We study the entanglement spectrum (ES) of two-dimensional $C_n$-symmetric second-order topological insulators (TIs). We show that some characteristic higher-order topological observables, e.g., the filling anomaly and its associated fractional corner charge, can be determined from the ES of atomic and fragile TIs. By constructing the relationship between the configuration of Wannier orbitals and the number of protected in-gap states in the ES for different symmetric cuts in real space, we express the fractional corner charge in terms of the number of protected in-gap states of the ES. We show that our formula is robust in the presence of electron-electron interactions as long as the interactions preserve $C_n$ rotation symmetry and charge-conservation symmetry. Moreover, we discuss the possible signatures of higher-order topology in the many-body ES. Our methods allow the identification of some classes of higher-order topology without requiring the usage of nested Wilson loops or nested entanglement spectra.

Zirconium pentatetelluride, ${\mathrm{ZrTe}}_5$, shows remarkable sensitivity to hydrostatic pressure. In this work we address the high-pressure transport and optical properties of this compound, on samples grown by flux and chemical vapor transport. The high-pressure resistivity is measured up to 2 GPa, and the infrared transmission up to 9 GPa. The dc conductivity anisotropy is determined using a microstructured sample. Together, the transport and optical measurements allow us to discern band parameters with and without the hydrostatic pressure, in particular the Fermi level, and the effective mass in the less conducting, out-of-plane direction. The results are interpreted within a simple two-band model characterized by a Dirac-type, linear in-plane band dispersion, and a parabolic out-of-plane dispersion.

A spin-Meissner effect occurs when the photoluminescence energy is dependent on interactions of otherwise magnetically sensitive particles. Under such a condition, the Zeeman energy splitting becomes zero when the chemical potentials for individual spin components of a spinor polariton condensate are equal or synchronized. Herein, we explore the types of topological spin-Meissner (TSM) states in the formation of a spinor dark soliton in semiconductor microcavities. The effects of nonlinear spin-anisotropic interactions between polaritons, spin-flipping rate from the introduced defects, and energy splitting are theoretically investigated. We observe that, below a critical energy splitting for a given pump power, multistable TSM states exist. However, above a critical energy splitting, the two spin components of the dark soliton pair become desynchronized.

Two-dimensional stacking fault defects embedded in a bulk crystal can provide a homogeneous trapping potential for carriers and excitons. Here we utilize state-of-the-art structural imaging coupled with density-functional and effective-mass theory to build a microscopic model of the stacking-fault exciton. The diamagnetic shift and exciton dipole moment at different magnetic fields are calculated and compared with the experimental photoluminescence of excitons bound to a single stacking fault in GaAs. The model is used to further provide insight into the properties of excitons bound to the double-well potential formed by stacking fault pairs. This microscopic exciton model can be used as an input into models which include exciton-exciton interactions to determine the excitonic phases accessible in this system.

Density functional theory has been used to investigate the behavior of the $\pi$ electrons in bilayer graphene and graphite under compression along the $c$ axis. We have studied both conventional Bernal (A-B) and A-A stackings of the graphene layers. In bilayer graphene, only about 0.5% of the $\pi$-electron density is squeezed through the $s{p}^2$ network for a compression of 20%, regardless of the stacking order. However, this has a major effect, resulting in bilayer graphene being about six times softer than graphite along the $c$ axis. Under compression along the $\mathit{c}$ axis, the heavily deformed electron orbitals (mainly those of the $\pi$ electrons) increase the interlayer interaction between the graphene layers as expected, but, surprisingly, to a similar extent for A-A and Bernal stackings. On the other hand, this compression shifts the in-plane phonon frequencies of A-A stacked graphene layers significantly and very differently from the Bernal stacked layers. We attribute these results to some $s{p}^2$ electrons in A-A stacking escaping the graphene plane and filling lower charge-density regions when under compression, hence, resulting in a nonmonotonic change in the $s{p}^2$-bond stiffness.

Magnetization, electrical resistivity, magnetoresistance, and Hall resistivity of $\mathrm{N}{\mathrm{i}}_{50}\mathrm{M}{\mathrm{n}}_{35}\mathrm{I}{\mathrm{n}}_{14.25}{\mathrm{B}}_{0.75}$ and $\mathrm{N}{\mathrm{i}}_{50}\mathrm{M}{\mathrm{n}}_{35}\mathrm{I}{\mathrm{n}}_{14.5}{\mathrm{B}}_{0.5}$ Heusler alloys were studied in a temperature range $T=80–400\mathrm{K}$ in magnetic fields up to 20 kOe. Both alloys exhibit a martensitic transformation from a high-temperature ferromagnetic austenite phase to a low-temperature, low-magnetization martensitic phase. The electrical resistivity nearly doubles as a result of the martensitic transformation, reaching 180 and 100 µΩ cm in the martensitic states of $\mathrm{N}{\mathrm{i}}_{50}\mathrm{M}{\mathrm{n}}_{35}\mathrm{I}{\mathrm{n}}_{14.25}{\mathrm{B}}_{0.75}$ and $\mathrm{N}{\mathrm{i}}_{50}\mathrm{M}{\mathrm{n}}_{35}\mathrm{I}{\mathrm{n}}_{14.5}{\mathrm{B}}_{0.5}$, respectively. The temperature dependence of the electrical resistivity does not corresponded with the Mooij correlation. The magnetoresistance is negative with a narrow negative peak at the martensitic transition. Normal and anomalous Hall effect coefficients were determined by fitting the field dependences of the Hall resistivity using magnetization data. The coefficients of the normal Hall effect for both compositions were found to decrease with temperature from positive values in the austenite to negative values in the martensite phase. None of the known correlations between the anomalous Hall effect coefficient and resistivity were satisfied. Significant changes in the values of the anomalous Hall coefficients during the martensitic transformation are explained by the difference in spin-up and spin-down state occupations in the martensite and austenite phases. First-principles calculations of the electronic structures confirm this explanation.

Synergic effect of electronic correlation and spin-orbit coupling is an emerging topic in topological materials. Central to this rapidly developing area are the prototypes of strongly correlated heavy-fermion systems. Recently, some Ce-based compounds are proposed to host intriguing topological nature, among which the electronic properties of CeSb are still under debate. In this paper, we report a comprehensive study combining magnetic and electronic transport measurements, and electronic band-structure calculations of this compound to identify its topological nature. Quantum oscillations are clearly observed in both magnetization and magnetoresistance at high fields, from which one pocket with a nontrivial Berry phase is recognized. Angular-dependent magnetoresistance shows that this pocket is elongated in nature and corresponds to the electron pocket as observed in LaBi. Nontrivial electronic structure of CeSb is further confirmed by first-principle calculations, which arises from spin splitting in the fully polarized ferromagnetic state. These features indicate that magnetic field can induce nontrivial topological electronic states in this prototypical Kondo semimetal.

We report magneto-dielectric properties of partially B-site ordered monoclinic ${\mathrm{Tb}}_2\mathrm{CoMn}{\mathrm{O}}_6$ double perovskite thin film epitaxially grown on $\mathrm{Nb}:\mathrm{SrTi}{\mathrm{O}}_3$(100) substrates by metalorganic aerosol deposition technique. Transmission electron microscopy and electron energy loss spectroscopy mapping shows the presence and distribution of both $\mathrm{C}{\mathrm{o}}^{2+}$ and $\mathrm{C}{\mathrm{o}}^{3+}$ ions in the film, evidencing a partial $B$-site disorder, which was further confirmed by the observation of reduced saturation magnetization at low temperatures. The ferromagnetic Curie temperature, $T_C=110\mathrm{K}$, is slightly higher as compared to the bulk value (100 K) probably due to an in plane epitaxy tensile strain. Temperature dependent dielectric study reveals an unexpected high temperature dipolar relaxor-glass-like transition at a temperature $T^{*}\sim 190\mathrm{K}>T_{\mathrm{C}}$, which depends on the applied frequency and indicates a superparaelectric behavior. Two different dielectric relaxation peaks have been observed; they merge at $T^{*}$ where likely a coupling to the disorder-induced short range charge-spin correlations results in a 4% magneto-dielectric coupling.

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature, in contrast to common intuition where low-energy quantum effects are washed away by strong thermal fluctuations at high temperature. By comparing numerical simulations with exact analytic results, we determine that this phenomenon has a topological origin and is highly generic, as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we show that the infinite-temperature OTOCs probe zero-temperature quantum phases via detecting the presence of Majorana zero modes at the ends of the chain that is associated with 1D $Z_2$ topological order. Hence, we show that strong zero modes also affect OTOCs and scrambling dynamics. Our results demonstrate an intriguing interplay between information scrambling and topological order, which leads to a new phenomenon in the scrambling of generic nonintegrable models: topological order induced prescrambling, paralleling the notion of prethermalization of two-time correlators that defines a timescale for the restricted scrambling of topologically protected quantum information.

Collective tunneling is a ubiquitous phenomenon in finite-size spin clusters that shows up in systems as diverse as molecular magnets or spin clusters adsorbed at surfaces. The basic problem we explore is to understand how small flipping terms can cooperate to flip a large spin to the opposite direction or a cluster of interacting elementary Ising spins into the time-reversed state. These high-order processes will involve at least two channels, a single spin-flip channel due to a transverse field and a two-spin flip channel due to exchange or other pairwise interactions or due to single-ion anisotropies. In view of the complexity of high-order perturbation theory, nonperturbative approaches based on large-spin path integrals were developed when this problem was first addressed in the context of single spin models. In the present paper, we show that high-order perturbation theory can in fact be formulated and evaluated with the help of simple recurrence relations, leading to a compact theory of tunneling in macroscopic spins, in one-dimensional clusters, as well as in small higher-dimensional clusters. This is demonstrated explicitly in the case of the Ising model with a transverse field and transverse exchange, and in the case of macroscopic spins with uniaxial anisotropy. Our approach provides a transparent theory of level crossings, where the tunneling between time-reversed configurations vanishes as a function of the external field. Those crossings result from the destructive quantum interferences between competing flipping channels. Destructive interferences are expected to be present as soon as the two-spin flip channels have an overall positive amplitude and thus compete with the intrinsically negative second-order processes due to the transverse field. Our theory consistently predicts $N$ crossings in chains of $N$ Ising spins and $2S$ crossings in single spins of magnitude $S$ and yields explicit analytical formulas for the level crossings of open chains and macroscopic spins. Disorder can be easily implemented in this perturbative formalism. Leading disorder effects can be treated analytically for spin rings. We find that at the smallest transverse field crossing the suppression of tunneling is most robust with respect to disorder and fluctuations in the parameters. We briefly discuss the implications of our findings for the use of realistic spin clusters on surfaces to store information.

A simple relation is established between the zero-$T$ penetration depth $\lambda \left(0\right)$ and the slope of ${\lambda }^{-2}\left(T\right)$ near $T_c$, similar to Helfand-Werthamer's relation for $H_{c2}\left(0\right)$ and the slope of $H_{c2}\left(T\right)$ at $T_c$ for the isotropic $s$-wave case with nonmagnetic scattering [E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966)]. When the scattering parameter $\rho =\hslash v/2\pi T_c\ell$ ($v$ is the Fermi velocity and $\ell$ is the mean free path) varies from 1 to 10, the coefficient of proportionality between ${\lambda }^{-2}\left(0\right)$ and $T_c{(d{\lambda }^{-2}/dT)}_{T_c}$ changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can express $\lambda \left(0\right)$ in terms of the slope ${(d{H}_{c2}/dT)}_{T_c}$ and the density of states.

We explore the evolution of the structural phase transition of ${(\mathrm{Sr},\mathrm{Ca})}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$, a model system to study the interplay between structural quantum criticality and superconductivity, by means of high-energy x-ray diffraction measurements at high pressures and low temperatures. Our results confirm a rapid suppression of the superlattice transition temperature $T^{*}$ against pressure, which extrapolates to zero at a critical pressure of $\approx 1.79\left(4\right)\mathrm{GPa}$. The temperature evolution of the superlattice Bragg peak in ${\mathrm{Ca}}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$ reveals a drastic decrease of the intensity and an increase of the linewidth when $T\to 0\mathrm{K}$ and $p\to p_c$. Such anomaly is likely associated with the emergence of quantum fluctuations that disrupt the formation of long-range superlattice modulation. The revisited temperature-pressure phase diagram of ${(\mathrm{Sr},\mathrm{Ca})}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$ thus highlights the intertwined nature of the distinct order parameters present in this system and demonstrates some similarities between this family and the unconventional superconductors.

We apply the charge-pumping argument to fermionic tensor network representations of $d$-dimensional topological insulators (TIs) to obtain tensor network states (TNSs) for $(d+1)$-dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair state (PEPS) for a Chern insulator starting from a matrix product state (MPS) in $d=1$ describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to second-order TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in $d=2$ for the obstructed atomic insulator (OAI) of the quadrupole model. The $(d+1)$-dimensional TNSs obtained in this way have a constant bond dimension inherited from the $d$-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the $d$-dimensional models, we identify gapped next-nearest-neighbor Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively.

We theoretically investigate the possibility of lasing in an electromagnetic resonator coupled to a voltage-biased hybrid double quantum dot comprised of a double quantum dot tunnel coupled simultaneously to a normal metal and a superconducting lead. Using a unitary transformation, we derive a resonator-double quantum dot interaction Hamiltonian in the rotating-wave approximation which reveals the fact that lasing in this system is mediated by electron transitions between Andreev energy levels in the system's density of states. Moreover, by employing a Markovian master equation incorporating dissipation effects for the electronic and photonic degrees of freedom, we numerically calculate the steady-state reduced density matrix of the system from which we determine the average photon number and its statistics in the resonator in various parameter regimes. We find that at some appropriate parameter configurations, lasing can be considerably enhanced due to the possibility of electron transitions between multiple Andreev levels in the system.

We investigate the entanglement entropy in the integer quantum Hall effect in the presence of an edge, performing an exact calculation directly from the microscopic two-dimensional wave function. The edge contribution is shown to coincide exactly with that of a chiral Dirac fermion, and this correspondence holds for an arbitrary collection of intervals. In particular, for a single interval, the celebrated conformal formula is recovered with left and right central charges $c+\overline{c}=1$. Using Monte Carlo techniques, we establish that this behavior persists for strongly interacting systems such as Laughlin liquids. This illustrates how entanglement entropy is not only capable of detecting the presence of massless degrees of freedom, but also of pinpointing their position in real space, as well as elucidating their nature.

GdNi is a ferrimagnetic material with a Curie temperature $T_C=69$ K which exhibits a large magnetocaloric effect, making it useful for magnetic refrigerator applications. We investigate the electronic structure of GdNi by carrying out x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) at $T=25$ K in the ferrimagnetic phase. We analyze the Gd $M_{4,5}$-edge ($3d-4f$) and Ni $L_{2,3}$-edge ($2p-3d$) spectra using atomic multiplet and cluster model calculations, respectively. The atomic multiplet calculation for Gd $M_{4,5}$-edge XAS indicates that Gd is trivalent in GdNi, consistent with localized $4f$ states. On the other hand, a model cluster calculation for Ni $L_{2,3}$-edge XAS shows that Ni is effectively divalent in GdNi and strongly hybridized with nearest-neighbor Gd states, resulting in a $d$-electron count of 8.57. The Gd $M_{4,5}$-edge XMCD spectrum is consistent with a ground-state configuration of $S=7/2$ and $L=0$. The Ni $L_{2,3}$-edge XMCD results indicate that the antiferromagnetically aligned Ni moments exhibit a small but finite total magnetic moment ($m_{tot}\sim 0.12{\mu }_B$) with the ratio $m_o/m_s\sim 0.11$. Valence band hard x-ray photoemission spectroscopy shows Ni $3d$ features at the Fermi level, confirming a partially filled $3d$ band, while the Gd $4f$ states are at high binding energies away from the Fermi level. The results indicate that the Ni $3d$ band is not fully occupied and contradicts the charge-transfer model for rare-earth based alloys. The obtained electronic parameters indicate that GdNi is a strongly correlated charge-transfer metal with the Ni on-site Coulomb energy being much larger than the effective charge-transfer energy between the Ni $3d$ and Gd $4f$ states.

Using high-energy x-ray diffraction and large-scale three-dimensonal structure modeling, we reveal the evolution of local lattice distortions in the archetypal charge density wave (CDW) system $2H-\mathrm{TaS}{\mathrm{e}}_2$ as it is cooled from its normal state above room temperature down to temperature where Ta atoms form a long-range ordered superstructure. In particular, we find that the structure is formed via a gradual in-plane clustering of Ta atoms exhibiting unusually short bonding distances already near room temperature, and not via a cooperative distortion of Ta atomic planes taking place at the critical ordering temperature. Our findings clarify the debated local symmetry and magnitude of the periodic lattice distortions in the CDW state of $2H-\mathrm{TaS}{\mathrm{e}}_2$, and emphasize the role of locally correlated lattice distortions as a precursor of CDWs in low-dimensional solids. Also, we demonstrate an efficient experimental approach to study them.

One distinguished property of the topological insulator (TI) is its robust quantized edge conductance against edge defect. However, this robustness, underlined by the topological principle of bulk-boundary correspondence, is conditioned by assuming a perfect bulk. Here, we investigate the robustness of the TI phase against bulk defects, including vacancy (VA), vacancy cluster (VC), and grain boundary (GB), instead of edge defect. Based on a tight-binding model analysis, we show that a two-dimensional (2D) TI phase, as characterized by a nonzero spin Bott index, will vanish beyond a critical VA concentration ($n_{\mathrm{v}}^{\mathrm{c}}$). Generally, $n_{\mathrm{v}}^{\mathrm{c}}$ decreases monotonically with the decreasing topological gap induced by spin-orbit coupling. Interestingly, the $n_{\mathrm{v}}^{\mathrm{c}}$ to destroy the topological order, namely, the robustness of the TI phase, is shown to be increased by the presence of VCs but decreased by GBs. As a specific example of a large-gap 2D TI, we further show that the surface-supported monolayer Bi can sustain a nontrivial topology up to $n_{\mathrm{v}}^{\mathrm{c}}\sim 17\%$, based on a density-functional theory–Wannier-function calculation. Our findings should provide useful guidance for future experimental studies of effects of defects on TIs.

Using the numerical renormalization group (NRG) and Anderson's poor man's scaling, we show that a system containing a quantum impurity (QI), strongly coupled to a semiconductor (with gap $2\mathrm{\Delta }$) and weakly coupled to a metal, displays a reentrant Kondo stage as one gradually lowers the temperature $T$. The NRG analysis of the corresponding single impurity Anderson model (SIAM), through the impurity's thermodynamic and spectral properties, shows that the reentrant stage is characterized by a second sequence of SIAM fixed points, viz., free orbital (FO) $\to$ local moment (LM) $\to$ strong coupling (SC). In the higher-temperature stage, the SC fixed point (with a Kondo temperature $T_{K1}$) is unstable, while the lower-temperature Kondo screening exhibits a much lower Kondo temperature $T_{K2}$, associated to a stable SC fixed point. The results clearly indicate that the reentrant Kondo screening is associated to an effective SIAM, with an effective Hubbard repulsion $U_{\mathrm{eff}}$, whose value is clearly identifiable in the impurity's local density of states. This low-temperature effective SIAM, which we dub as reentrant SIAM, behaves as a replica of the high-temperature (bare) SIAM. The second-stage RG flow (obtained through NRG), whose FO fixed point emerges for $T\approx \mathrm{\Delta }<T_{K1}$, takes over once the RG flows away from the unstable first-stage SC fixed point. The intuitive picture that emerges from our analysis is that the first Kondo state develops through impurity screening by semiconducting electrons, while the second Kondo state involves screening by metallic electrons, once the semiconducting electrons are out of reach to thermal excitations ($T<\mathrm{\Delta }$) and only the metallic (low) spectral weight inside the gap is available for impurity screening. This switch implies that the first Kondo cloud is much smaller than the second since the NRG results show that, for all parameter ranges analyzed, $T_{K2}\ll T_{K1}$. Last, but not least, we analyze a hybrid system formed by a QI “sandwiched” between an armchair graphene nanoribbon (AGNR) and a scanning tunneling microscope (STM) tip (an $\mathrm{AGNR}+\mathrm{QI}+\mathrm{STM}$ system), with respective couplings set to reproduce the generic model described above. The energy gap ($2\mathrm{\Delta }$) in the AGNR can be externally tuned by an electric-field-induced Rashba spin-orbit interaction. We analyzed this system for realistic parameter values, using NRG, and concluded that the reentrant SIAM, with its associated second-stage Kondo, is worthy of experimental investigation.