Doped strong topological insulators are one of the most promising candidates to realize a fully gapped three-dimensional topological superconductor (TSC). In this Letter, we revisit this system and reveal a possibility for higher-order topology which was previously missed. We find that over a finite range of doping, the Fu-Berg superconducting pairing can give rise to both Majorana surface states and nodal hinge states. Interestingly, we observe the coexistence of surface and hinge modes in the superconducting state only when there are both bulk and surface Fermi surfaces in the normal state. Also, we find that the hinge modes can appear for normal states consisting of doped strong or weak topological insulators. In summary, this work may allow for the discovery of superconducting hinge modes in a well explored class of materials, i.e., doped strong or weak topological insulators.

Microwave surface impedance measurements on cuprate superconductors provide crucial information about the effect of impurity scattering on quasiparticle transport; however, acquiring a full understanding of the effect of impurity scattering on quasiparticle transport is still challenging. Here, starting from a homogenous electron propagator and the related microscopic octet scattering model, which are obtained within the square-lattice $t\text{−}J$ model in the fermion-spin representation, the effect of impurity scattering on low-temperature microwave conductivity in cuprate superconductors is investigated in the self-consistent $T$-matrix approach. The impurity-dressed electron propagator obtained in the Fermi-arc-tip approximation of the quasiparticle excitations and scattering processes is employed to derive the electron current-current correlation function by taking into account the impurity-induced vertex correction. It is shown that the microwave conductivity spectrum is non-Drude-like, with a sharp cusplike peak extending to zero energy and a high-energy tail falling slowly with energy. Moreover, the microwave conductivity decreases with an increase in the impurity concentration or with an increase in the strength of the impurity scattering potential. In striking contrast to the domelike shape of the doping dependence of the superconducting transition temperature, the microwave conductivity exhibits a reverse domelike shape of the doping dependence. The theory also shows that the unconventional features of the microwave conductivity are generated by both the strong electron correlation and impurity scattering effects.

Quasiperiodic systems in one dimension can host nonergodic states, e.g., states localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e., spatially localized or ballistic. However, periodic quenches across these two nonergodic phases were thought to produce ergodic diffusivelike states even for noninteracting particles. We show that this expectation is not met at the thermodynamic limit where the system always attains a nonergodic state. We find that ergodicity may be recovered by scaling the Floquet quenching period with system size and determine the corresponding scaling function. Our results suggest that, while the fraction of spatially localized or ballistic states depends on the model's details, all Floquet eigenstates belong to one of these nonergodic categories. Our findings demonstrate that quasiperiodicity hinders ergodicity and thermalization, even in driven systems where these phenomena are commonly expected.

Understanding the high-pressure lattice dynamics is crucial to modulate the thermal transport in thermoelectric materials beyond the ambient environment. Herein, using molecular dynamics simulations in combination with an accurate machine-learning interatomic potential, we find the well-known double-peak feature of the transverse-optical (TO) mode in PbTe gradually vanishes when pressure is enhanced. An anomalous nonmonotonic pressure dependence of the frequency of the transverse-acoustic phonon in PbTe is computationally reproduced. The longitudinal-acoustic, longitudinal-optical, and TO phonons harden as expected when pressure increases. The theoretical results are compared with inelastic neutron scattering experimental data. We have also calculated the pressure-dependent lattice thermal conductivity and revealed the phonon transport mechanisms.

The Green-Kubo formalism is a formally exact method to determine lattice thermal conductivity of materials from heat-flux autocorrelation functions. However, evaluating heat flux in the context of electronic-structure-based molecular dynamics is nontrivial, hindering the formalism's wider application. Here we present an exact expression of heat flux for Slater-Koster tight binding (TB). This expression takes full advantage of the local orbitals and is straightforward to implement in various TB approaches. Using local orbitals, the present approach is computationally efficient and thus opens an alternative avenue to determine the thermal conductivity of a broad class of materials, especially for those complex systems unsuitable for more expensive ab initio simulations.

Magnetic multilayers with interlayer exchange coupling have been widely studied for both static and dynamic regimes. Their dynamical responses depend on the exchange coupling strength and magnetic properties of individual layers. Magnetic resonance spectra in such systems are conveniently discussed in terms of coupling of acoustic and optical modes. At a certain value of applied magnetic field, the two modes come close to being degenerate and the spectral gap indicates the strength of mode hybridization. In this work, we theoretically and experimentally study the mode hybridization of interlayer-exchange-coupled moments with dissimilar magnetization and thickness of two ferromagnetic layers. In agreement with symmetry analysis for eigenmodes, our low-symmetry multilayers exhibit sizable spectral gaps for all experimental conditions. The spectra agree well with the predictions from the Landau-Lifshitz-Gilbert equation at the macrospin limit whose parameters are independently fixed by static measurements.

In general, the energy spectrum of a non-Hermitian system turns out to be complex, which is not very satisfactory since the time evolution of eigenstates with complex eigenvalues is either exponentially growing or decaying. Here, we provide a sufficient and necessary condition of the real spectrum under open boundary conditions for one-dimensional non-Hermitian tight-binding Hamiltonians. The necessity is directly related to the fact that the generalized Brillouin zone in one dimension is a closed loop whose origin is in its interior. We also establish the sufficiency by analytically determining when the preimage of the characteristic polynomial contains a loop and showing that this loop is just the generalized Brillouin zone itself, using some simple models first and then general one-band models. We demonstrate our conclusions on various non-Hermitian model examples with longer-range hopping. Our results indicate that real spectra are more common than one may have expected in non-Hermitian systems and are helpful for designing non-Hermitian models with real spectra.

In this work we perform real-time simulations for the dynamics of braiding a pair of Majorana zero modes (MZMs) through a quantum dot in a minimal setup of pure one-dimensional realization. We reveal the strong nonadiabatic effect when the dot energy level approaches zero in order to achieve a geometric phase $\pi /4$ which is required for a full exchange between the MZMs. Rather than the strategies of nonuniformly manipulating the system according to adiabatic conditions and shortcuts to adiabaticity, we propose and illustrate a more feasible scheme to suppress the nonadiabatic transition, which allows for a full exchange between the Majorana modes.

We study the nonequilibrium Casimir-Lifshitz force between graphene-based parallel structures held at different temperatures and in the presence of an external thermal bath at a third temperature. The graphene conductivity, which is itself a function of temperature, as well as of chemical potential, allows us to tune in situ the Casimir-Lifshitz force. We explore different nonequilibrium configurations while considering different values of the graphene chemical potential. Particularly interesting cases are investigated, where the force can change sign going from attractive to repulsive or where the force becomes nonmonotonic with respect to chemical-potential variations, contrary to the behavior under thermal equilibrium.

We propose a protocol to certify the presence of entanglement in artificial on-surface atomic and molecular spin arrays using electron spin resonance carried by scanning tunnel microscopy (ESR-STM). We first generalize the theorem that relates global spin susceptibility as an entanglement witness to the case of anisotropic Zeeman interactions, relevant for surfaces. We then propose a method to measure the spin susceptibilities of surface-spin arrays combining ESR-STM with atomic manipulation. Our calculations show that entanglement can be certified in antiferromagnetically coupled spin dimers and trimers with state-of-the-art ESR-STM magnetometry.

We provide information about the progression of the structurally low-dimensional superconductor ${\mathrm{Sc}}_3{\mathrm{CoC}}_4$ from its high-temperature phase to its Peierls-type distorted low-temperature phase. Results from inelastic x-ray scattering, diffuse scattering, and high-resolution x-ray diffraction experiments provide conclusive evidence that the onset of a modulation in the atomic positions during the structural transition is primarily driven by a combination of phonon softening and order-disorder transition. The completion of the phonon softening process at $\sim 150$ K is found to be followed by two additional stages, i.e., an accumulation of gradual structural changes between 150 and 80 K and their saturation into the final low-temperature phase structure below $\sim 80$ K.

Density functional theory (DFT) is routinely employed in material science and quantum chemistry to simulate weakly correlated electronic systems. Recently, deep learning (DL) techniques have been adopted to develop promising functionals for the strongly correlated regime. DFT can be applied to quantum spin models too, but functionals based on DL have not been developed yet. Here, we investigate DL-based DFTs for random quantum Ising chains, both with nearest-neighbor and up to next-nearest-neighbor couplings. Our neural functionals are trained and tested on data produced via the Jordan-Wigner transformation, exact diagonalization, and tensor-network methods. An economical gradient-descent optimization is used to find the ground-state properties of previously unseen Hamiltonian instances. Notably, our nonlocal functionals drastically improve upon the common local density approximations, and they are designed to be scalable, allowing us to simulate chain sizes much larger than those used for training. The prediction accuracy is analyzed, paying attention to the spatial correlations of the learned functionals and to the role of quantum criticality. Our findings indicate a suitable strategy to extend the reach of other computational methods with a controllable accuracy.

Thermal and thermoelectric measurements are known as powerful tools to uncover the physical properties of quantum materials due to their sensitivity towards the scattering and chirality of heat carriers. We use these techniques to confirm the presence of momentum and real-space topology in ${\mathrm{ScMn}}_6{\mathrm{Sn}}_6$. There is an unconventional dramatic increase in the Seebeck coefficient on entering the transverse conical spiral (TCS) state below $T=200$ K, suggesting an unusual scattering of heat carriers. In addition, the observed anomalous thermal Hall effect and the anomalous Nernst effect indicate nonzero Berry curvature in $k$ space. Furthermore, we identify a significant topological contribution to the thermal Hall and Nernst signals in the TCS phase revealing the impacts of real-space Berry curvature. We discuss the presence of the topological thermal Hall effect and topological Nernst effect in the diverse ${\mathrm{HfFe}}_6{\mathrm{Ge}}_6$ family. This study illustrates the importance of transverse thermal and thermoelectric measurements to investigate the origin of topological transport in the noncoplanar magnetic phases in this family of kagome metals.

Dicalcium nitride $\left({\mathrm{Ca}}_2\mathrm{N}\right)$ is a two-dimensional (2D) electride with unique electronic behavior. In this study, we use pseudoatomic orbital (PAO) basis sets to investigate its electronic and optical properties. This methodology provides an accurate representation of the electronic structure associated with the interlayer and surface anionic states of the ${\mathrm{Ca}}_2\mathrm{N}$ bilayer, enabling a comprehensive study of its optical properties. We identify several peaks in the dielectric functions which correspond to interband transitions. Our analysis of the optical conductivity and linear optical spectra, derived from these dielectric functions, reveals distinct peaks in the linear optical spectra of both bulk and bilayer ${\mathrm{Ca}}_2\mathrm{N}$. These peaks are influenced by the in-plane and out-of-plane vectors. This investigation provides valuable insights into the interband transitions and optical behavior of this intriguing 2D electride. It also lays the foundation for future studies of promising 2D electrides.

We analyze the near-adiabatic dynamics in a ramp through the critical point (CP) of the classical transverse field Ising chain. This is motivated, conceptually, by the fact that this CP—unlike its quantum counterpart—experiences no thermal or quantum fluctuations, and technically by the tractability of its effective model. For a “half ramp” from a ferromagnet to the CP, the longitudinal and transverse magnetizations scale as ${\tau }^{-1/3}$ and ${\tau }^{-2/3}$, respectively, with $1/\tau$ the ramp rate, in accord with Kibble-Zurek theory. For ferro- to paramagnetic ramps across the CP, however, they stay closer, ${\tau }^{-1/2}$ and ${\tau }^{-1}$, to adiabaticity. This adiabaticity enhancement compared to the half ramp is understood by casting the dynamics in the paramagnet in the form of a non-Hermitian Dirac Hamiltonian, with the CP playing the role of an exceptional point, opening an additional decay channel.

Applying the Bir-Picus ansatz for strain-induced corrections to the electron momentum scattering time on impurities in a transition metal dichalcogenide monolayer, and taking the parameters of $\mathrm{Mo}{\mathrm{S}}_2$ for our estimations, we derive general analytical expressions describing the piezoresistive effect, the strain-induced corrections to (longitudinal) Drude conductivity, linear magnetoresistance, and the Hall conductivity of the monolayer for an arbitrary dependence of electron momentum scattering time on its energy. We show that a two-band model, even with the account of the trigonal warping of electron valleys, should be revisited for the description of the piezoresistive effect in the case of strongly degenerate electrons. Therefore, we extend the two-band model by accounting for the deformation of higher-energy bands and derive general expressions describing strain-induced corrections to the kinematic coefficients of the monolayer. Thus, the developed approach allows to estimate the deformation constants of higher-energy bands.

We investigate the effect of local electron-phonon coupling on nonlinear optical conductivity in an interacting ferroelectric system. Using real-time simulations, we show an enhancement in nonlinear conductivity under linearly polarized light due to generation of the phonon-assisted ballistic current in addition to the injection current generated by electron-hole pairs. The optically excited phonon modes generate an asymmetric carrier distribution that causes a strong directional ballistic current. The ballistic current enhances the photocurrent several times at above band-gap excitation frequencies and is sublinearly dependent on the excitation intensity. This strong phonon-assisted zero-frequency directional ballistic current demonstrates an alternative way to boost the bulk photovoltaic effect (BPVE) in electronic ferroelectric materials with strong local electron-phonon coupling.

In the large $N$ limit a physical system might acquire a residual entropy at zero temperature even without ground-state degeneracy. At the same time poles in the two-point function might coalesce and form a branch cut. Both phenomena are related to a high density of states in the large $N$ limit. In this paper we address the following question: Does a branch cut in the two-point function always lead to nonzero residual entropy? We argue that for generic fermionic systems in $0+1$ dimensions in the mean-field approximation the answer is positive: Branch cut $1/{\tau }^{2\mathrm{\Delta }}$ in the two-point function does lead to a lower bound $Nlog2(1/2-\mathrm{\Delta })$ for the entropy. We also comment on higher-dimensional generalizations and relations to the holographic correspondence.

Structure factors obtained from diffraction experiments are one of the most important quantities for characterizing the electronic and structural properties of materials. Methods for calculating this quantity from plane-wave density functional theory (DFT) codes are typically prohibitively expensive to perform, requiring the electron density to be constructed and evaluated on dense real-space grids. Making use of the projector functions found in both the Vanderbilt ultrasoft pseudopotential and projector augmented wave methods, we implement an approach to calculate structure factors that avoids the use of a dense grid by separating the rapidly changing contributions to the electron density and treating them on logarithmic radial grids. This approach is successfully validated against structure factors obtained from all-electron DFT and experiment for three prototype systems, allowing structure factors to be obtained at all-electron accuracy at a fraction of the cost of previous approaches for plane-wave DFT.