K and 14 T, whose origins have to be searched in the material's band structure. Here we combine angle-resolved photoelectron spectroscopy experiments, also with spin resolution, with ab initio calculations based on density functional theory in order to draw a connection between the Fermi surface topology and the measured transport properties. Simulations based on the calculated Fermi surface clarify that electron-hole compensation plays an important role for the observed MR in the bulk material. At the surface, the position of Fermi level differs, and it can be controlled by alkali metal deposition which accounts not only for the energy shift of the bands but it slightly modifies the dispersion of the valence and conduction bands. We propose that the observed band-gap renormalization might offer a route for engineering the topological phase in $\mathrm{Ta}{\mathrm{Se}}_{3}$, alternative to strain.

We theoretically study the superconducting properties of multiband two-dimensional transition metal oxide superconductors by analyzing not only the role played by conventional singlet pairings, but also by the triplet order parameters, favored by the spin-orbit couplings present in these materials. In particular, we focus on the two-dimensional electron gas at the (001) interface between ${\mathrm{LaAlO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ band insulators where the low electron densities and the sizable spin-orbit couplings affect the superconducting features. Our theoretical study is based on an extended superconducting mean-field analysis of the typical multiband tight-binding Hamiltonian, as well as on a parallel analysis of the effective electronic bands in the low-momentum limit, including static on-site and intersite intraband attractive potentials under applied magnetic fields. The presence of triplet pairings is able to strongly reduce the singlet order parameters which, as a result, are no longer a monotonic function of the charge density. The interplay between the singlet and the triplet pairings affects the dispersion of quasiparticle excitations in the Brillouin zone and also induces anisotropy in the superconducting behavior under the action of an in-plane and of an out-of-plane magnetic fields. Finally, nontrivial topological superconducting states become stable as a function of the charge density, as well as of the magnitude and of the orientation of the magnetic field. In addition to the chiral, time-reversal breaking, topological superconducting phase, favored by the linear Rashba couplings and by the on-site attractive potentials in the presence of an out-of-plane magnetic field, we find that a time-reversal invariant topological helical superconducting phase is promoted by nonlinear spin-orbit couplings and by the intersite attractive interactions in the absence of magnetic field.

In recent years, the exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in seeking for new topological phases and material realization. In this work, we propose a new family of TSMs which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE) at half-filling. Meanwhile, the CICE at half-filling guarantees the presence of a second pair of CICE beyond half-filling. Both CICEs are linked at four-fold degenerate points (FDPs) at zone boundaries. In addition, we identify the generic criteria for the existence of the CICE in a time reversal invariant {\it spinless} fermion system or a spinfull system with negligible spin-orbital coupling (SOC). Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICE whose location centers in the first Brillouin zone (BZ) are identified. We provide a simplest model with SG $Pbam$ (No. 55) which exhibits CICE, and the exotic intertwined drumhead surface states, induced by double-band-inversions. Finally, we propose a series of material candidates that host butterfly-like CICE NLs, such as, ZrX$_2$ (X=P,As), GeTe$_5$Tl$_2$, CYB$_2$ and Al$_2$Y$_3$., 6 pages, 3 figures

Ir and Pt thickness dependences of the interfacial Dzyaloshinskii-Moriya interaction (iDMI), the perpendicular magnetic anisotropy (PMA), and the damping in Co-based systems grown by sputtering on Si substrates, using Ir or Pt under or overlayer of variable thickness ($0\ensuremath{\le}{t}_{\mathrm{Pt}}\ensuremath{\le}3.5\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ and $0\ensuremath{\le}{t}_{\mathrm{Ir}}\ensuremath{\le}1.5\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$), were investigated using Brillouin light scattering. Vibrating sample magnetometry measurements revealed a significant decrease of the areal magnetic moment at saturation as the thickness ${t}_{\mathrm{Pt}}$ or ${t}_{\mathrm{Ir}}$ of the overlayer increases, most likely due to the increasing intermixing. The intermixing, found to be negligible for Ir and Pt underlayers, is stronger for Ir than Pt overlayers. Damping measurements for Pt-based systems allowed us to conclude with the strong spin-pumping contribution. The analysis of the ${t}_{\mathrm{Pt}}$ dependence of damping, within the spin-pumping model, allowed us to determine the spin-diffusion length of Pt, found to be greater when Pt is used as an underlayer. The ${t}_{\mathrm{Pt}}$ dependence of the effective PMA and iDMI constants, for which similar trends to that of damping were observed, were qualitatively analyzed to separate the contribution of each interface with Co. It was found that these constants are stronger when Co is grown on Pt, most probably due to weaker intermixing at the Pt/Co interface. Linear dependence of damping vs the PMA effective constant was evidenced, confirming their relationship with spin-orbit coupling (SOC). A linear variation of the PMA effective constant vs the iDMI constant was observed in systems using Pt underlayer, whereas quadratic or linear correlations are possible when Pt is used as an overlayer, probably due to change of the interface SOC by the strong intermixing at the Co/Pt interface. The qualitative analysis of the Ir thickness dependence of iDMI and PMA constants revealed a significant (weak) contribution of the Ir/Co interface to PMA (iDMI). The surface iDMI constant of the Co/Ir interface was estimated to be 0.4 \ifmmode\pm\else\textpm\fi{} 0.1 pJ/m, which confirms the similar iDMI sign of Co/Ir and Co/Pt interfaces.

Recently, the interplay between the non-Hermitian skin effect (NHSE) and topological phases has attracted a lot of attention. When the NHSE occurs in a topological system, the conventional bulk-boundary correspondence (BBC) based on the Bloch band theory is destroyed. In this work, we investigate a non-Hermitian nodal-ring semimetal with the $s$-wave superconducting (SC) term. We find that the SC term introduces the intrinsic coupling between the different general Brillouin zones (GBZs) of the particle and hole subbands in our model, which drives the total GBZ to the BZ. Furthermore, when the SC term is finite, we show a possibility that the GBZ is the same as the BZ. We also find that the Bloch winding number of the quasi-one-dimensional model can predict the number of Majorana zero states faithfully in this case, which implies that the conventional BBC is reconstructed in our model. The localization strengths of the Majorana zero states are also calculated to show the reconstruction of conventional BBC. The finite-size effect, related experimental regimes in the electric circuit, and the fragility of this reconstructed conventional BBC are also discussed in this work.

Crystallographic point group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin zone (BZ) from one $k$-point to another for a fixed CPGS, it is expected that the wave vector point group symmetry (WPGS) can change, and consequently, a qualitative change in the texture of the spin polarization can occur [the expectation value of spin operator ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ in Bloch state $u(n,k)$ and the wave vector ${k}_{0}$]. However, the nature of the spin texture (ST) change is generally unsuspected. In this paper, we determine a full classification of the linear-in-$k$ ST patterns based on the polarity and chirality reflected in the WPGS at ${k}_{0}$. The spin-polarization vector ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes, and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wave vector $k$ in nonpolar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry of the crystal. For example, it is usually established that spin-momentum locking effect (spin vector always perpendicular to the wave vector) requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple STs near band edges at different $k$ valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different STs near band edges. The ST classification as well as the predicted compounds with multiple STs can be a platform for potential application for spin-valleytronics and the control of the ST by accessing different valleys.

Atomic and electronic structure investigations of the substitutional ${\mathrm{Au}}_{2}\mathrm{Sn}$ surface alloy formed on Au(111) are presented. Low energy electron diffraction and scanning tunneling microscopy (STM) reveal a structure with a local $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ periodicity with a superimposed modulation resulting in a $26\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ unit cell. STM images show a striped structure that resembles the herringbone reconstruction of clean Au(111), but with a longer periodicity compared to the $22\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ unit cell of clean Au(111). Angle-resolved photoelectron spectroscopy data along the high-symmetry lines $\overline{\mathrm{\ensuremath{\Gamma}}}\ensuremath{-}{\overline{K}}^{\ensuremath{'}}\ensuremath{-}{\overline{M}}^{\ensuremath{'}}$ and $\overline{\mathrm{\ensuremath{\Gamma}}}\ensuremath{-}{\overline{M}}^{\ensuremath{'}}\ensuremath{-}\phantom{\rule{4pt}{0ex}}{\overline{\mathrm{\ensuremath{\Gamma}}}}^{\ensuremath{'}}$ of a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ surface Brillouin zone show two bands from the ${\mathrm{Au}}_{2}\mathrm{Sn}$ surface alloy layer. The experimental bands are compared to the calculated band structure of the local $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ periodicity. Most of the experimental band dispersions are qualitatively reproduced by the theoretical band structure including a spin split of one of the alloy bands. However, our detailed data reveal a band split, not present in the calculated bands of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ model, which is a consequence of the striped atomic structure of the ${\mathrm{Au}}_{2}\mathrm{Sn}$ surface alloy.

We study the electronic structures of chiral, Eshelby-twisted van der Waals atomic layers with a particular focus on a chiral twisted graphite (CTG), a graphene stack with a constant twist angle $\theta$ between successive layers. We show that each CTG can host infinitely many resonant states which arise from the interaction between the degenerate monolayer states of the constituent layers. Each resonant state has a screw rotational symmetry, and may have a smaller reduced Brillouin zone than other non-resonant states in the same structure. And each CTG can have the resonant states with up to four different screw symmetries. We derive the energies and wave functions of the resonant states in a universal form of a one-dimensional chain regardless of $\theta$, and show that these states exhibit a clear optical selection rule for circularly polarized light. Finally, we discuss the uniqueness and existence of the exact center of the lattice and the self-similarity of the wave amplitudes of the resonant states., Comment: 20 pages, 13 figures

Hybridization between $f$ electrons and conduction bands ($c$-$f$ hybridization) is a driving force for many unusual phenomena. To provide insight into it, systematic studies of CeCoIn$_5$ heavy fermion superconductor have been performed by angle-resolved photoemission spectroscopy (ARPES) in a large angular range at temperature of $T=6$ K. The used photon energy of 122 eV corresponds to Ce $4d$-$4f$ resonance. Calculations carried out with relativistic multiple scattering Korringa-Kohn-Rostoker method and one-step model of photoemission yielded realistic simulation of the ARPES spectra indicating that Ce-In surface termination prevails. Surface states, which have been identified in the calculations, contribute significantly to the spectra. Effects of the hybridization strongly depend on wave vector. They include a dispersion of heavy electrons and bands gaining $f$-electron character when approaching Fermi energy. We have also observed a considerable variation of $f$-electron spectral weight at $E_F$, which is normally determined by both matrix element effects and wave vector dependent $c$-$f$ hybridization. Fermi surface scans covering a few Brillouin zones revealed large matrix element effects. A symmetrization of experimental Fermi surface, which reduces matrix element contribution, yielded a specific variation of $4f$-electron enhanced spectral intensity at $E_F$ around $\bar{\Gamma}$ and $\bar{M}$ points. Tight-binding approximation calculations for Ce-In plane provided the same universal distribution of $4f$-electron density for a range of values of the parameters used in the model., Comment: 15 pages, 9 figures

The study of neutral electronic excitations directly probed by electron energy loss spectroscopy experiments allows obtaining important insight about the physical origin of the charge density wave (CDW) transition in solids. In particular it allows us to disentangle purely phononic mechanisms from the excitonic insulator scenario which is associated to a purely electronic mechanism. As a matter of fact, while the the loss function of the excitonic insulators should display negative dispersive features associated to the softening of neutral electronic excitations at the CDW wave vector above the critical temperature, no softening is expected when the driving force is purely phononic. Here we perform a microscopic analysis of the dynamical charge response of CuTe, a material that displays a low-temperature Peierls-like CDW instability. By means of first-principles time-dependent density functional calculations of the loss function, we characterize the plasmon dispersion along the different directions, highlighting the role of the intrinsic structural anisotropy and the effects of the crystal local fields that are responsible for the periodic reappearance of the spectra of the first Brillouin zone as well as the formation of an acousticlike plasmon. Finally, we demonstrate that also in this system, in analogy with other materials displaying excitonic insulator instability, the low energy region of the loss function presents negative dispersive structures at momentum transfer close to the CDW wave vector. This is a feature common to both excitonic insulator transition and Peierls distortion that further highlights how the difference between the two mechanisms is at most quantitative.

We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such 2D exponentially localized -- yet valley polarized -- Wannier states, centered on the sites of the honeycomb lattice, paying particular attention to maintaining all the unobstructed symmetries. This includes the unitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and the chiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remains topologically obstructed and is not represented in a simple site-to-site fashion. We also analyze the gap and the dispersion of single particle and single hole excitations above a strong coupling ground state at integer fillings, which we find to be dominated by the on-site and the nearest neighbor terms of a triangular lattice hopping model, with a minimum at the center of the moire Brillouin zone. Finally, we use the insight gained from this real space description to understand the dependence of the gap and the effective mass on the range of the screened Coulomb interaction., Comment: 19 pages; (14p main text + 1.2p references + 4p supplementary) 7 figures

Three-, four-, and sixfold excitations have significantly extended the subjects of condensed-matter physics. There is an urgent need for a realistic material that can have coexisting three-, four-, and sixfold excitations. However, these materials are uncommon because these excitations in electronic systems are usually broken by spin-orbit coupling (SOC) and are normally far from the Fermi level. Unlike the case in electronic systems, phonon systems with a negligible SOC effect, not constrained by the Pauli exclusion principle, provide a feasible platform to realize these excitations in a wide frequency range. Hence, in this work, we demonstrate by first-principles calculations and symmetry analysis that perfect three-, four-, sixfold excitations appear in the phonon dispersion rather than the band structures of ${\mathrm{Zr}}_{3}{\mathrm{Ni}}_{3}{\mathrm{Sb}}_{4}$, which is a well-known indirect-gap semiconductor with an ${\mathrm{Y}}_{3}{\mathrm{Au}}_{3}{\mathrm{Sb}}_{4}$-type structure. This material features a threefold-degenerate quadratic contact triple-point phonon, fourfold-degenerate Dirac point phonon, and sixfold degenerate point phonon. Moreover, these nodal point phonons are very robust to uniform strain. Two obvious phonon surface arcs of the (001) plane are extended in the whole Brillouin zone, which will facilitate their detection in future experimental studies. The current work provides an ideal model to investigate rich excitations in a single material.

Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the hourglass dispersion can be jointly protected by symmorphic and nonsymmorphic symmetries, instead of the conventional nonsymmorphic symmetry. Moreover, using first-principles calculations, we realize our proposal in the phonon spectra of realistic materials that share an antiperovskite structure with space group $P4$/nmm. Importantly, the neck points of these hourglass dispersions trace out two nodal rings tangential to four nodal lines, forming a unique hourglass nodal cage in the bulk Brillouin zone. The Berry phase analysis reveals the nontrivial topology of these nodal rings and nodal lines. Furthermore, nontrivial surface states and isofrequency surface arcs are visible, facilitating their experimental confirmation of such exotic quasiparticles. work not only offers different insights into the hourglass dispersion, but also expands aspects for studying promising topological quasiparticles in condensed-matter systems.

By using first-principles calculations and symmetry analysis, we uncover that the rubidium-catena-telluridoaurate-family materials in space group (SG) 51 can exhibit ideal nodal-surface phonons separately in the three-dimensional Brillouin zone, characterized by nearly flat phonon bands in their phonon spectra. The nodal surfaces are protected both by the screw rotation symmetry and the time reversal symmetry. Moreover, our theoretical calculations demonstrate that the nodal surfaces are composed by twofold degenerate nodal points, which can form a straight singularity nodal line in the (001) surface, and that the (001) surface states display Dirac-type crossings and surface flat-band phononic states, confirming the topologically nontrivial nature of nodal-surface phonons. Our findings not only support that another class of nodal phononic states, i.e., one-node surface phonons, can exist in realistic materials in 230 SGs, but also put forward an effective way to search for nodal-surface phonons.

The topological characterization of nonequilibrium topological matter is highly nontrivial because familiar approaches designed for equilibrium topological phases may not apply. In the presence of crystal symmetry, Floquet topological insulator states cannot be easily distinguished from normal insulators by a set of symmetry eigenvalues at high symmetry points in the Brillouin zone. This work advocates a physically motivated, easy-to-implement approach to enhance the symmetry analysis to distinguish between a variety of Floquet topological phases. Using a two-dimensional inversion-symmetric periodically-driven system as an example, we show that the symmetry eigenvalues for anomalous Floquet topological states, of both first-order and second-order, are the same as for normal atomic insulators. However, the topological states can be distinguished from one another and from normal insulators by inspecting the occurrence of stable symmetry inversion points in their microscopic dynamics. The analysis points to a simple picture for understanding how topological boundary states can coexist with localized bulk states in anomalous Floquet topological phases., Comment: 4+ pages of main text, plus 3 pages of supplementary material, 7 figures in total, comments welcome

Based on first-principles calculations and effective model analysis, all possible straight nodal-line (NL) phonons in symmorphic and nonsymmorphic space groups are uncovered. A classification of two-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models at an arbitrary point on the NLs is carried out, and these NL phonons are found to locate along the high-symmetry lines of the Brillouin zone. According to our classification, there are two types of NL phonons. The first type is topologically nontrivial with a linear dispersion, while the second type is topologically trivial, exhibiting a quadratic dispersion. The second type hosts the highest order of NLs in phonon systems, and it is a promising platform for investigating topological phase transitions. All the minimum symmetries that guarantee the existence of straight NL phonons are uncovered, which can be used to distinguish the types of straight NLs. This paper not only classifies NL phonons but also provides guidance to search for topological NLs in bosonic systems.

The effects of downfolding a Brillouin zone can open gaps and quench the kinetic energy by flattening bands. Quasiperiodic systems are extreme examples of this process, which leads to new phases and critical eigenstates. We analytically and numerically investigate these effects in a two dimensional topological insulator with a quasiperiodic potential and discover a complex phase diagram. We study the nature of the resulting eigenstate quantum phase transitions; a quasiperiodic potential can make a trivial insulator topological and induce topological insulator-to-metal phase transitions through a unique universality class distinct from random systems. This wealth of critical behavior occurs concomitantly with the quenching of the kinetic energy, resulting in flat topological bands that could serve as a platform to realize the fractional quantum Hall effect without a magnetic field., Comment: 6 pages, 4 figures, and supplement materials. Updated results on the flatness ratio, the Berry curvature, and the Chern number of individual bands

Topological physics of phonon spectra has been attracting great interest. Using the first-principle calculations and symmetry analysis, we show the realistic ternary nitride ${\mathrm{Li}}_{6}{\mathrm{WN}}_{4}$ features ideal (nearly flat) nodal-surface and nodal-line structures in its phonon spectra. These nodal degeneracies are shaped like lanterns, and their existence is guaranteed by nonsymmorphic symmetry. The corresponding topological phonon surface state covers exactly half the surface Brillouin zone and can thereby be distinguished from those of conventional nodal-line and nodal-surface semimetals. Our study enriches the classification of topological quantum phases, predicts ideal material candidates, and provides a good platform for investigating the interaction between nodal-line and nodal-surface phonons.

By using symmetry analysis and first-principles calculations, we propose that the simple cubic structure of copper chloride (CuCl) in high-pressure phase can be worked as a three-dimensional (3D) topological phononic material, hosting the so-called topological phononic nodal links (TPNLs) in phonon spectra, which are intersected around the center of the Brillouin zone (BZ). More interestingly, another class of nodal-line phonons, i.e., the topological phononic nodal hexahedron net (TPNHN), exists at all the boundaries of 3D BZ and is composed of interconnected quadruply degenerate straight nodal lines. Their topologically nontrivial natures are confirmed by the Berry phase calculations. The TPNHN-induced Dirac cones and the TPNLs-induced drumheadlike surface states are observed in the surface BZ. In addition, the appearance of large surface arcs strongly supports the robustness of nodal-link phonons. Our theoretical results not only pave a route to explore new nodal-line phonons but also reveal that the semiconductor CuCl in high-pressure phase is an ideal material candidate to realize TPNHN and TPNLs.

The group V and VI transition metals share a common Fermi surface feature of hole ellipsoids at the $N$ point in the Brillouin zone. In clear contrast to the other Fermi surface sheets, which are purely of $d$ character, these arise from a band that has a significant proportion of $p$ character. By performing local density approximation (LDA), generalized gradient approximation (GGA), strongly constrained and appropriately normed (SCAN) meta-GGA, and $GW$ approximation calculations, we find that the $p$ character part of this band (and therefore the Fermi surface) is particularly sensitive to the exchange-correlation approximation. LDA and GGA calculations inadequately describe this feature, predicting $N$ hole ellipsoid sizes that are consistently too large in comparison to various experimental measurements, whereas quasiparticle self-consistent $GW$ calculations predict a size that is slightly too small (and non-self-consistent $GW$ calculations that use an LDA starting point predict a size that is much too small). Overall, for the metals tested here, SCAN provides the most accurate Fermi surface predictions, mostly correcting the discrepancies between measurements and calculations that were observed when LDA calculations were used. However, none of the tested exchange-correlation approximations succeeds in simultaneously bringing all of the measurable properties of these metals into good experimental agreement, particularly where magnetism is concerned. The SCAN calculations predict antiferromagnetic moments for Cr that are 3 times larger than the experimental value ($1.90\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ compared to $0.62\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$).

This paper identifies a general class of electronic configurations that in a magnetic background necessarily induce topological structure. The phases additionally feature a correspondence relating antiferromagnetic and ferro/ferrimagnetic realizations. More importantly, the authors find novel types of magnetic topology upon considering this mechanism in all space groups. These phases are exclusively mapped out in this analysis that takes into account planes and lines in the Brillouin zone, prompting a new notion of subdimensional topology that nonetheless has full 3D physical signatures, such as Fermi arcs.

We consider a hitherto unexplored setting of a stacked multilayer ($\mathcal{N}$) Lieb lattice which undergoes an unusual topological transition in the presence of intralayer spin-orbit coupling (SOC). The specific stacking configuration induces an effective nonsymmorphic two-dimensional lattice structure, even though the constituent monolayer Lieb lattice is characterized by a symmorphic space group. This emergent nonsymmorphicity leads to multiple doubly degenerate bands extending over the edge of the Brillouin zone (i.e., quadratic band crossing lines). In the presence of intralayer SOC, these doubly degenerate bands typically form three $\mathcal{N}$-band subspaces, mutually separated by two band gaps. We analyze the topological properties of these multiband subspaces, using specially devised Wilson loop operators to compute non-Abelian Berry phases in order to show that they carry a higher Chern number $\mathcal{N}$.

Three-dimensional Weyl semimetals have pairs of topologically protected Weyl nodes, whose projections onto the surface Brillouin zone are the end points of zero energy surface states called Fermi arcs. At the endpoints of the Fermi arcs, surface states extend into and are hybridized with the bulk. Here, we consider a two-dimensional junction of two identical Weyl semimetals whose surfaces are twisted with respect to each other and tunnel-coupled. Confining ourselves to commensurate angles (such that a larger unit cell preserves a reduced translation symmetry at the interface) enables us to analyze arbitrary strengths of the tunnel-coupling. We study the evolution of the Fermi arcs at the interface, in detail, as a function of the twisting angle and the strength of the tunnel-coupling. We show unambiguously that in certain parameter regimes, all surface states decay exponentially into the bulk, and the Fermi arcs become Fermi loops without endpoints. We study the evolution of the `Fermi surfaces' of these surface states as the tunnel-coupling strengths vary. We show that changes in the connectivity of the Fermi arcs/loops have interesting signatures in the optical conductivity in the presence of a magnetic field perpendicular to the surface., Comment: 18 pages, 12 figures

Inelastic neutron scattering spectra in the antiferromagnetic ferroborates ${\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Tb}}_{x}{\mathrm{Fe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ ($x$ = 0, 0.1, 0.2, and 1) reveal various magnetic excitations of the interacting iron and rare-earth subsystems. We observe an evolution of the magnetic system from ``easy-plane'', in the Tb-free ($x$ = 0) case, to ``easy-axis'' anisotropy for samples substituted with Tb. The spectra show hybridized Fe and Nd branches, which are determined by the Fe-Nd exchange splitting of the ground-state ${\mathrm{Nd}}^{3+}$ doublet. In the easy-plane configuration, near the Brillouin zone center, there are two different pairs of anticrossing quasiacoustic Fe and Nd modes in contrast to the easy-axis state, where the two corresponding pairs of the branches are degenerated. The high-energy (exchange) branches are similar in both spin configurations. The Ising-type anisotropy of the Tb ion prevents the magnetic moment from precession. The increasing of the Tb content changes the effective magnetic anisotropy and stabilizes the easy-axis state. The spin-wave dispersion in the substituted and pure $\mathrm{Tb}{\mathrm{Fe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ compounds, which have the same, easy-axis magnetic structure, but different crystal symmetry, strongly differ. The observed spectra were analysed in the frame of linear spin-wave theory and the exchange parameters were determined.

CrGe belongs to the family of cubic B20 intermetallics. From experimental investigations by susceptibility and de Haas-van Alphen (dHvA) measurements and from calculations of its electronic band structure by density-functional theory (DFT), CrGe is found to form a metallic paramagnetic ground state. Combining dHvA and DFT data, a detailed picture of the Fermi surface of CrGe is provided. The proximity to a magnetic long-range ordering in CrGe is suggested from a prominent thermal magnetic susceptibility. The possibility to induce magnetic long-range order in CrGe is discussed based on calculated properties for CrGe substituting Ge by As or Sn, and from a comparison with MnGe and the alloy series ${\mathrm{Cr}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Ge}$. Owing to the noncentrosymmetric and nonsymmorphic crystal structure of CrGe, in absence of broken time reversal symmetry, its band structure is marked by forced nodal lines at the Fermi edge. Moreover, this material hosts degenerate unconventional electronic quasiparticles. In particular, CrGe exhibits a sixfold degeneracy of fermions crossing within about 5 meV of the Fermi energy at the $R$ point of the Brillouin zone.

Berg, Metlitski and Sachdev, Science 338, 1606 (2012), have shown that the exchange of hidden spin fluctuations by conduction electrons with two orbitals can result in high-temperature superconductivity in copper-oxide materials. We introduce a similar model for high-temperature iron-selenide superconductors that are electron doped. Conduction electrons carry the minimal 3d xz and 3d yz iron-atom orbitals. Low-energy hidden spin fluctuations at the checkerboard wavevector Q_AF result from nested Fermi surfaces at the center and at the corner of the unfolded (one-iron) Brillouin zone. Magnetic frustration from super-exchange interactions via the selenium atoms stabilize hidden spin fluctuations at Q_AF versus true spin fluctuations. At half filling, Eliashberg theory based purely on the exchange of hidden spin fluctuations reveals a Lifshitz transition to electron/hole Fermi surface pockets at the corner of the folded (two-iron) Brillouin zone, but with vanishing spectral weights. The underlying hidden spin-density wave groundstate is therefore a Mott insulator. Upon electron doping, Eliashberg theory finds that the spectral weights of the hole Fermi surface pockets remain vanishingly small, while the spectral weights of the larger electron Fermi surface pockets become appreciable. This prediction is therefore consistent with the observation of electron Fermi surface pockets alone in electron-doped iron selenide by angle-resolved photoemission spectroscopy (ARPES). Eliashberg theory also finds an instability to S+- superconductivity at electron doping, with isotropic Cooper pairs that alternate in sign between the visible electron Fermi surface pockets and the faint hole Fermi surface pockets. Comparison with the isotropic energy gaps observed in electron-doped iron selenide by ARPES and by scanning tunneling microscopy (STM) is consistent with short-range hidden magnetic order., Comment: 48 pages, 7 figures, plus supplemental material (11 pages, 4 figures)

Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the 3D Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. In this work, we investigate the semi-classical optical response of two nodal loops in linked, unlinked and touching configurations, focusing particularly on the interplay of response anisotropy and non-linearity. We provide a geometric picture that unifies these aspects and sheds light on the effects of nodal topology and geometry. Based on a model abstracted from generic multi nodal loop scenarios, both with or without linkages, our findings will be applicable for a large class of nodal semimetal materials with multiple nodal lines or loops., Comment: 17 figures, 24 pages

Boron-rich materials combine chemical stability with refractory properties and, consequently, are interesting for high-temperature thermoelectric applications. Therefore, the magnetic, electrical, and thermal transport properties of the ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CrB}}_{4}$ series have been investigated here to employ the concept of correlation-enhanced thermoelectric properties. Combining x-ray diffraction and energy- or wavelength-dispersive spectrometry, we find a rather narrow stability range of ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CrB}}_{4}$, only samples on the Y- and Ce-rich substitution limits $(x=0,\phantom{\rule{0.28em}{0ex}}0.05,\phantom{\rule{0.28em}{0ex}}0.95,\phantom{\rule{0.28em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}1)$ were obtained. Electrical resistivity data show a change from semiconducting $(x=0)$ to metallic behavior upon Ce substitution $(x\ensuremath{\ge}0.95)$. From magnetic susceptibility measurements and x-ray absorption spectroscopy, we find a temperature-dependent intermediate valence state of Ce of about $+3.5$. However, a fit of the magnetic susceptibility data to the Coqblin-Schrieffer model yields a surprisingly high Kondo temperature of about 1100 K. Together with the good thermal conductivity for the studied substitution series this impedes a suitable thermoelectric performance. Electronic structure calculations for ${\mathrm{YCrB}}_{4}$ support its narrow gap semiconducting nature in contrast to previous studies. Surprisingly, its electronic structure is characterized by pronounced van Hove singularities very close to the Fermi-level ${E}_{\mathrm{F}}$. They originate from nearly dispersionless Cr $3{d}_{{z}^{2}\ensuremath{-}{r}^{2}}$-derived bands in a large part of the Brillouin zone, suggesting the appearance of electronic instabilities upon rather small electron doping into these states.

The topology of electronic states in band insulators with mirror symmetry can be classified in two different ways. One is in terms of the mirror Chern number, an integer that counts the number of protected Dirac cones in the Brillouin zone of high-symmetry surfaces. The other is via a Z2 index that distinguishes between systems that have a nonzero quantized orbital magnetoelectric coupling (“axion-odd”), and those that do not (“axion-even”); this classification can also be induced by other symmetries in the magnetic point group, including time reversal and inversion. A systematic characterization of the axion Z2 topology has previously been obtained by representing the valence states in terms of hybrid Wannier functions localized along one chosen crystallographic direction, and inspecting the associated Wannier band structure. Here we focus on mirror symmetry, and extend that characterization to the mirror Chern number. We choose the direction orthogonal to the mirror plane as the Wannierization direction and show that the mirror Chern number can be determined from the winding numbers of the touching points between Wannier bands on mirror-invariant planes and from the Chern numbers of flat bands pinned to those planes. In this representation, the relation between the mirror Chern number and the axion Z2 index is readily established. The formalism is illustrated by means of ab initio calculations for SnTe in the monolayer and bulk forms, complemented by tight-binding calculations for a toy model., Work by T.R. was supported by the Deutsche Forschungsgemeinschaft Grant No. Ra 3025/1-1 from the Deutsche Forschungsgemeinschaft. Work by D.V. was supported by National Science Foundation Grant DMR-1954856. Work by I.S. was supported by Grant No. FIS2016-77188-P from the Spanish Ministerio de Economía y Competitividad.

The topological metal states in electronic systems have been extensively studied, but topological phonons were explored only in a few examples so far. Here, we expose that the topological type-I and type-II Weyl phonons simultaneously appear in a recently realized new carbon allotrope, $T$-carbon, and the topological surface states of phonons are well separated from its bulk phonon spectra that are suitable for experiments. At about 15.2 THz, we find that there exist three mutually orthogonally intersecting nodal loops (named nodal gimbal phonons) centered at the $\mathrm{\ensuremath{\Gamma}}$ point, and two pairs of type-I Weyl phonons on the boundary of Brillouin zone around each $X$ point. In addition, there exist three pairs of type-II Weyl phonons at about 14.5 THz around each $L$ point. It is shown that these exotic topological phonons are protected by corresponding symmetries, and lead to topologically nontrivial surface states. Our findings not only afford plenty of intriguing topological phonon states in a simple material like $T$-carbon but also provide a platform to study novel properties of topological phonons, which would facilitate further both experimental and theoretical works in future.

Motivated by the absence of experimental superconductivity in the metallic $\mathit{Pm}\overline{3}\mathit{n}$ phase of ${\mathrm{AlH}}_{3}$ despite the predictions, we reanalyze its vibrational and superconducting properties at pressures $P\ensuremath{\ge}99$ GPa making use of first-principles techniques. In our calculations based on the self-consistent harmonic approximation method that treats anharmonicity beyond perturbation theory, we predict a strong anharmonic correction to the phonon spectra and demonstrate that the superconducting critical temperatures predicted in previous calculations based on the harmonic approximation are strongly suppressed by anharmonicity. The electron-phonon coupling concentrates on the lowest-energy hydrogen-character optical modes at the X point of the Brillouin zone. As a consequence of the strong anharmonic enhancement of their frequency, the electron-phonon coupling is suppressed by at least 30%. The suppression in $\ensuremath{\lambda}$ makes ${T}_{c}$ smaller than 4.2 K above 120 GPa, which is well consistent with the experimental evidence. Our results underline that metal hydrides with hydrogen atoms in interstitial sites are subject to huge anharmonic effects.

We show that the valley Chern number of the low-energy band in twisted double bilayer graphene can be tuned through two successive topological transitions, where the direct band gap closes, by changing the electric field perpendicular to the plane of the graphene layers. The two transitions with Chern number changes of $\ensuremath{-}3$ and $+1$ can be explained by the formation of three satellite Dirac points around the central Dirac cone in the moir\'e Brillouin zone due to the presence of trigonal warping. The satellite cones have opposite chirality to the central Dirac cone. Considering the overlap of the bands in energy, which lead to metallic states, we construct the experimentally observable phase diagram of the system in terms of the indirect band gap and the anomalous valley Hall conductivity. We show that while most of the intermediate phase becomes metallic, there is a narrow parameter regime where the transition through three insulating phases with different quantized valley Hall conductivity can be seen. We systematically study the effects of variations in the model parameters on the phase diagram of the system to reveal the importance of particle-hole asymmetry and trigonal warping in constructing the phase diagram. We also study the effect of changes in interlayer tunneling on this phase diagram.

By using ab initio calculations and symmetry analysis, we define a class of Weyl phonons: charge-four Weyl phonons (CFWPs) characterized by Chern number $\ifmmode\pm\else\textpm\fi{}4$ in their acoustic phonon spectra due to chiral point-group symmetries. Some high-symmetry points in the chiral space groups (SGs) of phononic systems behaving as quadratic Weyl points tend to form CFWPs. As enumerated in this paper, the CFWPs are located at the boundaries or the center of the three-dimensional Brillouin zone and are protected by the time-reversal symmetry $\mathcal{T}$ and the corresponding point-group symmetries. Moreover, in a realistic chiral crystal example of BiIrSe in SG 198, a monopole CFWP is confirmed at point $\mathrm{\ensuremath{\Gamma}}$ with quadratic twofold degeneracies, and in another example of ${\mathrm{Li}}_{3}{\mathrm{CuS}}_{2}$ in SG 214, the CFWPs are found at the high-symmetry points $\mathrm{\ensuremath{\Gamma}}$ and $H$. Our theoretical results not only uncover a class of Weyl phonons but also put forward an effective way to search for CFWPs in spinless systems.

In recent research, it has been shown that non-Hermitian systems exhibit sensitivity to boundaries, and it is caused by the non-Hermitian skin effect. In this work, we construct the non-Bloch band theory in bosonic Bogoliubov--de Gennes (BdG) systems. From our theory, we can calculate the generalized Brillouin zone and the energy spectrum in such systems with open boundary conditions in the thermodynamic limit, and we can thus discuss its non-Hermitian nature, despite Hermiticity of an original Hamiltonian. In fact, we find that the bosonic Kitaev-Majorana chain exhibits rich aspects of the non-Hermitian skin effect, such as instability against infinitesimal perturbations and reentrant behavior, in terms of the non-Bloch band theory. This result indicates that our theory is powerful tool for studying non-Hermitian nature in bosonic BdG systems., 9 pages, 3 figures

We analyze the valley selection rules for optical transitions from impurity states to the conduction band in two-dimensional Dirac materials, taking a monolayer of MoS2 as an example. We employ the analytical model of a shallow impurity potential which localizes electrons described by a spinor wave function, and, first, find the system eigenstates taking into account the presence of two valleys in the Brillouin zone. Then, we find the spectrum of the absorbance and calculate the photon-drag electric current due to the impurity-band transitions, drawing the general conclusions regarding the valley optical selection rules for the impurity-band optical transitions in gapped Dirac materials., Comment: 5 pages, 4 figures

We present a detailed study of the spin-wave dynamics in single Pt/Co/W and double Pt/Co/W/Co/Pt ferromagnetic layer systems. The dispersion of spin waves was measured by wavevector-resolved Brillouin light scattering spectroscopy while the in-plane and out-of-plane magnetization curves were measured by alternating gradient field magnetometry. The interfacial Dzyaloshinskii-Moriya interaction induced nonreciprocal dispersion relation was demonstrated for both single and double ferromagnetic layers and explicated by numerical simulations and theoretical formulas. The results indicate the crucial role of the order of layers deposition on the magnetic parameters. A significant difference between the perpendicular magnetic anisotropy constant in double ferromagnetic layer systems conduces to the decline of the interlayer interactions and different dispersion relations for the spin-wave modes. Our study provides a significant contribution to the realization of the multifunctional nonreciprocal magnonic devices based on ultrathin ferromagnetic/heavy-metal layer systems., Comment: This version of the manuscript is a prereview first-submission version. 10 pages, 4 figures

Nodal-line semimetals are typically characterized by a nodal ring, a closed line of Dirac points in the Brillouin zone, whose topology is characterized by a quantized Berry phase. The nodal loop is protected by the combined inversion and time-reversal ($\mathcal{PT}$) symmetry in the absence of spin-orbit coupling, exhibiting the parity anomaly. Introduction of the $\mathcal{PT}$-break mass term can lead to the transverse Hall response at each point in the nodal ring, but the net Hall current vanishes due to the existence of inversion-symmetry points that contribute to the transverse current with opposite signs. We show that the combination of an inversion-broken tilt term and finite Fermi energy can cause the nonzero anomalous Hall effect. We explore the DC and AC anomalous Hall conductivity in tilted nodal-line semimetals using Kubo formula and focus on the contribution of the free carriers to the Hall conductivity. We find that the interband transition of free carriers dominates the nonvanishing dynamic Hall conductivity over the filled band contribution. The resulting anomalous Hall conductivity exhibits the parity anomaly for the DC case, and rich characteristic frequencies for the AC case which is closely related to the change of the geometry of the Fermi surface. These features may serve as a diagnostic tool to characterize the topological property, tilting parameter, or the radius of the nodal line.

Exchange coupling between localized spins and band or topological states accounts for giant magnetotransport and magnetooptical effects as well as determines spin-spin interactions in magnetic insulators and semiconductors. However, even in archetypical dilute magnetic semiconductors such as Cd$_{1-x}$Mn$_x$Te and Hg$_{1-x}$Mn$_x$Te the evolution of this coupling with the wave vector is not understood. A series of experiments have demonstrated that exchange-induced splitting of magnetooptical spectra of Cd$_{1-x}$Mn$_x$Te and Zn$_{1-x}$Mn$_x$Te at the L points of the Brillouin zone is, in contradiction to the existing theories, more than one order of magnitude smaller compared to its value at the zone center and can show an unexpected sign of the effective Land\'e factors. The origin of these findings we elucidate quantitatively by combining: (i) relativistic first-principles density functional calculations; (ii) a tight-binding approach that takes carefully into account k-dependence of the potential and kinetic sp-d exchange interactions; (iii) a theory of magnetic circular dichroism (MCD) for $E_1$ and $E_1$ + $\Delta_1$ optical transitions, developed here within the envelope function $kp$ formalism for the L point of the Brillouin zone in zinc-blende crystals. This combination of methods leads to the conclusion that the physics of MCD at the boundary of the Brillouin zone is strongly affected by the strength of two relativistic effects in particular compounds: (i) the mass-velocity term that controls the distance of the conduction band at the L point to the upper Hubbard band of Mn ions and, thus, a relative magnitude and sign of the exchange splittings in the conduction and valence bands; (ii) the spin-momentum locking by spin-orbit coupling that reduces exchange splitting depending on the orientation of particular L valleys with respect to the magnetization direction., Comment: 20 pages, 6 figures

In the warm dense regime, where the electron temperature is increased to the same order of the Fermi temperature, the dynamical stability of elemental metals depends on its electronic band structure as well as its crystal structure. It has been known that phonon hardening occurs due to an enhanced internal pressure caused by electron excitations as in close-packed simple metals, whereas phonon softening occurs at a specific point in the Brillouin zone as in body-centered cubic metals. Here, we investigate the dynamical stability of binary ordered alloys (Au and Cu) in the L1$_0$ and L1$_2$ structures. By performing first principles calculations on phonon dispersions, we demonstrate that warm dense Au-Cu systems show phonon hardening behavior except the lowest frequency phonon mode at point R of AuCu in the L1$_0$ structure. We show that when a phonon mode is stabilized by long-range interatomic interactions at ambient condition, such a phonon will be destabilized by the short-range nature of the warm dense matters., 8 pages, 6 figures

We present an ab initio study of the thermodynamic properties of cubic $\mathrm{Ca}\mathrm{Si}{\mathrm{O}}_{3}$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate ab initio free energy in the thermodynamic limit ($N\ensuremath{\rightarrow}\ensuremath{\infty}$) within the framework of the phonon gas model. Accurate free energy calculations enable us to investigate cubic CaPv's thermodynamic properties, e.g., thermal expansivity, Gr\"uneisen parameter, bulk modulus, heat capacity and thermal equation of state, where anharmonic effects are demonstrated. The present methodology provides an important theoretical approach for exploring phase boundaries, thermodynamic, and thermoelastic properties of strongly anharmonic materials at high pressures and temperatures.

We present investigations of the frequency and magnetic field dependent properties of ordered magnetic nanoparticles (MNPs) arrangements consisting of magnetite (${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$) nanoparticles with an average diameter of 20 nm by employing micro Brillouin light scattering microscopy. We utilized electron beam lithography to prepare hexagonally arranged, circularly shaped MNP assemblies consisting of a single layer of MNPs using a variant of the Langmuir-Blodgett technique. By comparing the results with nonstructured, layered superlattices of MNPs, further insight into the influence of size and geometry of the arrangement on the collective magnetic properties is obtained. We show that at low static external field strengths, two signals occur in frequency dependent measurements for both nonstructured and structured assemblies. Increasing the static external field strength results in a sharpening of the main signal, while the satellite signal decreases in its intensity and increases in its linewidth. The occurrence of multiple signals at low external field strengths is also confirmed by sweeping the static external field and keeping the excitation frequency constant. Furthermore, two-dimensional spatial mapping of the resonances reveals that the main and the satellite signal originate from the center and the edge, respectively, of a single circular MNP assembly. Micromagnetic simulations confirm these assignments and the dependence of the two signals on the static external field strength, justifying an interpretation of the observed characteristics in terms of different local environments of MNPs forming the MNP assembly.

Locally resonant acoustic materials were proposed to control sound using structures with feature size orders of magnitude smaller than the acoustic wavelength in air. We analytically derive the effective, frequency-dependent mass densities of resonant oscillators consisting of a heavy mass within a light shell, embedded in foam, in two dimensions, using a rigid core-shell approximation. The effective mass is expressible in closed form by elementary functions, enabling a mapping of the low-frequency physics to a simple one-dimensional model involving a point mass harmonically coupled within a box. The acoustic band structure of a two-dimensional square lattice of these oscillators is evaluated in the effective, frequency-dependent mass density model and compared with the exact solution. For the out-of-plane oscillation within this two-dimensional phononic crystal, the nonlinear eigenvalue equation resulting from the frequency-dependent density is solved with the Cutting Surface Method to yield the acoustic band structure. This agrees with the exact band structure obtained by finite element method calculations within $2%$ numerical error. For the in-plane oscillations involving internal translations or rotations within the core-shell resonators, the one-dimensional mass-in-a-box model recaptures the exact acoustic modes at only certain high-symmetry points of the two-dimensional Brillouin zone. The description of more complex resonances within acoustic metamaterials requires a fundamental generalization of current effective mass models.

Aperiodic metamaterials can host topological or localized wave modes, and gradually changing structures are known to induce conversion between elastic wave types. This work describes a family of one dimensional, aperiodic elastic structures that can host localized modes or achieve low-frequency attenuation by varying a single geometrical parameter, i.e., the ratio between the sizes of two interacting periodic structures. Two periodic sets of slits on the top and bottom of a slender beam scatter bending waves. The thickness profile and cross section of beams with a period ratio close to 1 varies slowly, resulting in localized wave modes. The localization happens because of spatially confined band gaps and is only triggered for certain excitation locations, unlike wave localization due to a local defect. If the periods differ more, broad band gaps appear at wave numbers equal to linear combinations of the individual Brillouin zone edges of each set of slits. We call these interaction band gaps, since they result from the interplay between two periodic sets of slits. Low-frequency wave attenuation is achieved while maintaining a high overall bending stiffness.