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In a system of charged chiral fermions driven out of equilibrium, an electric current parallel to the magnetic field can generate a dynamic instability by which electromagnetic waves become amplified. Whether a similar instability can occur in chiral solid-state systems remains an open question. Using time-domain terahertz (THz) emission spectroscopy, we detect signatures of what we dub a ``dynamic magneto-chiral instability" in elemental tellurium, a structurally chiral crystal. Upon transient photoexcitation in a moderate external magnetic field, tellurium emits THz radiation consisting of coherent modes that amplify over time. An explanation for this amplification is proposed using a theoretical model based on a dynamic instability of electromagnetic waves interacting with infrared-active oscillators of impurity acceptor states in tellurium to form an amplifying polariton. Our work not only uncovers the presence of a magneto-chiral instability but also highlights its promise for THz-wave amplification in chiral materials., Comment: Supplementary Information (SI) available as a PDF in the TeX source

Altermagnets break time-reversal symmetry, preserve the crystal translation invariance, and have a spin density with $d$-wave, $g$-wave, etc. momentum dependencies which do not contribute to the magnetization. When an $s$-wave spin-density contribution cannot be excluded by symmetry a small magnetization and an anomalous Hall effect (AHE) emerge. However, for so-called "pure" altermagnets, where the $s$-wave component is symmetry forbidden even in the presence of SOC, both the zero-field magnetization and the AHE vanish. We show that altermagnets generally exhibit a non-zero elasto-Hall-conductivity, by which application of strain leads to a non-zero AHE. For pure altermagnets it is the only contribution to the AHE. This elasto-Hall-conductivity is caused by strain coupling to the Berry curvature quadrupole that characterizes altermagnets and allows for the determination of the altermagnetic order using transport measurements that are linear in the electrical field. We further show that the emergence of a non-zero magnetization in the presence of strain arises from a different response function: piezomagnetism. While this magnetization gives rise to an additional contribution to the elasto-Hall conductivity, the corresponding Berry curvature is qualitatively different from the distorted Berry curvature quadrupole originating from the altermagnetic order parameter. This insight also helps to disentangle AHE and weak ferromagnetism for systems with symmetry-allowed $s$-wave contribution. Quantitatively, the elasto-Hall conductivity is particularly pronounced for systems with a Dirac spectrum in the altermagnetic state. The same mechanism gives rise to anomalous elasto-thermal Hall, Nernst, and Ettinghausen effects., Comment: 17 pages, 12 figures

We study the phase ordering dynamics of the classical antiferromagnetic $J_1$-$J_2$ (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime ($J_2/J_1 > 1/2$). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a non-conserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. We also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized., Comment: 9 pages, 9 figures

The recent discovery of an axial amplitude (Higgs) mode in the long-studied charge density wave (CDW) systems GdTe$_3$ and LaTe$_3$ suggests a heretofore unidentified hidden order. A theoretical study proposed that the axial Higgs results from a hidden ferroaxial component of the CDW, which could arise from non-trivial orbital texture. Here, we report extensive experimental studies on ErTe$_3$ and HoTe$_3$ that possess a high-temperature CDW similar to other RTe$_3$ (R = rare earth), along with an additional low-temperature CDW with an orthogonal ordering vector. Combining Raman spectroscopy with large-angle convergent beam electron diffraction (LACBED), rotational anisotropy second-harmonic generation (RA-SHG), and muon-spin relaxation ($\mu$SR), we provide unambiguous evidence that the high-temperature CDW breaks translation, rotation, and all vertical and diagonal mirror symmetries, but not time-reversal or inversion. In contrast, the low-temperature CDW only additionally breaks translation symmetry. Simultaneously, Raman scattering shows the high-temperature CDW produces an axial Higgs mode while the low-temperature mode is scalar. The weak monoclinic structural distortion and clear axial response in Raman and SHG are consistent with a ferroaxial phase in RTe$_3$ driven by coupled orbital and charge orders. Thus, our study provides a new standard for uncovering unconventional orders and confirms the power of Higgs modes to reveal them., Comment: 28 pages, 5 figures

Altermagnets represent a new class of magnetic phases without net magnetization that are invariant under a combination of rotation and time reversal. Unlike conventional collinear antiferromagnets (AFM), altermagnets could lead to new correlated states and important material properties deriving from their non-relativistic spin-split band structure. Indeed, they are the magnetic analogue of unconventional superconductors and can yield spin polarized electrical currents in the absence of external magnetic fields, making them promising candidates for next-generation spintronics. Here, we report altermagnetism in the correlated insulator, magnetically-ordered tetragonal oxychalcogenide, La$_2$O$_3$Mn$_2$Se$_2$. Symmetry analysis reveals a $\mathit{d}_{x^2 - y^2}$-wave type spin momentum locking, which is supported by density functional theory (DFT) calculations. Magnetic measurements confirm the AFM transition below $\sim$166 K while neutron pair distribution function analysis reveals a 2D short-range magnetic order that persists above the N\'eel temperature. Single crystals are grown and characterized using X-ray diffraction, optical and electron microscopy, and microRaman spectroscopy to confirm the crystal structure, stoichiometry, and uniformity.

Model lattices such as the kagome and Lieb lattices have been widely investigated to elucidate the properties of interacting flat-band systems. While a quasicrystal does not have proper bands, the non-interacting density of states of several of them displays the typical signature of a flat band pinned at the Fermi level: a delta-function zero-energy peak. Here, we employ quantum Monte Carlo simulations to determine the effect of onsite repulsion on these quasicrystals. While global properties such as the antiferromagnetic structure factor and the specific heat behave similarly as in the case of periodic lattices undergoing a Mott transition, the behavior of the local density of states depends on the coordination number of the site. In particular, sites with the smallest coordination number, which give the dominant spectral-weight contribution to the zero-energy peak, are the ones most strongly impacted by the interaction. Besides establishing site-selective correlations in quasicrystals, our work also points to the importance of the real-space structure of flat bands in interacting systems., Comment: 7 pages, 4 figures

The recent discovery of altermagnets has opened new perspectives in the field of ordered phases in condensed matter. In strongly-correlated superfluids, the nodal p-wave and d-wave ordered phases of $^{3}$He and cuprates play a prominent role in physics for their rich phenomenology of the symmetry-breaking order parameters. While the p-wave and d-wave superfluids have been extensively studied over the past half a century, material realizations of their magnetic counterparts have remained elusive for many decades. This is resolved in altermagnets, whose recent discovery was driven by research in the field of spintronics towards highly scalable information technologies. Altermagnets feature d, g or i-wave magnetic ordering, with a characteristic alternation of spin polarization and spin-degenerate nodes. Here we review how altermagnetism can be identified from symmetries of collinear spin densities in crystal lattices, and can be realized at normal conditions in a broad family of insulating and conducting materials. We highlight salient electronic-structure signatures of the altermagnetic ordering, discuss extraordinary relativistic and topological phenomena that emerge in their band structures, and comment on strong-correlation effects. We then extend the discussion to non-collinear spin densities in crystals, including the prediction of p-wave magnets, and conclude with a brief summary of the reviewed physical properties of the nodal magnetically-ordered phases., Comment: 17 pages, 6 figures

The Holstein model on a square lattice at half-filling has a well-established finite temperature phase transition to an insulating state with long range charge density wave (CDW) order. Because this CDW formation suppresses pairing, a superconducting (SC) phase emerges only with doping. In this work, we study the effects of dilution of the local phonon degrees of freedom in the Holstein model while keeping the system at half filling. We find not only that the CDW remains present up to a dilution fraction $f \sim 0.15$, but also that long range pairing is stabilized with increasing $f$, resulting in a {\it supersolid} regime centered at $f \approx 0.10$, where long range diagonal and off-diagonal correlations coexist. Further dilution results in a purely SC phase, and ultimately in a normal metal. Our results provide a new route to the supersolid phase via the introduction of impurities at fixed positions which both increase quantum fluctuations and also are immune to the competing tendency to phase separation often observed in the doped case., Comment: 11 pages and 11 figures. Accepted for publication as a Letter in Physical Review B

Displacement fields are one of the main tuning knobs employed to engineer flat electronic band dispersions in twisted van der Waals multilayers. Here, we show that electric fields can also be used to tune the phonon dispersion of moir\'e superlattices formed by non-centrosymmetric materials, focusing on twisted transition metal dichalcogenide homobilayers. This effect arises from the intertwining between the local stacking configuration and the formation of polar domains within the moir\'e supercell. For small twist angles, increasing the electric field leads to a universal moir\'e phonon spectrum characterized by a substantially softened longitudinal acoustic phason mode and a flat optical phonon mode, both of which cause a significant enhancement in the vibrational density of states. The phasons also acquire a prominent chiral character, displaying a nonzero angular momentum spread across the Brillouin zone. We discuss how the tunability of the moir\'e phonon spectra may affect electronic properties, focusing on the recently discovered phenomenon of van der Waals ferroelectricity., Comment: 6 pages + SM; comments are welcome

Kagome vanadates {\it A}V$_3$Sb$_5$ display unusual low-temperature electronic properties including charge density waves (CDW), whose microscopic origin remains unsettled. Recently, CDW order has been discovered in a new material ScV$_6$Sn$_6$, providing an opportunity to explore whether the onset of CDW leads to unusual electronic properties. Here, we study this question using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The ARPES measurements show minimal changes to the electronic structure after the onset of CDW. However, STM quasiparticle interference (QPI) measurements show strong dispersing features related to the CDW ordering vectors. A plausible explanation is the presence of a strong momentum-dependent scattering potential peaked at the CDW wavevector, associated with the existence of competing CDW instabilities. Our STM results further indicate that the bands most affected by the CDW are near vHS, analogous to the case of {\it A}V$_3$Sb$_5$ despite very different CDW wavevectors., Comment: 33 pages, 4 figures

Altermagnetism refers to a wide class of magnetic orders featuring magnetic sublattices with opposite spins related by rotational symmetries, resulting in non-trivial spin splitting and magnetic multipoles. However, the direct observation of the altermagnetic order parameter remains elusive. Here, by combining theoretical analysis, electrical transport, X-ray and optical spectroscopies, we establish a phase diagram in hybrid molecular beam epitaxy-grown RuO2/TiO2 (110) films, mapping symmetries along with altermagnetic/electronic/structural phase transitions as functions of film thickness and temperature. This features a novel altermagnetic metallic polar phase in epitaxially-strained 2 nm films, extending the concept of multiferroicity to altermagnets. Such a clear signature of a magnetic phase transition at ~500 K is observed exclusively in ultrathin strained films, unlike in bulk RuO2 single crystals. These results demonstrate the potential of epitaxial heterostructure design to induce altermagnetism, paving the way for emergent novel phases with multifunctional properties., Comment: 23 pages

Recent progress in the understanding of the collective behavior of electrons and ions have revealed new types of ferroic orders beyond ferroelectricity and ferromagnetism, such as the ferroaxial state. The latter retains only rotational symmetry around a single axis and reflection symmetry with respect to a single mirror plane, both of which are set by an emergent electric toroidal dipole moment. Due to this unusual symmetry-breaking pattern, it has been challenging to directly measure the ferroaxial order parameter, despite the increasing attention this state has drawn. Here, we show that off-diagonal components of the piezoresistivity tensor (i.e., the linear change in resistivity under strain) transform the same way as the ferroaxial moments, providing a direct probe of such order parameters. We identify two new proper ferroaxial materials through a materials database search, and use first-principles calculations to evaluate the piezoconductivity of the double-perovskite CaSnF$_6$, revealing its connection to ferroaxial order and to octahedral rotation modes.

Motivated by recent experiments reporting unconventional collective modes in the charge density-wave (CDW) state of rare-earth tritellurides $R$Te$_3$, we derive from a multi-orbital microscopic model on the square net a CDW Ginzburg-Landau theory that allows for non-trivial orbital order. Our analysis reveals unconventional CDWs where order parameters with distinct orbital character coexist due to an approximate symmetry of the low-energy model, which becomes exact in the limit of nearest-neighbor-only hopping and decoupled $p_x$, $p_y$ orbitals. Because of this coexistence, the resulting CDW pattern displays an orbital texture that generally breaks additional symmetries of the lattice besides those explicitly broken by the CDW wave-vector. In particular, we find two competing phases that differ in whether they break or preserve inversion and vertical mirror symmetries. We explain the mechanisms that favor each outcome, and discuss experimental probes that can distinguish the different phases., Comment: Added references

Nematic phases, where electrons in a solid spontaneously break rotational symmetry while preserving the translational symmetry, exist in several families of unconventional superconductors [1, 2]. Although superconductivity mediated by nematic fluctuations is well established theoretically [3-7], it has yet to be unambiguously identified experimentally [8, 9]. A major challenge is that nematicity is often intertwined with other degrees of freedom, such as magnetism and charge order. The FeSe$_{1-x}$S$_x$ family of iron based superconductors provides a unique opportunity to explore this concept, as it features an isolated nematic phase that can be suppressed by sulfur substitution at a quantum critical point (QCP) near $x_c = 0.17$, where nematic fluctuations are the largest [10-12]. Here, we performed scanning tunneling spectroscopy measurements to visualize Boguliubov quasiparticle interference patterns, from which we determined the momentum structure of the superconducting gap near the Brillouin zone $\Gamma$ point of FeSe$_{0.81}$S$_{0.19}$. The results reveal an anisotropic, near nodal gap with minima that are $45^\circ$ rotated with respect to the Fe-Fe direction, characteristic of a nematic pairing interaction, contrary to the usual isotropic gaps due to spin mediated pairing in other tetragonal Fe-based superconductors. The results are also in contrast with pristine FeSe, where the pairing is mediated by spin fluctuations and the gap minima are aligned with the Fe-Fe direction. Therefore, the measured gap structure demonstrates not only a fundamental change of the pairing mechanism across the phase diagram of FeSe$_{1-x}$S$_x$, but it also indicates the existence of superconductivity mediated by nematic fluctuations in FeSe$_{0.81}$S$_{0.19}$.

Electronic nematic order has been reported in a rich landscape of materials, encompassing not only a range of intertwined correlated and topological phenomena, but also different underlying lattice symmetries. Motivated by these findings, we investigate the behavior of electronic nematicity as the spherical symmetry of three-dimensional (3D) space is systematically lowered by the lattice environment. We consider all 32 crystallographic point groups as well as 4 major classes of quasicrystalline point groups, given the recent observations of electronic phases of interest in quasicrystalline materials and artificial twisted quasicrystals. Valuable insights are gained by establishing a mapping between the five-component charge-quadrupolar nematic order parameter of the electronic fluid and the 3D tensorial order parameter of nematic liquid crystals. We find that a uniaxial nematic state is only generically realized in polyhedral point groups (icosahedral and cubic), with the nematic director pointing along different sets of rotational symmetry axes. Interestingly, icosahedral point groups are the only ones in which the five nematic order parameter components transform as the same irreducible representation, making them the closest analog of 3D isotropic nematics. In axial point groups, one of the nematic components is always condensed, whereas the other four components decompose into an in-plane and an out-of-plane nematic doublet, resulting in biaxial nematic ground states. Because these two nematic doublets behave as $Z_q$-clock order parameters, this allows us to identify the types of crystals and quasicrystals that can host interesting electronic nematic phenomena enabled by the critical properties of the $q\geq 4$ clock model, such as emergent continuous nematic fluctuations in 3D, critical phases with quasi-long-range nematic order in 2D, and Ashkin-Teller nematicity in 2D., Comment: 39 pages, 7 figures, 2 tables

The iron-based high-$T_c$ superconductors exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and re-entrant tetragonality as the origin of this transition, and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a sub-dominant pairing instability that competes strongly with the dominant $s^\pm$ instability. Our results thus motivate a re-examination of the pairing state and its interplay with nematicity in this extensively studied iron-based superconductor, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

We report an investigation of the effect of substitution of Y for Tm in $Tm_{1-x}Y_xVO4$ via low-temperature heat capacity measurements, with the yttrium content $x$ varying from $0$ to $0.997$. Because the Tm ions support a local quadrupolar (nematic) moment, they act as reporters of the local strain state in the material, with the splitting of the ion's non-Kramers crystal field groundstate proportional to the quadrature sum of the in-plane tetragonal symmetry-breaking transverse and longitudinal strains experienced by each ion individually. Analysis of the heat capacity therefore provides detailed insights into the distribution of local strains that arise as a consequence of the chemical substitution. These local strains suppress long-range quadrupole order for $x>0.22$, and result in a broad Schottky-like feature for higher concentrations. Heat capacity data are compared to expectations for a distribution of uncorrelated (random) strains. For dilute Tm concentrations, the heat capacity cannot be accounted for by randomly distributed strains, demonstrating the presence of significant strain correlations between sites. For intermediate Tm concentrations, these correlations must still exist, but the data cannot be distinguished from that which would be obtained from a 2D Gaussian distribution. The cross-over between these limits is discussed in terms of the interplay of key length scales in the substituted material. The central result of this work, that local strains arising from chemical substitution are not uncorrelated, has implications for the range of validity of theoretical models based on random effective fields that are used to describe such chemically substituted materials, particularly when electronic nematic correlations are present.

The electronic spectra of altermagnets are a fertile ground for non-trivial topology due to the unique interplay between time-reversal and crystalline symmetries. This is reflected in the unconventional Zeeman splitting between bands of opposite spins, which emerges in the absence of spin-orbit coupling (SOC) and displays nodes along high-symmetry directions. Here, we argue that even for a small SOC, the direction of the magnetic moments in the altermagnetic state has a profound impact on the electronic spectrum, enabling novel topological phenomena to appear. By investigating microscopic models for two-dimensional (2D) and three-dimensional (3D) altermagnets, motivated in part by rutile materials, we demonstrate the emergence of hitherto unexplored Dirac crossings between bands of same spin but opposite sublattices. The direction of the moments determines the fate of these crossings when the SOC is turned on. We focus on the case of out-of-plane moments, which forbid an anomalous Hall effect and thus ensure that no weak magnetization is triggered in the altermagnetic state. In 2D, the SOC gaps out the Dirac crossings, resulting in mirror Chern bands that enable the quantum spin Hall effect and undergo a topological transition to trivial bands upon increasing the magnitude of the magnetic moment. On the other hand, in 3D the crossings persist even in the presence of SOC, forming Weyl nodal loops protected by mirror symmetry. Finally, we discuss possible ways to control these effects in altermagnetic material candidates., Comment: 7 pages, 4 figures; Suppl.: 22 pages, 3 figures

The crystallographic restriction theorem constrains two-dimensional nematicity to display either Ising ($Z_{2}$) or three-state-Potts ($Z_{3}$) critical behaviors, both of which are dominated by amplitude fluctuations. Here, we use group theory and microscopic modeling to show that this constraint is circumvented in a $30^{\circ}$-twisted hexagonal bilayer due to its emergent quasicrystalline symmetries. We find a critical phase dominated by phase fluctuations of a $Z_{6}$ nematic order parameter and bounded by two Berezinskii-Kosterlitz-Thouless (BKT) transitions, which displays only quasi-long-range nematic order. The electronic spectrum in the critical phase displays a thermal pseudogap-like behavior, whose properties depend on the anomalous critical exponent. We also show that an out-of-plane magnetic field induces nematic phase fluctuations that suppress the two BKT transitions via a mechanism analogous to the Hall viscoelastic response of the lattice, giving rise to a putative nematic quantum critical point with emergent continuous symmetry. Finally, we demonstrate that even in the case of an untwisted bilayer, a critical phase emerges when the nematic order parameter changes sign between the two layers, establishing an odd-parity nematic state., Comment: Manuscript (7 pages, 3 figures) plus Supplementary Material (5 pages, 1 figure)

Orbital magnetism and the loop currents (LC) that accompany it have been proposed to emerge in many systems, including cuprates, iridates, and kagome superconductors. In the case of cuprates, LCs have been put forward as the driving force behind the pseudogap, strange-metal behavior, and $d_{x^2-y^2}$-wave superconductivity. Here, we investigate whether fluctuating intra-unit-cell loop currents can cause unconventional superconductivity. For odd-parity LCs, we find that they are strongly repulsive in all pairing channels near the underlying quantum-critical point (QCP). For even-parity LCs, their fluctuations do give rise to unconventional pairing. However, this pairing is not amplified in the vicinity of the QCP, in sharp contrast to other known cases of pairing mediated by intra-unit-cell order parameters, such as spin-magnetic, nematic, or ferroelectric ones. Applying our formalism to the cuprates, we conclude that pairing mediated by fluctuating intra-unit-cell LCs is unlikely to yield $d_{x^2-y^2}$-wave superconductivity. We also show that loop currents, if relevant for the cuprates, must vary between unit cells and break translation symmetry., Comment: 12 pages, 7 figures

In the fluctuation regime that precedes the onset of pairing in multi-component superconductors, such as nematic and chiral superconductors, the normal state is generally unstable towards the formation of charge-$4e$ order $-$ an exotic quantum state in which electrons form coherent quartets rather than Cooper pairs. However, charge-$4e$ order is often suppressed by other competing composite orders, such as nematics. Importantly, the formation of nematic domains is unavoidable due to the long-range strains generated, leading to one-dimensional regions where the competing nematic order is suppressed. Here, we employ a real-space variational approach to demonstrate that, in such nematic domain walls, charge-$4e$ order is locally condensed via a vestigial-order mechanism. We explore the experimental manifestations of this effect and discuss materials in which it can be potentially observed., Comment: 8 pages, 3 figures

BaNi$_2$As$_2$ is a structural analog of the pnictide superconductor BaFe$_2$As$_2$, which, like the iron-based superconductors, hosts a variety of ordered phases including charge density waves (CDWs), electronic nematicity, and superconductivity. Upon isovalent Sr substitution on the Ba site, the charge and nematic orders are suppressed, followed by a sixfold enhancement of the superconducting transition temperature ($T_c$). To understand the mechanisms responsible for enhancement of $T_c$, we present high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements of the Ba$_{1-x}$Sr$_{x}$Ni$_2$As$_2$ series, which agree well with our density functional theory (DFT) calculations throughout the substitution range. Analysis of our ARPES-validated DFT results indicates a Lifshitz transition and reasonably nested electron and hole Fermi pockets near optimal substitution where $T_c$ is maximum. These nested pockets host Ni $d_{xz}$/$d_{yz}$ orbital compositions, which we associate with the enhancement of nematic fluctuations, revealing unexpected connections to the iron-pnictide superconductors. This gives credence to a scenario in which nematic fluctuations drive an enhanced $T_c$., Comment: 19 pages, 12 figures, 1 table

Despite their highly anisotropic complex-oxidic nature, certain delafossite compounds (e.g., PdCoO2, PtCoO2) are the most conductive oxides known, for reasons that remain poorly understood. Their room-temperature conductivity can exceed that of Au, while their low-temperature electronic mean-free-paths reach an astonishing 20 microns. It is widely accepted that these materials must be ultrapure to achieve this, although the methods for their growth (which produce only small crystals) are not typically capable of such. Here, we first report a new approach to PdCoO2 crystal growth, using chemical vapor transport methods to achieve order-of-magnitude gains in size, the highest structural qualities yet reported, and record residual resistivity ratios (>440). Nevertheless, the first detailed mass spectrometry measurements on these materials reveal that they are not ultrapure, typically harboring 100s-of-parts-per-million impurity levels. Through quantitative crystal-chemical analyses, we resolve this apparent dichotomy, showing that the vast majority of impurities are forced to reside in the Co-O octahedral layers, leaving the conductive Pd sheets highly pure (~1 ppm impurity concentrations). These purities are shown to be in quantitative agreement with measured residual resistivities. We thus conclude that a previously unconsidered "sublattice purification" mechanism is essential to the ultrahigh low-temperature conductivity and mean-free-path of metallic delafossites.

Layered van der Waals magnets have attracted much recent attention as a promising and versatile platform for exploring intrinsic two-dimensional magnetism. Within this broader class, the transition metal phosphorous trichalcogenides $M$P$X_3$ stand out as particularly interesting, as they provide a realization of honeycomb lattice magnetism and are known to display a variety of magnetic ordering phenomena as well as superconductivity under pressure. One example, found in a number of different materials, is commensurate single-$Q$ zigzag antiferromagnetic order, which spontaneously breaks the spatial threefold $(C_3)$ rotation symmetry of the honeycomb lattice. The breaking of multiple distinct symmetries in the magnetic phase suggests the possibility of a sequence of distinct transitions as a function of temperature, and a resulting intermediate $\mathbb{Z}_3$-nematic phase which exists as a paramagnetic vestige of zigzag magnetic order -- a scenario known as vestigial ordering. Here, we report the observation of key signatures of vestigial Potts-nematic order in rhombohedral FePSe$_3$. By performing linear dichroism imaging measurements -- an ideal probe of rotational symmetry breaking -- we find that the $C_3$ symmetry is already broken above the N\'eel temperature. We show that these observations are explained by a general Ginzburg-Landau model of vestigial nematic order driven by magnetic fluctuations and coupled to residual strain. An analysis of the domain structure as temperature is lowered and a comparison with zigzag-ordered monoclinic FePS$_3$ reveals a broader applicability of the Ginzburg-Landau model in the presence of external strain, and firmly establishes the $M$P$X_3$ magnets as a new experimental venue for studying the interplay between Potts-nematicity, magnetism and superconductivity., Comment: 6 pages, 4 figures + supplementary material

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents. The recently discovered family of kagome superconductors AV$_3$Sb$_5$ (A = K, Rb, or Cs), hosting an exotic charge-density wave (CDW) state, has emerged as a strong candidate for this phase. While initial experiments suggested that the CDW phase breaks time-reversal symmetry, this idea is being intensely debated due to conflicting experimental data. In this work we use laser-coupled scanning tunneling microscopy (STM) to study RbV$_3$Sb$_5$. STM data shows that the Fourier intensities of all three CDW peaks are different, implying that the CDW breaks rotational and mirror symmetries. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong non-linear electron-phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry-breaking. We show that the simplest CDW that satisfies these constraints and reconciles previous seemingly contradictory experimental data is an out-of-phase combination of bond charge order and loop currents that we dub congruent CDW flux phase. Our laser-STM data opens the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials., Comment: main text: 21 pages, 5 figures // Methods and Extended Data: 25 pages, 14 figures

In an altermagnet, the symmetry that relates configurations with flipped magnetic moments is a rotation. This makes it qualitatively different from a ferromagnet, where no such symmetry exists, or a collinear antiferromagnet, where this symmetry is a lattice translation. In this paper, we investigate the impact of the crystalline environment, enabled by the spin-orbit coupling, on the magnetic and electronic properties of an altermagnet. We find that, because each component of the magnetization acquires its own angular dependence, the Zeeman splitting of the bands has symmetry-protected nodal lines residing on mirror planes of the crystal. Upon crossing the Fermi surface, these nodal lines give rise to pinch points that behave as single or double type-II Weyl nodes. We show that an external magnetic field perpendicular to these mirror planes can only move the nodal lines, such that a critical field value is necessary to collapse the nodes and make the Weyl pinch points annihilate. This unveils the topological nature of the transition from a nodal to a nodeless Zeeman splitting of the bands. We also classify the altermagnetic states of common crystallographic point groups in the presence of spin-orbit coupling, revealing that a broad family of magnetic orthorhombic perovskites can realize altermagnetism., Comment: revised manuscript accepted for publication as an Editors' Suggestion in PRB

The combined rotational and time-reversal symmetry breakings that define an altermagnet lead to an unusual d-wave (or g-wave) magnetization order parameter, which in turn can be modeled in terms of multipolar magnetic moments. Here, we show that such an altermagnetic order parameter couples to the dynamics of the lattice even in the absence of an external magnetic field. This coupling is analogous to the non-dissipative Hall viscosity and describes the stress generated by a time-varying strain under broken time-reversal symmetry. We demonstrate that this effect generates a hybridized paramagnon-polaron mode, which allows one to assess altermagnetic excitations directly from the phonon spectrum. Using a scaling analysis, we also demonstrate that the dynamic strain coupling strongly affects the altermagnetic phase boundary, but in different ways in the thermal and quantum regimes. In the ground state for both 2D and 3D systems, we find that a hardening of the altermagnon mode leads to an extended altermagnetic ordered regime, whereas for non-zero temperatures in 2D, the softening of the phonon modes leads to increased fluctuations that lower the altermagnetic transition temperature. In 3D even at finite temperatures the dominant effect is the suppression of quantum fluctuations. We also discuss the application of these results to standard ferromagnetic systems., Comment: 15 pages, 7 figures. Generalised to two-dimensional systems and corrected one figure, added section on static coupling and gap closing of phonon and magnon spectra

Recent experiments have shown that the phase diagrams of the kagome superconductors $A\mathrm{V}_3\mathrm{Sb}_5$ are strongly impacted by changes in the $c$-axis lattice parameter. Here, we show that $c$-axis deformations impact primarily the Sb apical bonds and thus the overlap between their $p_z$ orbitals. Changes in the latter, in turn, substantially affect low-energy electronic states with significant Sb character, most notably the central electron pocket and the van Hove singularities located above the Fermi level. Based on the orbital-selective character of $c$-axis strain, we argue that these electronic states experience a non-negligible attractive electron-phonon pairing interaction mediated by fluctuations in the apical Sb bonds. We thus propose a multi-band model for superconductivity in $A\mathrm{V}_3\mathrm{Sb}_5$ that includes both the Sb pocket and the V-derived van Hove singularities. Upon comparing the theoretical phase diagram with the experimentally observed vanishing of the $T_c$ dome across a Lifshitz transition of the Sb pocket, we propose that either an $s^{+-}$ or an $s^{++}$ state is realized in $A\mathrm{V}_3\mathrm{Sb}_5$., Comment: 7+5 pages, 2+4 figures. Accepted in Phys. Rev. B

We study pseudogap behavior in a metal near a spin density wave (SDW) instability due to thermal magnetic fluctuations. We consider the $t-t'$ Hubbard model on a square lattice at a finite doping, at intermediate coupling strength, and analyze the thermal evolution of the electron spectral function between a SDW ordered state at low temperatures and a normal Fermi liquid at high temperatures. We argue that for proper description of the pseudogap one needs to sum up infinite series of diagrams for both the fermionic self-energy and the SDW order parameter in the SDW state or the magnetic correlation length in the paramagnetic state. We use the eikonal approach to sum up an infinite series of diagrammatic contributions from thermal fluctuations. Earlier studies found that in the SDW state, the spectral function $A_{\bf k}(\omega)$ of a hot fermion at a finite $T$ is exponentially small below the energy scale $\Delta (T)$, which scales with SDW order and vanishes at the ordering temperature $T_N$, and has a hump at a larger frequency $\Delta_{\rm pg}$, comparable to the zero-temperature SDW gap $\Delta (T=0)$. We argue that the hump, which we associate with the pseudogap, survives in some $T$ range above $T_N$. We show that this range is split by regions of strong and weak pseudogap behavior. In the first region, $\Delta_{\rm pg}$ is weakly temperature dependent, despite that it comes from thermal fluctuations. Such a behavior has been seen in numerical studies of the Hubbard model. We show that to obtain it, one needs to go beyond the one-loop approximation and sum up the infinite series of diagrams. In the second regime, $\Delta_{\rm pg}$ decreases with increasing $T$ and eventually vanishes. We further argue that a magnetic pseudogap at a finite $T$ emerges only if the ground state is magnetically ordered. We present the phase diagram and apply the results to high-$T_c$ cuprates., Comment: v1: 22+3 pages, 16 figures. v2: 22+3 pages, 15 figures, published version

Achieving electrostatic control of quantum phases is at the frontier of condensed matter research. Recent investigations have revealed superconductivity tunable by electrostatic doping in twisted graphene heterostructures and in two-dimensional (2D) semimetals such as WTe$_2$. Some of these systems have a polar crystal structure that gives rise to ferroelectricity, in which the interlayer polarization exhibits bistability driven by external electric fields. Here we show that bilayer $T_d$-MoTe$_2$ simultaneously exhibits ferroelectric switching and superconductivity. Remarkably, a field-driven, first-order superconductor-to-normal transition is observed at its ferroelectric transition. Bilayer $T_d$-MoTe$_2$ also has a maximum in its superconducting transition temperature ($T_\textrm{c}$) as a function of carrier density and temperature, allowing independent control of the superconducting state as a function of both doping and polarization. We find that the maximum $T_\textrm{c}$ is concomitant with compensated electron and hole carrier densities and vanishes when one of the Fermi pockets disappears with doping. We argue that this unusual polarization-sensitive 2D superconductor is driven by an interband pairing interaction associated with nearly nested electron and hole Fermi pockets.

Motivated by recent observations of threefold rotational symmetry breaking in twisted moir\'e systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first-order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two non-zero values while the nematic director remains pinned, leading to a symmetry-preserving meta-nematic transition that terminates at a quantum critical end-point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moir\'e superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second-order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At non-zero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first-order in 3D, but to change to second-order in 2D. As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end-points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. We discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order., Comment: 17 pages, 7 figures

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In the partially-melted phases, known as vestigial phases, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multi-component superconductors are thus natural candidates for vestigial order, since they break both the U(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-$4e$ condensate, which itself can have an underlying $s$-wave, $d_{x^2-y^2}$-wave, or $d_{xy}$-wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-$4e$ order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and $s$-wave charge-4e vestigial states are degenerate. We discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4e states in material candidates., Comment: 26 pages, 4 figures, 2 tables

Due to its incommensurate nature, moir\'e superlattices host not only acoustic phonons but also another type of soft collective modes called phasons. Here, we investigate the impact of electron-phason scattering on the transport properties of moir\'e systems. We show that the resistivity can scale linearly with temperature down to temperatures much lower than the Bloch-Gr\"uneisen scale defined by electron kinematics on the Fermi surface. This result stems from the friction between layers, which transfers phason spectral weight to a broad diffusive low-energy peak in the mechanical response of the system. As a result, phason scattering becomes a very efficient channel for entropy production at low temperatures. We also consider the contributions of phasons to thermodynamic properties at low temperatures and find a ''metallic-like'' linear-in-$T$ behavior for the specific heat, despite the fact that this behavior is due to mechanical and not electronic degrees of freedom. We discuss the implications of this finding to reports of linear-in-$T$ resistivity in the phase diagram of twisted bilayer graphene., Comment: 12 pages, 5 figures; new calculations of the resistivity and the specific heat added

Elucidating the microscopic mechanisms responsible for the charge density wave (CDW) instability of the AV$_3$Sb$_5$ (A=Cs, K, Rb) family of kagome metals is critical for understanding their unique properties, including superconductivity. In these compounds, distinct CDW phases with wave-vectors at the $M$ and $L$ points are energetically favorable, opening the possibility of tuning the type of CDW order by appropriate external parameters. Here, we shed light on the CDW landscape of CsV$_3$Sb$_5$ via a combination of first-principles calculations and phenomenology, which consists of extracting the coefficients of the CDW Landau free-energy expansion from density functional theory. We find that while the main structural distortions of the kagome lattice in the staggered tri-hexagonal CDW phase are along the nearest-neighbor V-V bonds, distortions associated with the Sb ions play a defining role in the energy gain in this and all other CDW states. Moreover, the coupling between ionic displacements from different unit cells is small, thus explaining the existence of multiple CDW instabilities with different modulations along the c-axis. We also investigate how pressure and temperature impact the CDW phase of CsV$_3$Sb$_5$. Increasing pressure does not change the staggered tri-hexagonal CDW ground state, even though the $M$-point CDW instability disappears before the $L$-point one, a behavior that we attribute to the large nonlinear coupling between the order parameters. Upon changing the temperature, we find a narrow regime in which another transition can take place, toward a tri-hexagonal Star-of-David CDW phase. We discuss the implications of our results by comparing them with experiments on this compound.

We revisit the intriguing magnetic behavior of the paradigmatic itinerant frustrated magnet $\rm{Sr}\rm{Co}_2\rm{As}_2$, which shows strong and competing magnetic fluctuations yet does not develop long-range magnetic order. By calculating the static spin susceptibility $\chi(\mathbf{q})$ within a realistic sixteen orbital Hubbard-Hund model, we determine the leading instability to be ferromagnetic (FM). We then explore the effect of doping and calculate the critical Hubbard interaction strength $U_c$ that is required for the development of magnetic order. We find that $U_c$ decreases under electron doping and with increasing Hund's coupling $J$, but increases rapidly under hole doping. This suggests that magnetic order could possibly emerge under electron doping but not under hole doping, which agrees with experimental findings. We map out the leading magnetic instability as a function of doping and Hund's coupling and find several antiferromagnetic phases in addition to FM. We also quantify the degree of itinerant frustration in the model and resolve the contributions of different orbitals to the magnetic susceptibility. Finally, we discuss the dynamic spin susceptibility, $\chi(\mathbf{q}, \omega)$, at finite frequencies, where we recover the anisotropy of the peaks at $\mathbf{Q}_\pi = (\pi, 0)$ and $(0, \pi)$ observed by inelastic neutron scattering that is associated with the phenomenon of itinerant magnetic frustration. By comparing results between theory and experiment, we conclude that the essential experimental features of doped SrCo$_2$As$_2$ are well captured by a Hubbard-Hund multiorbital model if one considers a small shift of the chemical potential towards hole doping., Comment: 19 pages, 12 figures

The possibility of realizing pair density wave (PDW) phases, in which Cooper pairs have a finite momentum, presents an interesting challenge that has been studied in a wide variety of systems. In conventional superconductors, this is only possible when external fields lift the spin degeneracy of the Fermi surface, leading to pair formation at an incommensurate momentum. Here, we study a second possibility, potentially relevant to transition metal dichalcogenides, in which the Fermi surface consists of a pair of pockets centered at the $\pm K$ points of the Brillouin zone as well as a central pocket at the $\Gamma$ point. In the limit where these three pockets are identical, the pairing susceptibility has a logarithmic divergence at the non-zero wave-vectors $\pm \mathbf{K}$, allowing for a weak-coupling analysis of the PDW instability. We find that repulsive electronic interactions combine to yield effective attractive interactions in the singlet and triplet PDW channels, as long as the $\Gamma$ pocket is present. Because these PDW channels decouple from the uniform superconducting channel, they can become the leading unconventional pairing instability of the system. Upon solving the linearized gap equations, we find that the PDW instability is robust against small trigonal warping of the $\pm K$ pockets and small detuning between the $\Gamma$ and $\pm K$ pockets, which affect the PDW transition in a similar way as the Zeeman magnetic field affects the uniform superconducting transition. We also derive the Ginzburg-Landau free energy for the PDW gaps with momenta $\pm \mathbf{K}$, analyzing the conditions for and consequences of the emergence of FF-type and LO-type PDW ground states. Our classification of the induced orders in each ground state reveals unusual phases, including an odd-frequency charge-$2e$ superconductor in the LO-type PDW., Comment: 24 pages, 11 figures

A variety of compounds, for example doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the normal state properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. Starting from a minimal model of electrons coupled to a \emph{transverse} polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second order, first order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.

Experiments in the recently discovered vanadium-based kagome metals have suggested that their charge-ordered state displays not only bond distortions, characteristic of a ``real" charge density-wave (rCDW), but also time-reversal symmetry-breaking, typical of loop currents described by an ``imaginary" charge density-wave (iCDW). Here, we combine density-functional theory, group-theory, and phenomenological modeling to investigate the complex charge-ordered states that arise from interactions between the low-energy van Hove singularities present in the electronic structure of $A$V$_3$Sb$_5$. We find two broad classes of mixed iCDW-rCDW configurations: triple-$\mathbf{Q}$ iCDW, triple-$\mathbf{Q}$ rCDW order, dubbed $3\mathbf{Q}$-$3\mathbf{Q}$, and double-$\mathbf{Q}$ iCDW, single-$\mathbf{Q}$ rCDW order, dubbed $2\mathbf{Q}$-$1\mathbf{Q}$. Moreover, we identify seven different types of iCDW order, stemming from the different vanadium-orbital and kagome-sublattice structures of the two pairs of van Hove singularities present above and below the Fermi level. While the $2\mathbf{Q}$-$1\mathbf{Q}$ states trigger an orthorhombic distortion that breaks the threefold rotational symmetry of the kagome lattice, the $3\mathbf{Q}$-$3\mathbf{Q}$ states induce various types of subsidiary uniform magnetic orders, from conventional ferromagnetism to magnetic octupolar, magnetic toroidal, and even magnetic monopolar order. We show that these exotic orders display unique magneto-striction, magneto-electric, and magneto-electric-striction properties that can be probed experimentally to identify which iCDW state is realized in these compounds. We briefly discuss the impact of an out-of-plane modulation of the charge order and the interplay between these complex charge-ordered states and superconductivity., Comment: 20 pages, 8 figures

We demonstrate the formation of robust zero energy modes close to magnetic impurities in the iron-based superconductor FeSe$_{1-x}$Te$_x$. We find that the Zeeman field generated by the impurity favors a spin-triplet inter-orbital pairing as opposed to the spin-singlet intra-orbital pairing prevalent in the bulk. The preferred spin-triplet pairing preserves time-reversal symmetry and is topological, as robust, topologically-protected zero modes emerge at the boundary between regions with different pairing states. Moreover, the zero modes form Kramers doublets that are insensitive to the direction of the spin polarization or to the separation between impurities. We argue that our theoretical results are consistent with recent experimental measurements on FeSe$_{1-x}$Te$_x$., Comment: 6+2 pages, 3 figures

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice -- such as $(p_{x},\,p_{y})$-wave and $(d_{x^{2}-y^{2}},\,d_{xy})$-wave. Such a system has two possible superconducting states: the chiral state (e.g. $p+ip$ or $d+id$), which breaks time-reversal symmetry, and the nematic state (e.g. $p+p$ or $d+d$), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A non-analytic cubic term arises, as in the case of a conventional $s$-wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. We analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene., Comment: 17 pages, 13 figures

Despite intense experimental efforts, the nature of the unconventional superconducting order parameter of UTe$_2$ remains elusive. This puzzle stems from different reported numbers of superconducting transitions at ambient pressure, as well as a complex pressure-temperature phase diagram. To bring new insights into the superconducting properties of UTe$_2$, we measured the heat capacity and electrical resistivity of single crystals under compressive uniaxial stress $\sigma$ applied along different crystallographic directions. We find that the critical temperature $T_{\rm c}$ of the single observed bulk superconducting transition decreases with $\sigma$ along $[100]$ and $[110]$ but increases with $\sigma$ along $[001]$. Aside from its effect on $T_{\rm c}$, we notice that $c$-axis stress leads to a significant piezoresistivity, which we associate with the shift of the zero-pressure resistivity peak at $T^\star \approx 15\, \rm K$ to lower temperatures under stress. Finally, we show that an in-plane shear stress $\sigma_{xy}$ does not induce any observable splitting of the superconducting transition over a stress range of $\sigma_{xy}\approx 0.17 \, \rm GPa$. This result suggests that the superconducting order parameter of UTe$_2$ may be single-component at ambient pressure.

In the quasi-two-dimensional (quasi-2D) copper- and iron-based superconductors, the onset of superconductivity is accompanied by a prominent peak in the magnetic spectrum at momenta close to the wave-vector of the nearby antiferromagnetic state. Such a peak is well described in terms of a spin resonance mode, i.e., a spin-1 exciton theoretically predicted for quasi-2D superconductors with a sign-changing gap. The same theories, however, indicate that such a resonance mode should be absent in a three-dimensional (3D) system with a spherical Fermi surface. This raises the question of the fate of the spin resonance mode in layered unconventional superconductors that are not strongly anisotropic, such as certain heavy-fermion compounds and potentially the newly discovered nickelate superconductor NdNiO$_2$. Here, we use the random-phase-approximation to calculate the dynamical spin susceptibility of 3D superconductors with a $d_{x^2-y^2}$-wave gap symmetry and corrugated cylindrical-like Fermi surfaces. By varying the out-of-plane hopping anisotropy $t_z/t$, we demonstrate that the appearance of a spin resonance mode is determined by the topology of the hot lines -- i.e. lines on the Fermi surface that are connected by the magnetic wave-vector. For an in-plane antiferromagnetic wave-vector, the hot lines undergo a topological transition from open lines to closed loops at a critical $t_z/t$ value. The closed hot lines cross the nodal superconducting lines, making the spin resonance mode overdamped and incoherent. In contrast, for an out-of-plane antiferromagnetic wave-vector, the hot lines remain open and the spin resonance mode remains sharp. We discuss the experimental implications of our results for the out-of-plane dispersion of the spin resonance mode and, more generally, for inelastic neutron scattering experiments on unconventional superconductors., Comment: 12 pages, 11 figures

NiS$_2$ has been widely regarded as a model system to study the bandwidth-controlled Mott transition, as enabled by isovalent Se chemical substitution on the S sites. Motivated by advances in electrolyte gating, we theoretically investigate the filling-controlled Mott transition induced by gating, which has the advantage of avoiding dopant disorder and stoichiometric changes. We use combined Density Functional Theory (DFT) and Dynamical Mean Field Theory (DMFT) to study such a filling-controlled transition and compare it with the case of bandwidth control. We draw a temperature-filling phase diagram and find that the Mott-insulator to metal transition occurs with modest added electron concentrations, well within the capabilities of existing electrolyte gating experiments. We find that there is significant incoherent weight at the Fermi level in the metallic phase when the transition is induced by gating. In contrast, the spectral weight remains rather coherent in the case of the bandwidth-controlled transition.

The recently discovered vanadium-based kagome metals $A$V$_{3}$Sb$_{5}$ ($A$~=~K,~Rb,~Cs) exhibit superconductivity at low-temperatures and charge density wave (CDW) order at high-temperatures. A prominent feature of the charge ordered state in this family is that it breaks time-reversal symmetry (TRSB), which is connected to the underlying topological nature of the band structure. In this work, a powerful combination of zero-field and high-field muon-spin rotation/relaxation is used to study the signatures of TRSB of the charge order in CsV$_3$Sb$_5$, as well as its anisotropic character. By tracking the temperature evolution of the in-plane and out-of-plane components of the muon-spin polarization, an enhancement of the internal field width sensed by the muon-spin ensemble was observed below $T_{\rm TRSB}=T_{\rm CDW}\simeq95$~K. Additional increase of the internal field width, accompanied by a change of the local field direction at the muon site from the $ab$-plane to the $c$-axis, was detected below $T^\ast\simeq30$~K. Remarkably, this two-step feature becomes well pronounced when a magnetic field of 8~T is applied along the crystallographic $c-$axis, thus indicating a field-induced enhancement of the electronic response at the CDW transition. These results point to a TRSB in CsV$_3$Sb$_5$ by charge order with an onset of ${\simeq}~95$~K, followed by an enhanced electronic response below ${\simeq}~30$~K. The observed two-step transition is discussed within the framework of different charge-order instabilities, which, in accordance with density functional theory calculations, are nearly degenerate in energy., Comment: 10 pages, 4 figures

The kagome metals of the family $A$V$_3$Sb$_5$, featuring a unique structural motif, harbor an array of intriguing phenomena such as chiral charge order and superconductivity. CsV$_3$Sb$_5$ is of particular interest because it displays a double superconducting dome in the region of the temperature-pressure phase diagram where charge order is still present. However, the microscopic origin of such an unusual behavior remains an unsolved issue. Here, to address it, we combine high-pressure, low-temperature muon spin relaxation with first-principles calculations. We observe a pressure-induced threefold enhancement of the superfluid density, which also displays a double peak feature, similar to the superconducting critical temperature. This leads to three distinct regions in the phase diagram, each of which features distinct slopes of the linear relation between superfluid density and the critical temperature. These results are attributed to a possible evolution of the charge order pattern from the superimposed tri-hexagonal Star-of-David phase at low pressures (within the first dome) to the staggered tri-hexagonal phase at intermediate pressures (between the first and second domes). Our findings suggest a change in the nature of the charge ordered state across the phase diagram of CsV$_3$Sb$_5$, with varying degrees of competition with superconductivity., Comment: 9 pages, 4 figures