We carry out temperature-dependent scanning tunneling microscopy (STM) studies of the charge density wave (CDW) compound ${\mathrm{ZrTe}}_3$, which is intentionally doped with Hf. Previous bulk studies tie Hf doping to an enhancement of the CDW transition temperature $T_{\mathrm{CDW}}$. In our work, by combining STM measurements with density functional theory calculations, we observe and identify multiple defects in ${\mathrm{Zr}}_{0.95}{\mathrm{Hf}}_{0.05}{\mathrm{Te}}_3$. Surprisingly, instead of finding clear structural or electronic signatures associated with Hf dopants, we determine that the observed defects are consistent with Te and Zr vacancies. Further, our temperature-dependent STM measurements allow us to examine CDW pinning to both types of observed defects below and above $T_{\mathrm{CDW}}$.

We investigate the steady state of two single-mode, uniform, spatially separated polaritonic condensates exposed to resonant pumping with entangled pairs of photons in the presence of incoherent exciton reservoirs created by nonresonant optical pumping. We demonstrate the principal possibility of driving the system to an entangled state despite its exposure to noises arising from the excitonic reservoirs and photon leakage through the microcavity mirrors. We estimate the minimum pair-induced polariton influx required to drive the system into a steady state that violates the partial-transpose criterion for entanglement. Furthermore, we trace the evolution of the system after a sudden switch-off of the entangled pumping. Our analysis provides estimates for the entanglement lifetime in a system of two exciton-polariton condensates.

Periodic π-vacancies in graphene superlattices (GSLs) provide a symmetry-based route to band gap opening in graphene by modifying the π-band dispersion, yet the symmetry conditions that determine whether a vacancy motif can open a band gap remain unclear. Here, we investigate periodic π-vacancy GSLs using a nearest-neighbor tight-binding model with one $p_z$ orbital per carbon site to identify the symmetry requirements for band gap opening. Here, π vacancies, resembling functionalized, substituted, or missing carbon sites, are modeled as site deletions in the π basis, and the corresponding hopping matrix elements to and from the deleted sites are set to zero. We focus on π-vacancy motifs with $C_2$ and $C_3$ point groups. A $3n\times 3n$ GSL, where $n=1,2,3,\cdots$ is the integer scaling factor multiplying the honeycomb primitive-cell vectors, is required to fold $K$ and $K^{\prime }$ to $\mathrm{\Gamma }$, which is one of the requirements for opening a band gap. For $C_3$-type vacancies, the Dirac cones are pinned at the high-symmetry points, thus remaining at $\mathrm{\Gamma }$ in the folded $3n$ GSLs. However, those $C_2$-type vacancies, which reduce the global point group of the GSL to $D_{2h}$ by preserving a pair of perpendicular mirror symmetries (${\sigma }_v\perp {\sigma }_d)$, can constrain the positions of Dirac cones at $\mathrm{\Gamma }$. The absence of the ${\sigma }_v$ and ${\sigma }_d$ planes allows the cones to shift around $\mathrm{\Gamma } \left(\pm \mathrm{\Delta }\mathbf{q},\pm \mathrm{\Delta }\mathbf{q}\right)$ in the $3n$ superlattice. The $C_3$-type vacancies open a relatively larger band gap than the $C_2$-type vacancies due to twofold degeneracy at $\mathrm{\Gamma }$, while the $C_2$-type vacancies leave the GSL with nondegenerate bands. The energy contours near the Dirac cone for $C_3$-symmetric vacancies remain isotropic, while the absence of $C_3$ generates anisotropic cones. The band gap openings in $3n$ superlattices scale linearly with defect concentration for each vacancy motif, with the $D_{6h}$ motif yielding the largest gap, reaching 314 meV at only 3.7% defect concentration. Disorder of the superlattice by missing vacancies or by vacancy displacements of one or two primitive lattice vectors of graphene breaks the $C_3$ symmetry, lifts the degeneracy, and reduces the gap toward the pristine graphene limit.

Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling $\nu =\frac{1}{3}$ of the lowest Landau level in each layer, we show that (i) the limit of decoupled Laughlin states is stable upon introducing interlayer interactions and (ii) the system can enter a spontaneously layer-trimerized foliated non-Abelian Fibonacci phase. We support our claims by numerical exact diagonalization of up to ten layers as well as perturbative analytical calculations. Specifically, we show that the foliated Fibonacci phase exists in the nine-layer system with pseudopotential interactions within and between neighboring layers. We identify the phase via quasihole counting and by calculating the overlap with a model wave function which we derive from the associated conformal field theory. Our numerical results suggest the possibility of realizing these phases in layered van der Waals crystals in strong magnetic fields, as well as in multilayer heterostructures.

Kagome metals exhibit rich correlated-electron physics, yet a systematic understanding of the degree of correlation across transition-metal species remains elusive. Using density-functional theory plus multiorbital slave-spin mean-field theory, we investigate electronic correlations in the Ti-, V-, and Cr-based 135 compounds with Sb and Bi pnictogens. We find that the significantly stronger degree of correlation of the Cr-based materials compared to Ti and V can only be explained through the synergy of two effects: the larger electron filling of the $d$ shell and the reduced characteristic kinetic energy. We put forward that the substitution of Sb with Bi strengthens correlations in all compounds and make the prediction that the-yet-to-be-synthesized ${\mathrm{CsCr}}_3{\mathrm{Bi}}_5$ must be the most strongly correlated member of the entire family. These findings provide a quantitative, band-structure-based framework for understanding and predicting correlation strength in Kagome metals.

We study strongly interacting topological Floquet systems in one dimension and symmetry class BDI and introduce two Floquet Green's-function-based topological invariants to characterize phases hosting Majorana zero modes and Majorana $\pi$ modes at the edge. While applicable also to interacting systems, these invariants reproduce winding numbers of noninteracting Floquet unitaries discussed in the literature. We further analytically evaluate the Green's function in interacting Kitaev-like Floquet chains (or equivalently transverse field Ising circuits) both in the bulk and at the edge at various analytically tractable points in parameter space corresponding to a variety of topological phases. Just as in the case of continuum time evolution, topological bands of Green's function zeros may also contribute to the topological invariant and display a bulk-boundary correspondence. However, contrary to the case of continuum time evolution, Floquet Green's functions can have zeros even in the absence of interactions. Finally, we also discuss an implementation of this Floquet system in a digital quantum emulator: We present a circuit which encodes the interaction under consideration and pinpoint the observables carrying information about the topological Green's function boundary zeros.

Strong electronic correlations generally require nonperturbative treatment. Local correlations are captured by dynamical mean-field theory, while nonlocal correlations can be treated with diagrammatic extensions such as the dual fermion approach. Dual fermion is built on physically motivated but in principle uncontrolled approximations, so careful benchmarking is needed to understand the strengths and limitations of the method. In this work, we benchmark ladder dual fermion and dynamical mean-field theory for the Falicov–Kimball model with the exact classical Monte Carlo solution. We focus on the thermodynamics, electronic structure, and susceptibility, especially on the combined frequency and momentum structure, and find that dual fermion clearly outperforms dynamical mean-field theory. Somewhat surprisingly, dual fermion is not as accurate for the relation between orbital density and chemical potential in the doped system. These results demonstrate the need for rigorous benchmarking of diagrammatic extensions of dynamical mean-field theory for models with inequivalent orbitals, a capability that is essential for modeling materials.

One-dimensional non-Hermitian quasicrystals with parity and time-reversal ($\mathcal{PT}$) symmetry can simultaneously exhibit a localization-delocalization transition, a topological phase transition, and a $\mathcal{PT}$-symmetry-breaking transition. This motivates us to investigate how the absence of $\mathcal{PT}$ symmetry impacts topological metal-insulator transitions in non-Hermitian quasicrystals. We propose a non-Hermitian quasiperiodic model that generally does not preserve $\mathcal{PT}$ symmetry but, in most parameter regions, hosts a generic triple-transition scenario encompassing localization, topological, and degeneracy-breaking transitions. These transitions can be understood within the dual momentum-space representation featuring asymmetric couplings. Specifically, the localization boundary is obtained from the dual momentum-space representation by comparing the Lyapunov exponent, or inverse localization length, of the reciprocal Aubry-André model with the nonreciprocal hopping-asymmetry ratio of the dual lattice. The accompanying topological transition is characterized by a point-gap winding number defined with respect to a reference energy inside the complex spectral gap, whereas the degeneracy-breaking transition is understood from the loss of the reciprocal $n\leftrightarrow -n$ spectral symmetry. The system also exhibits a localization-delocalization transition analogous to that in the Hermitian case, which occurs without accompanying topological or degeneracy-breaking transitions. Our work extends the topological metal-insulator transitions previously studied in $\mathcal{PT}$-symmetric systems to a more general class with a non-Hermitian setting and further reveals that non-Hermitian systems can host distinct types of localization behavior.

Altermagnetism is a recently identified magnetic phase with zero net magnetization but momentum-dependent spin splitting, for which unambiguous experimental signatures remain scarce. We show that thin superconducting films coexisting with collinear $d$-wave altermagnetic order exhibit characteristic fourfold anisotropies in their critical temperature, in-plane critical field, and critical current density. We demonstrate that these anisotropies originate from the interplay between a paramagnetic-type coupling—generated by an exchange or Zeeman fields—and the orbital coupling also induced by the magnetic field. The altermagnetic contributions to the predicted anisotropies are odd in the applied magnetic field. Observed together with zero net magnetization, these signatures directly indicate the presence of altermagnetic order and allow it to be distinguished from anisotropies of other origins. Our results, applicable to intrinsic altermagnetic superconductors and to superconductor/altermagnetic-insulator heterostructures, provide directly measurable signatures for identifying altermagnetic order in thin-film geometries.

We perform hybrid density functional calculation to study the energetics, electronic properties, optical transitions, and migration barriers of native defects in ${\mathrm{CaWO}}_4$. Oxygen and calcium vacancies are most likely to form in the absence of doping, but interstitials could also incorporate. Tungsten-related defects are unlikely to be present. The positively charged $V_{\mathrm{O}}$ and the negatively charged $V_{\mathrm{Ca}}$ are likely to form complexes. Calculated optical transition levels indicate that experimentally observed absorption and emission peaks can be attributed mainly to oxygen-related defects. Calculations of migration barriers allow us to conclude that ${\mathrm{Ca}}_i^{2+}, V_{\mathrm{O}}^{2+}$, and ${\mathrm{O}}_i^{2-}$ are highly mobile, even below room temperature. We have also examined Er dopants, finding that erbium easily substitutes on the Ca site in a positive charge state. Erbium can form complexes with $V_{\mathrm{Ca}}$ and ${\mathrm{O}}_i$, which would deactivate the Er. If Er is introduced by implantation, Er interstitials are likely present, which will produce emission that is prone to spectral diffusion and blinking. Our calculated properties of ${\mathrm{Er}}_i$ explain why annealing at modest temperatures allows the interstitials to move into substitutional sites and point defects to move away, resulting in stable emission.

We report a comprehensive high-temperature structural investigation of the B-site ordered double perovskite ${\mathrm{SrLaCoNbO}}_6$ using combined Raman spectroscopy and x-ray diffraction (XRD) over the range 25–900 ${}^{\circ }\mathrm{C}$. Two distinct temperature-driven anomalies are identified at $T_{\mathrm{OD}}=300\pm 25{}^{\circ }\mathrm{C}$ and $T_{\mathrm{PT}}=750\pm 25{}^{\circ }\mathrm{C}$ through pronounced renormalizations in the phonon frequency and linewidth, accompanied by the evolution and suppression of characteristic XRD reflections. The low-temperature anomaly at $T_{\mathrm{OD}}$ is associated with an isostructural octahedral distortion within the monoclinic $P{2}_1/n$ phase. At $T_{\mathrm{OD}}$, the radial and angular distortion parameters of the ${\mathrm{CoO}}_6$ and ${\mathrm{NbO}}_6$ octahedra decrease to near-zero values before reversing upon further heating due to an inversion of the in-plane Co–O and Nb–O bond-length hierarchy. The high-temperature anomaly at $T_{\mathrm{PT}}$ corresponds to a symmetry-breaking structural phase transition from $P{2}_1/n$ to the monoclinic $I2/m$ phase, confirmed by group-theoretical analysis and Rietveld refinement. These results demonstrate that integrating temperature-dependent Raman spectroscopy with laboratory-based XRD, complemented by quantitative octahedral distortion analysis, provides a robust approach to disentangle isostructural octahedral distortions from symmetry-breaking phase transitions in complex double perovskite oxides without recourse to synchrotron or neutron diffraction facilities.

Long-lived hyperfine coherences in rare-earth-ion doped (REID) crystals provide controlled phase evolution windows for metrology. We use this resource to propose an experimental protocol for accessing strain shifts of ground state hyperfine transitions in non-Kramers REID materials, a quantity that is difficult to access directly with conventional spectroscopic methods. Starting from the crystal field Hamiltonian, we relate the response to strain-dependent effective quadrupole and Zeeman tensors, including changes in electronic wave functions, virtual electronic admixtures, and the bare nuclear quadrupole interaction. The protocol optically prepares a selected hyperfine class, uses a phase-controlled rf $\pi /2$ pulse to create the sensing coherence, and applies synchronized dynamical decoupling pulses during the phase evolution interval so that a coherent ac strain drive accumulates phase rather than averaging away. The accumulated phase is then retrieved by Raman heterodyne readout. The resulting framework provides a route to understanding strain-induced hyperfine shifts in non-Kramers REID systems.

The interplay among electronic nematicity, charge density wave (CDW), and superconductivity in correlated electronic systems has induced extensive research interest. Here, we discover the existence of nematic fluctuations in a ${\mathrm{TiSe}}_2$ single crystal and investigate its evolution with Cu intercalation. It is observed that the elastoresistivity coefficient $m_{E_g}$ exhibits a divergent temperature dependence following a Curie-Weiss law at high temperature. Similar to the evolution of CDW, upon Cu intercalation, the characteristic temperature $T^{*}$ of nematic fluctuation is progressively suppressed and becomes near zero when the superconductivity is optimized. Further intercalation of Cu leads to the sign change of $T^{*}$ and the suppression of superconductivity. These results indicate an intricate relationship among nematic fluctuations, CDW, and superconductivity in ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$. Therefore, this system provides a unique material platform to explore the coexistence and competition among multiple symmetry-broken states.

Solid solutions of ${\mathrm{PbZr}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_3$ (PZT) with $x\le 0.06$ undergo a phase transition from the cubic paraelectric phase to a phase usually characterized as ferroelectric. In this case, a complex system of superstructure peaks appears in the vicinity of the positions $\vec{Q}=(h+\frac{1}{2}k+\frac{1}{2}l)$, indicating the formation of incommensurate modulation of the structure. The absence of extinctions indicates a connection between the superstructure and cation displacements. A clear understanding of the relevant critical dynamics is still absent. We analyze synchrotron radiation scattering data on a PZT2.4 single crystal, focusing on diffuse scattering around the $M$ point of the Brillouin zone. We describe the data using a model that explicitly accounts for the coupling between the transverse acoustic and antiferrodistortive (AFD) phonon branches, which become symmetry allowed along the $\mathrm{\Sigma }$ line. The inverse dynamical response is represented by a $2\times 2$ matrix, and the resulting hybridized modes are used to compute the energy-integrated diffuse intensity in the high-temperature limit. The temperature dependence is governed solely by the softening of the AFD mode, which follows a Curie-Weiss law. The model successfully reproduces the observed line shapes at several temperatures. The obtained dispersion curves reveal a mixed soft mode with a minimum at an incommensurate wave vector, whose position near the phase transition agrees qualitatively with the satellite peaks observed below $T_c$. The present analysis indicates that the satellites observed in the intermediate polar phase originate from an incommensurate phase transition, driven by a mixed soft mode. Based on the obtained results, we propose a description of the observed complete pattern of superstructure reflections as a result of a transition to an incommensurate phase characterized by a 24-ray star of the wave vector $\mathbf{q}=(1/2-\delta ,1/2-\delta ,\delta )$. In this case, the $M$-type reflections turn out to be second-order reflections. The proposed description resolves the contradictions between models that interpret the observed superstructure as arising from either oxygen octahedra rotations or antiparallel cation displacements. The proposed structure is in good agreement with selected area electron diffraction data.

We investigate orbital-to-spin conversion in heavy metals (HMs) by measuring the current-induced damping-like torque in $\mathrm{Ti}/R/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ trilayers and $R/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ bilayers ($R=\mathrm{Pt}, \alpha \text{−}\mathrm{W}$, or $\beta \text{−}\mathrm{W}$) using spin–torque ferromagnetic resonance. Comparison with the corresponding bilayers reveals a Ti-induced torque that is positive for Pt, negative for $\beta \text{−}\mathrm{W}$, and negligible for $\alpha \text{−}\mathrm{W}$. Analysis with a coupled spin–orbital drift-diffusion model shows that spin- and orbital-sink corrections play only minor roles and that orbital-to-spin conversion in the $\mathrm{HM}$ provides the dominant contribution. The Ti-thickness dependence identifies the bulk orbital Hall effect in Ti as the source of the injected orbital current. The fits yield effective conversion amplitudes of opposite signs and of the same order of magnitude for Pt and $\beta \text{−}\mathrm{W}$, together with nanometer-scale orbital diffusion lengths. The signs of the Pt and $\beta \text{−}\mathrm{W}$ responses follow their respective spin Hall responses, whereas the overall material dependence of the response magnitude does not scale quantitatively with the spin Hall conductivity. The pronounced contrast between the two phases of W shows that the observable coupled spin–orbital transport response is not determined solely by the strength of atomic spin–orbit coupling and highlights the importance of crystal structure.

Delafossite compounds containing rare-earth ions have been proven to be an ideal platform to investigate frustrated magnetic ground states. Here, we discuss two triangular-lattice antiferromagnets, ${\mathrm{TlErSe}}_2$ and ${\mathrm{TlTmSe}}_2$, as potential candidates for hosting exotic quantum states. Powder x-ray diffraction data analysis of the black polycrystalline $\mathrm{Tl}M{\mathrm{Se}}_2$ ($M$: Er and Tm) samples confirms the phase purity. Both materials crystallize in the trigonal $\alpha \text{−}{\mathrm{NaFeO}}_2$ structure ($R\overline{3}m$) with lattice parameters $a=4.1070\left(4\right)\text{Å}$ and $c=23.1472\left(1\right)\text{Å}$ for the erbium compound and $a=4.0916\left(1\right)\text{Å}$ and $c=23.1483\left(2\right)\text{Å}$ for the thulium compound. Magnetic susceptibility measurements show an effective moment of ${\mu }_{\text{eff}}=9.6\left(2\right){\mu }_B/\mathrm{f}.\mathrm{u}.$ ($7.5\left(1\right){\mu }_B/\mathrm{f}.\mathrm{u}.$) for ${\mathrm{TlErSe}}_2$ (${\mathrm{TlTmSe}}_2$) for temperatures above 200 K. While ${}^3\mathrm{He}$ specific heat measurements reveal long-range magnetic order below $T_N=0.42\mathrm{K}$ for ${\mathrm{TlErSe}}_2$, no sign of long-range magnetic order was observed for ${\mathrm{TlTmSe}}_2$. Combining both experimental and computational results, we discuss the striking difference in the magnetic behavior of ${\mathrm{TlTmSe}}_2$ and map out the $T-H$ phase diagram for polycrystalline ${\mathrm{TlErSe}}_2$.

Two-dimensional (2D) metal borocarbide superconductors represent an emerging category of low-dimensional materials consisting of boron, carbon, and metal atoms, which hold substantial promise for applications in next-generation low-power superconducting electronics and quantum devices. Here, we design a family of 2D metal borocarbide superconductors with the chemical formula $X{\mathrm{B}}_6{\mathrm{C}}_6 (X=\mathrm{Al},\mathrm{Ga},\mathrm{In})$ using a high-throughput structural search combined with first-principles calculations. These compounds crystallize in a graphene-like metal-intercalated structure, belonging to the layer group with $P\overline{6}2m$ symmetry, where metal atoms are intercalated between the honeycomb boron–carbon (B–C) layers. These compounds have an extremely low metal content, with 83% less metal than ${\mathrm{MgB}}_2$ on a per-light-atom basis. The calculated results indicate that superconducting transition temperatures ($T_c$) of 2D ${\mathrm{InB}}_6{\mathrm{C}}_6, {\mathrm{GaB}}_6{\mathrm{C}}_6$, and ${\mathrm{AlB}}_6{\mathrm{C}}_6$ are 43.61 K, 42.20 K, and 39.97 K, respectively, all of which exceed the $T_c$ values of the conventional ${\mathrm{MgB}}_2$ superconductor (39 K). The high-$T_c$ values of these 2D metal borocarbide superconductors are mainly attributed to the strong coupling between the metallized $\sigma /\pi$ orbitals and the in-plane phonon vibrations of the B–C frameworks. These findings confirm that moderate metal doping in 2D light-element frameworks constitutes an effective strategy for achieving high-temperature superconductivity, thereby offering insights for the exploration of further superconductors.

In rare-earth ion-doped crystals, inhomogeneous absorption profiles reflect the distribution of local environments experienced by individual ions. While each optical transition probes this distribution differently, their fine spectral structures may retain correlations arising from shared local perturbations. In this paper, we present a low-temperature, high-resolution spectroscopic study in ${\mathrm{Er}}^{3+}:\mathrm{YSO}$ of the transition ${}^{4}I_{15/2}\to {}^{4}I_{11/2}$ at 980 nm and compare it to the well-known transition ${}^{4}I_{15/2}\to {}^{4}I_{13/2}$ at 1.5 $\mu \mathrm{m}$. Using spectral hole burning on one transition while monitoring the other, we uncover spectral correlations across two transitions connecting distinct spin-orbit multiplets, providing insight into the microscopic origin of inhomogeneous distributions in rare-earth doped crystals.