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Starting from a realistic extended Hubbard model for a $p_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation on the possible electron instabilities in the MA-TBG near the van Hove (VH) dopings. Here we focus on the interplay between the approximate SU(2)$\times$SU(2) symmetry and the $D_3$ symmetry, which leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic RPA based calculations followed by a succeeding mean-field energy minimization for the ground state energy. At the SU(2)$\times$SU(2) symmetric point, the degenerate inter-valley SDW and VDW are mixed into a new state of matter dubbed as the chiral SO(4) spin-valley DW. This state simultaneously hosts three 4-component vectorial spin-valley DW orders with each adopting one wave vector, and the polarization directions of the three DW orders are mutually perpendicular to one another. %in the $\mathbb{R}^4$ space. In the presence of a tiny inter-valley exchange interaction with coefficient $J_H\to 0^{-}$ which breaks the SU(2)$\times$SU(2) symmetry, a pure chiral SDW state is obtained. In the case of $J_H\to 0^{+}$, a nematic VDW+SDW state emerges which possesses a stripy distribution of the charge density, consistent with the recent STM observations. On the aspect of SC, while the triplet $p+ip$ and singlet $d+id$ topological SCs are degenerate at $J_H=0$ near the VH dopings, the former (latter) is favored for $J_H\to 0^{-}$ ($J_H\to 0^{+}$). In addition, the two asymmetric doping-dependent behaviors of the obtained pairing phase diagram are well consistent with experiments., Comment: Published version in PRB. 16 pages plus Appendices

Topological invariants play an important role in characterizing topological phases. However, the topological invariants of Hermitian systems usually fail to characterize non-Hermitian topological systems due to non-Hermiticity. In this work, we generalize the Majorana polarization, which is initially defined to describe Hermitian topological superconductors, as a topological edge invariant to characterize the non-Hermitian topological superconductors. The definition of the generalized Majorana polarization depends upon two inequivalent particle-hole symmetries in non-Hermitian systems. The spinless Kitaev chain model and topological superconductor model on the honeycomb lattice are considered to examine the reliability and validity of the generalized Majorana polarization. We find that the phase transitions obtained by using Majorana polarization are consistent with the commonly used complex-energy point gap descriptions, which indicates the Majorana polarization is a reliable topological invariant to characterize the topological phase transition in non-Hermitian topological superconductors. In addition, the non-Hermitian skin effect on Majorana bound states in non-Hermitian topological superconductors is also discussed.

We study the transport of a hybrid superconductor--quantum-dot--superconductor junction, dominated by the interplay between the Kondo effect and the proximity-induced $p$-wave pairing states. Each superconductor lead is fabricated with a semiconductor with Rashba spin-orbit coupling (RSOC) and the combination of an $s$-wave superconductor and a ferromagnet. The RSOC breaks the SU(2) spin-rotation symmetry and creates the spin-triplet pairing components under the proximity-induced superconducting pairing interaction. Different from the s-wave pairing case, the Kondo screening of the dot spin involves the orbital angular momentum conserved transitions between the $p$-wave pairing states. The Zeeman field inherent from the ferromagnet removes the spin degeneracy of the quasiparticles excited in the triplet states. As a result, the spin-induced Yu-Shiba-Rusinov (YSR) state exhibits Zeeman-dependent splitting behaviors, and the splitting of the YSR state leads to the 0-$\ensuremath{\pi}$ phase transition when the ground state is a Kondo singlet. The temperature-dependent magnetic susceptibility indicates that the dot spin should be partially screened due to the breaking of time-reversal symmetry.

The unified mathematical theory of gapped and gapless edges of two-dimensional (2d) topological orders was developed by two of the authors. According to this theory, the critical point of a purely edge topological phase transition of a 2d topological order can be mathematically characterized by an enriched fusion category. In this work, we provide a physical proof of this fact in a concrete example: the 2d ${\mathbb{Z}}_{2}$ topological order. In particular, we construct an enriched fusion category, which describes a gappable nonchiral gapless edge of the 2d ${\mathbb{Z}}_{2}$ topological order. Then, we use an explicit lattice model construction to realize a topological phase transition between the two well-known gapped edges of the 2d ${\mathbb{Z}}_{2}$ topological order, and show that all the ingredients of the above enriched fusion category can be realized explicitly in this lattice model.

Layered copper oxides have the highest superconducting transition temperatures at ambient pressure. Its mechanism remains a major challenge in condensed matter physics. The essential physics lying in two-dimensional copper-oxygen layers is well described by a single-band Hubbard model or its strong-coupling limit $t\ensuremath{-}J$ model in a two-dimensional square lattice. The recently discovered high-temperature superconductor ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ with $\ensuremath{\delta}\ensuremath{\sim}0.2$ has a different crystal structure with a large portion of in-plane oxygen vacancies. We observe that an oxygen vacancy breaks the bond of its two neighboring copper atoms, and propose the ordered vacancies in ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ lead to an extended $t\ensuremath{-}J$ model on an effective brick-wall lattice. For the nearest-neighbor hopping, the brick-wall model can be mapped onto the $t\ensuremath{-}J$ model on a honeycomb lattice. Our theory explains the superconductivity of ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ at a high charge carrier density, and predicts a time-reversal symmetry-broken pairing state.

The orbital degree of freedom plays a critical role in contemporary condensed-matter physics, with recent discoveries of orbital-dependent many-body effects including electron correlation and superconductivity. Nevertheless, these orbital-dependent many-body effects have mainly been observed in bulk materials, wherein the electrons' orbital attribute is challenging to tailor selectively. Here, by planar tunneling into the two-dimensional electron system (2DES) at the ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface, we observed a Kondo resonance, a model many-body phenomenon. The observation of the Kondo resonance provides an ideal opportunity to quantitatively exploit the emerging interfacial Kondo physics. Furthermore, it was found that the Kondo coupling strength and resonance line shape can be effectively regulated by electrostatic gating and show a sharp transition at the Lifshitz point, where the orbital occupancy of the 2DES changes from only ${d}_{\mathrm{xy}}$ to both ${d}_{\mathrm{xy}}$ and ${d}_{\mathrm{xz}/\mathrm{yz}}$. This unusual behavior is attributed to the orbital selectivity effect in this unique multiple-$d$-band system, wherein the itinerant ${d}_{\mathrm{xy}}$ and ${d}_{\mathrm{xz}/\mathrm{yz}}$ electrons have different orbital symmetries and therefore different Kondo exchange coupling with the localized ${d}_{\mathrm{xy}}$ electrons. The present study may pave the way for manipulating many-body effects in 2D multiband materials via orbital engineering of itinerant electrons.

We report an experimental work on simulating the Kitaev chain of one-dimensional $p$-wave superconductivity with long-range coupling using superconducting quantum circuits. The effective Hamiltonian of this model in the momentum space is mapped onto that of a qubit driven by a tunable microwave control field. By monitoring the dynamics of the qubit, we generate intuitive yet precise visualization of topological characteristics of different quantum phases of the system. Topological invariants can be directly deduced from the experimental results, without relying on indirect extraction from measurements such as microwave spectroscopy and temporal averaging. Therefore a much enhanced efficiency of measurement can be realized compared to other methods that are often used to simulate topological phase transitions. As a consequence, a comprehensive phase diagram covering a wide range of the parameter space is obtained. Topological phase transitions and quantum multicritical points are clearly demonstrated. In particular, new topological phases emerge as a consequence of long-range coupling. The method used here can be readily generalized to simulate more complex systems on different experimental platforms.

Twisted bilayer graphene is one of the simplest van der Waals structures, and its inhomogeneous interlayer coupling can induce rich electronic properties. In twisted bilayer graphene nanoribbons (tBLGNRs), the interlayer coupling strengths are different for two ribbon edges due to the inhomogeneous bonding, which splits the edge states into two individuals in energy. The lower-energy state, localizing at the ribbon edge with the stronger interlayer coupling, is a good candidate to generate one-dimensional (1D) topological superconductivity in the presence of Rashba spin-orbit coupling, Zeeman field, and $s$-wave superconductivity. Majorana zero modes (MZMs) are found to be localized at both ends of this edge. The topological invariants of the system are explored by evaluating the Berry phase for infinite-length ribbons and Majorana polarization for quasi-1D ribbons, giving the same topological phase diagram. More importantly, by adjusting interlayer dislocation and uniaxial strain of tBLGNRs across the critical values, the lower-energy edge changes and 1D topological superconductivity can ``jump'' from one ribbon edge to the other one. Finally, by applying a gate voltage bias between bilayers or changing the interlayer distance, a MZM can transfer along the ribbon edge. The tBLGNRs provide an alternative platform to study 1D topological superconductivity and MZMs.

We theoretically study the localized magnetic states and the Kondo screening of a magnetic impurity in the bulk of Weyl semimetals (SMs). The linear dispersion near the Weyl nodes and the anomalous broadening of the impurity level lead to a nonvanishing magnetic moment in a wide region of parameters. The magnetic susceptibility is significantly enhanced by increasing the chirality imbalance for the chemical potential fixed at the Weyl nodes. The Kondo effect takes place whenever the chemical potential is tuned away from the nodes. The low-temperature susceptibility is determined by both the Kondo screening and the broadening of the magnetic impurity level. In the presence of chiral anomaly, the Kondo screening displays opposite behaviors for the chemical potential situated below and above the Weyl nodes. The magnetic susceptibility can be tuned by the charge imbalance of the nodes, which provides a scheme to study the chiral anomaly in Weyl SMs.

We study the Kondo screening of a magnetic impurity in a two-dimensional superconductor with Rashba spin-orbit coupling (SOC). It is found that the Rashba interaction generates a novel Kondo screening channel, in which the local moment is screened by the exchange coupling with conduction electrons in different spin and orbital states. The Kondo temperature associated with this process is determined by the interplay between the Rashba SOC and superconducting energy gap. As a result, the quantum phase transition between the magnetic doublet and Kondo singlet ground states is significantly affected by increasing Rashba SOC in such a system. This result uncovers that the Rashba SOC plays an instructive role and provides a novel screening channel for the Kondo effect, which is expected to be observed in future experiments., 8 pages, 3 figures

We present a detailed analysis on the hopping between monolayer ${\mathrm{CuO}}_{2}$ and bulk ${\mathrm{CuO}}_{2}$ plane in the ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ substrate. With a two-band model, we demonstrate that the nodeless gap can only exist when the hole concentration in the monolayer ${\mathrm{CuO}}_{2}$ plane is very large. We argue that the possible phase separation may play an important role in the recent experimental observation of a nodeless gap.

Motivated by experimental observation of the Kondo-enhanced Andreev transport [R. S. Deacon et al., Phys. Rev. B 81, 121308(R) (2010)] in a hybrid normal metal--quantum dot--superconductor (N-QD-S) device, we theoretically study the Kondo effect in such a device and clarify the different roles played by the normal and superconducting leads. Due to the Andreev reflection in a QD-S system, a pair of Andreev energy levels form in the superconducting gap, which is able to carry the magnetic moment if the ground state of the QD is a magnetic doublet. In this sense, the Andreev energy levels play a role of effective impurity levels. When the normal lead is coupled to the QD-S system, on the one hand, the Andreev energy levels broaden to form the so-called Andreev bound states (ABSs); on the other hand, it can screen the magnetic moment of the ABSs. By tuning the couplings between the QD and the normal (superconducting) leads, the ABSs can simulate the Kondo, mixed-valence, and even empty orbit regimes of the usual single-impurity Anderson model. The above picture is confirmed by the Green's function calculation of the hybrid N-QD-S Anderson model and is also able to explain qualitatively experimental phenomena observed by Deacon et al. These results can further stimulate related experimental study in the N-QD-S systems.

Recent angle resolved photoemission spectroscopy experiments on strongly underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ cuprates have reported an unusual gap in the nodal direction. Transport experiments on these cuprates observed variable-range hopping behavior. These cuprates have both electron and hole doping, which has led to proposals that this cuprate is analogous to partially compensated semiconductors. The nodal gap then corresponds to the Efros-Shklovskii (ES) gap in such semiconductors. We calculate the doping and temperature dependence of an ES gap model and find support for an Efros-Shklovskii model.

We investigate theoretically the Andreev transport through a quantum dot strongly coupled with a normal metal/ferromagnet and a superconductor (N/F-QD-S), in which the interplay between the Kondo resonance and the Andreev bound states (ABSs) has not been clearly clarified yet. Here we show that the interference between the Kondo resonance and the ABSs modifies seriously the lineshape of the Kondo resonance, which manifests as a Fano resonance. The ferromagnetic lead with spin-polarization induces an effective field, which leads to splitting both of the Kondo resonance and the ABSs. The spin-polarization together with the magnetic field applied provides an alternative way to tune the lineshape of the Kondo resonances, which is dependent of the relative positions of the Kondo resonance and of the ABSs. These results indicate that the interplay between the Kondo resonance and the ABSs can significantly affect the Andreev transport, which could be tested by experiments., 8pages, 7figures

Conventional Cooper pairing arises from attractive interaction of electrons in the metallic bands. A recent experiment on Co-doped LiFeAs shows superconductivity in the insulating valence band, which is evolved from a metallic hole band upon doping. Here we examine this phenomenon by studying superconductivity in a three-orbital Hamiltonian relevant to the doped LiFeAs. We show explicitly that Cooper pairing of the insulating hole band requires a finite pairing interaction strength. For strong coupling, the superconductivity in the hole band is robust against the sink of the hole band below the Fermi level. Our theory predicts a substantial upward shift of the chemical potential in the superconducting transition for Co-doped LiFeAs.

We consider the Josephson current through the carbon nanotube quantum dot with twofold orbital degeneracy connected by two superconductor leads. We show that the removal of orbital and spin degeneracies due to strong spin-orbit coupling and external magnetic field has a significant influence on the subgap Andreev bound states and the 0-π transition of the Josephson current. The 0-π transition point is determined by the level crossing of the lowest branch of the bound states and the Fermi level, and is given by [TK − � SO/2 − (μ + 1)B]/� ∼ 1, with TK as the Kondo temperature, � SO the spin-orbit coupling, � the superconducting gap, μ the ratio of orbital momentandBohrmagneton, and B theZeemansplittingloadedbythemagneticfield.TheinterplayoftheKondo effect and superconductivity in such a quantum dot device provides a route to manipulate the 0-π transition of the Josephson current.

We investigate the high-temperature phase of layered manganites, and demonstrate that the charge-orbital phase transition without magnetic order in La${}_{0.5}$Sr${}_{1.5}$MnO${}_{4}$ can be understood in terms of the density-wave instability. The orbital ordering is found to be induced by the nesting between segments of Fermi surface with different orbital characters. The simultaneous charge and orbital orderings are elaborated with a mean-field theory. The ordered orbitals are shown to be ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\ifmmode\pm\else\textpm\fi{}{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$.

We report theoretical and experimental studies of the effect of Zn impurity in Fe-based superconductors. Zn impurity is expected to severely suppress sign reversed ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave pairing. The experimentally observed suppression of T${}_{c}$ under Zn doping strongly depends on the materials and the charge-carrier contents, which suggests competition of ${s}_{++}$ and ${s}_{\ifmmode\pm\else\textpm\fi{}}$ pairings in Fe-based superconductors. We study a model incorporating both ${s}_{++}$- and ${s}_{\ifmmode\pm\else\textpm\fi{}}$-pairing couplings by using the Bogoliubov de-Gennes equation, and we show that the Zn impurity strongly suppresses ${s}_{\ifmmode\pm\else\textpm\fi{}}$ pairing and may induce a transition from the ${s}_{\ifmmode\pm\else\textpm\fi{}}$ to ${s}_{++}$ wave. Our theory is consistent with various experiments on the impurity effect. We present new experimental data on the Zn-doping SmFe${}_{1\ensuremath{-}x}$Zn${}_{x}$AsO${}_{0.9}$F${}_{0.1}$ of T${}_{c}=$ 50 K, in further support of our proposal.

The two-dimensional Kane-Mele model with attractive Hubbard interaction $U$ is studied by using a self-consistent mean-field theory. At $U=0$, the ground state is a topological insulator. At $U$ larger than a critical value ${U}_{c}$, the ground state is a bulk superconductor. At $0lUl{U}_{c}$, the bulk remains insulating while the edge state shows superconducting correlation. The effective model for the edge superconducting state is discussed.

It has been recently discovered that the superconducting (SC) ternary iron selenides have a block antiferromagnetic (AFM) long-range order. Many experiments show a possible mesoscopic phase separation of the superconductivity and antiferromagnetism, while a neutron experiment reveals a sizable suppression of magnetic moment due to the superconductivity, indicating a possible phase coexistence. Here we propose that the observed suppression of the magnetic moment may be explained by the proximity effect within a phase-separation scenario. We use a two-orbital model to study the proximity effect on a layer of the block AFM state induced by neighboring SC layers via an interlayer tunneling mechanism. We argue that the proximity effect in ternary Fe selenides should be large because of the large interlayer coupling and weak electron correlation. The result of our mean-field theory is compared with the neutron experiments semiquantitatively. The suppression of the magnetic moment due to the SC proximity effect is found to be more pronounced in $d$-wave superconductivity and may be enhanced by the frustrated structure of the block AFM state.

We examine the nature of Josephson junction between two identical Fe-pnictides with antiphase $s$-wave pairing. $\ensuremath{\pi}$-phase shift is found if the junction barrier is thick and the two Fe-pnictides are oriented in certain directions relative to the interface. Our theory provides a possible explanation for the observed half integer flux quantum transitions in a niobium/polycrystal NdFeAsO loop, and attributes the $\ensuremath{\pi}$-phase shift to intergrain junctions of Fe-pnictides.

We study the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction mediated by helical edge states in quantum spin hall system. The helical edge states induce an in-plane noncollinear exchange coupling between two local spins, in contrast to the isotropic coupling induced in normal metal. The angle between the two local spins in the ground state depends on the Fermi level. This property may be used to control the angle of spins by tuning the electric gate., 4 pages, 1 figure

We present a numerical study of the spin Hall effect in a two-dimensional hole gas (2DHG) system in the presence of disorder. We find that the spin Hall conductance (SHC), extrapolated to the thermodynamic limit, remains finite in a wide range of disorder strengths for a closed system on torus. But there is no intrinsic spin Hall accumulation as induced by an external electric field once the disorder is turned on. The latter is examined by performing a Laughlin's Gedanken gauge experiment numerically with the adiabatical insertion of a flux quantum in a belt-shaped sample, in which the absence of level crossing is found under the disorder effect. Without disorder, on the other hand, energy levels do cross each other, which results in an oscillating spin-density-modulation at the sample boundary after the insertion of one flux quantum in the belt-shaped system. But the corresponding net spin transfer is only about one order of magnitude smaller than what is expected from the bulk SHC. These apparently contradictory results can be attributed to the violation of the spin conservation law in such a system. We also briefly address the dissipative Fermi surface contribution to spin polarization, which may be relevant to experimental measurements., Comment: 9 pages, 11 figures; final version to appear in Phys. Rev. B

We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped-Mott-insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mott insulator is described by a mean-field theory based on the phase string formulation of the t-J model. We show that the spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system., 24 pages, 17 figures, revised version to appear in Phys. Rev. B