The transverse field Ising model (TFIM) on the half-infinite chain possesses an edge zero mode. This work considers an impurity model: TFIM perturbed by a boundary integrability-breaking interaction. For sufficiently large transverse field, but in the ordered phase of the TFIM, the zero mode is observed to decay. The decay is qualitatively different from zero modes where the integrability-breaking interactions are nonzero all along the chain. It is shown that for the impurity model, the zero mode decays by relaxing to a nonlocal quasiconserved operator, the latter being exactly conserved when the opposite edge of the chain has no noncommuting perturbations so as to ensure perfect degeneracy of the spectrum. In the thermodynamic limit, the quasiconserved operator vanishes, and a regime is identified where the decay of the zero mode obeys Fermi's golden rule. A toy model for the decay is constructed in Krylov space and it is highlighted how Fermi's golden rule may be recovered from this toy model.

Recent experiments on nonmagnetic Weyl semimetals have seen separate bulk and surface superconductivity in Weyl semimetals, which raises the question of whether the surface Fermi arcs can support intrinsic superconductivity while the bulk stays in the normal state. A theoretical answer to this question is hindered by the absence of a well-defined surface Hamiltonian since the Fermi arcs merge with the bulk states at their endpoints. Using an alternate, Green's functions-based approach on a phenomenological model that can yield arbitrary Fermi arcs, we show—within mean-field theory—that the surface can support a standard Cooper instability while the bulk remains in the normal state. Although the surface has lower dimensionality, a higher density of states compared to the bulk allows it to have a higher mean-field superconducting transition temperature. The surface superconductivity is presumably of the Berezinskii-Kosterlitz-Thouless type.

We study the similarities and differences in the shift photocurrent contribution to the bulk photovoltaic effect between transition-metal dichalcogenide monolayers and nanotubes. Our analysis is based on density functional theory in combination with the Wannier interpolation technique for the calculation of the shift photoconductivity tensor. Our results show that for nanotube radii of practical interest, $r>60$ Å, the shift photoconductivity of a single-wall nanotube is well described by that of the monolayer. Additionally, we quantify the shift photocurrent generated under realistic experimental conditions like device geometry and absorption capabilities. We show that a typical nanotube can generate a photocurrent of around 10 nA, while the monolayer only attains a maximum of 1 nA. This enhancement is mainly due to the larger conducting cross section of a nanotube in comparison to a monolayer. Finally, we discuss our results in the context of recent experimental measurements on ${\mathrm{WS}}_2$ monolayer and nanotubes [Zhang et al., Nature (London) 570, 349 (2019)].

We investigate the role of quantum coherence and higher harmonics resulting from multiple-path interference in nonlinear thermoelectricity in a two-terminal triangular triple-dot Aharonov-Bohm (AB) interferometer. We quantify the trade-off between efficiency and power in the nonlinear regime of our simple setup comprising three noninteracting quantum dots (two connected to two biased metallic reservoirs) placed at the vertex of an equilateral triangle, and a magnetic flux $\mathrm{\Phi }$ pierces it perpendicularly. For a spatially symmetric setup, we achieve optimal efficiency and power output when the interdot tunneling strength is comparable to the dot-lead coupling, AB phase $\varphi =\pi /2$. Our analysis reveals that the presence of higher harmonics is necessary but not sufficient to achieve optimal power output. The maximal constructive interference represented by three close-packed resonance peaks of the unit transmission can enhance the power output $(P_{\text{max}}\sim 2.35\mathrm{fW})$ almost 3.5 times as compared to the case where only a single channel participates in the transport, and the corresponding efficiency is about $0.80{\eta }_c$, where ${\eta }_c$ is the Carnot efficiency. Geometric asymmetries and their effects on efficiency and power output are also investigated. An asymmetric setup characterized by the ratio of the coupling to the source and the drain terminals $\left(x\right)$ can further enhance the maximum power output $P_{\text{max}}\sim 3.85\mathrm{fW}$ for $x=1.5$ with the same efficiency as that of the symmetric case. Our investigation reveals that the output power and efficiency are optimal in the wide-band limit. The power output is significantly reduced for the narrow-band case. On the other hand, disorder effects radically reduce the performance of the heat engine.

In this study, we investigate the many-body non-Hermitian skin effect at finite temperatures in the thermodynamic limit. Our findings indicate an interesting correspondence between the non-Hermitian skin effect and a linear electric potential effect in this case. This correspondence leads to a unique distribution in non-Hermitian systems; particles in these many-body non-Hermitian systems do not inhabit the energy eigenstates of their single-body counterparts. As a result, the many-body non-Hermitian skin effect is significantly different from the single-body non-Hermitian skin effect. Specifically, for fermionic systems the non-Hermitian skin effect disrupts the original phase, leading to a real-space Fermi surface. For bosonic systems, it can direct bosons to condense in corners at a decay rate that surpasses exponential, even at high temperatures. It also triggers a remarkable phase transition, resulting in spontaneous $\text{U}\left(1\right)$ symmetry breaking. Uniquely, this does not generate a Goldstone mode, presenting a deviation from traditional expectations as per the Goldstone theorem.

A peculiar charge-density wave (CDW) phase, absent in the bulk, has been widely studied in monolayer $1T\text{−}{\mathrm{TiTe}}_2$ and newly observed in monolayer $1T\text{−}{\mathrm{ZrTe}}_2$, while its origin and physical properties remain unclear. Here, we study the distorted lattice and associated energy band renormalization for ${\mathrm{TiTe}}_2$ and ${\mathrm{ZrTe}}_2$ monolayers using first-principles calculations. Both systems are found to exhibit a soft phonon mode at the $M$ point leading to a $2\times 2$ CDW order with similar distortion pattern as in ${\mathrm{TiSe}}_2$ case. Electronic structure results with semilocal functional indicate that the CDW phases of monolayer ${\mathrm{TiTe}}_2$ and ${\mathrm{ZrTe}}_2$ maintain semimetallicity owing to their smaller lattice distortion than in the ${\mathrm{TiSe}}_2$ semiconducting CDW state. The unfolded band structure for monolayer ${\mathrm{TiTe}}_2$ reveals CDW-reconstructed features consistent with experiments, including backfolded bands from $\mathrm{\Gamma }$ to $M$ and vice versa, as well as a stronger energy gapping of the outer valence band along $\mathrm{\Gamma }\text{−}M$ due to orbital-dependent $p\text{−}d$ hybridization. We also explore the role of exchange interaction in the CDW formation. The nonlocal exchange effect enlarges the lattice distortion amplitude and causes an overcorrection of the electronic structure for monolayer ${\mathrm{TiTe}}_2$, while it barely affects the CDW distortion of monolayer ${\mathrm{ZrTe}}_2$, despite inducing a metal-semiconductor transition. Comparison of the CDW properties of monolayer ${\mathrm{TiSe}}_2, {\mathrm{TiTe}}_2$, and ${\mathrm{ZrTe}}_2$ suggests that the judgment of relative CDW strength in these systems should involve coupled electron-lattice modifications. Our work paves the way for elucidating the CDW order in two-dimensional group-IV transition-metal dichalcogenides.

Maximization of the ratio between Kitaev and residual Heisenberg interactions is a major goal in the current research on Kitaev-Heisenberg magnets. Here we investigate Kitaev-Heisenberg exchange in a recently discovered crystalline phase of $\alpha \text{−}{\mathrm{RuCl}}_3$ under pressure—it displays unusually high symmetry, with only one type of Ru-Ru links and uniform Ru-Cl-Ru bond angles of $\approx {93}^{\circ }$. Using quantum chemical calculations, we find a very small nearest-neighbor Heisenberg $J$, which yields a $K/J$ ratio between Kitaev and Heisenberg exchange as large as $\sim 100$. We also find that this is associated with vanishingly small $d$-shell trigonal splittings, i.e., minimal departure from ideal $j_{\mathrm{eff}}=1/2$ moments. This reconfirms ${\mathrm{RuCl}}_3$ as a most promising platform for materializing the much sought-after Kitaev spin-liquid phase and should stimulate further experiments under strain and pressure.

Electrons on honeycomb or pi-flux lattices obey the effective massless Dirac equation at low energies and at the neutrality point, and should suffer quantum phase transitions into various Mott insulators and superconductors at strong two-body interactions. We show that 35 out of 36 such order parameters that provide Lorentz-invariant mass gaps to Dirac fermions belong to a single irreducible tensor representation of the $SO\left(8\right)$ symmetry of the two-dimensional Dirac Hamiltonian for the spin-1/2 lattice fermions. The minimal interacting Lagrangian away from the neutrality point has the $SO\left(8\right)$ symmetry reduced to $U\left(1\right)\times SU\left(4\right)$ by finite chemical potential, and it allows only two independent interaction terms. When the Lagrangian is nearly $SO\left(8\right)$ symmetric and the ground state insulating at the neutrality point, we show it turns superconducting at the critical value of the chemical potential through a “flop” between the tensor components, by exactly solving the $SU\left(4\right)\to SU\left(N\right)$ generalization in the large-$N$ limit. A lattice Hamiltonian that may exhibit this transition, parallels with and the consequences for the Gross-Neveu model, and applicability to related electronic systems are briefly discussed.

The limitation of Fermi liquid theory to very low energies and temperatures poses a fundamental problem for describing the temperature evolution of the Kondo peak. Here Fermi liquid theory for the single impurity Anderson model is extended beyond the low-energy and low-temperature regime by means of an ansatz for the impurity self-energy based on the accurate description of the Kondo peak by the Frota function, the similarity between energy and temperature in the second-order self-energy, and by exploiting Fermi liquid conditions. Analytic expressions for the temperature dependence of the Kondo peak height and width derived from this ansatz are in excellent agreement with numerical renormalization group data for temperatures beyond the Kondo temperature. The derived expression thus allows to unambiguously determine the intrinsic Kondo peak width and Kondo temperature from finite temperature measurements of the Kondo resonance.

Recently, astronomers have reached a significant milestone on a journey of Universe exploration with more than 5400 confirmed exoplanets. Therefore determining the physical properties of minerals in the terapascal area has become an urgent mission to gain insights into exoplanetary dynamics and evolution. Herein, we develop a theoretical model to obtain a more reliable picture of the ultrahigh-pressure structural transformation in iron, which is the most prominent metal in the core of super-Earths, gas giants, and ice giants. First, we revisit the previously computed hcp-fcc boundary under extreme conditions between 3 and 7 TPa. Available ab initio data for the ground-state energy are utilized to construct the Rydberg pairwise potential for iron. On that basis, the statistical moment method is improved to calculate the total vibrational free energy without enormous computational workloads. Our analyses reveal that the widely employed quasiharmonic approximation is insufficient to capture the hcp-fcc phase-transition behaviors of iron. The primary reason is that the lack of inversion symmetry creates strong odd-order anharmonic effects, thereby enhancing the thermodynamic stability of the hcp structure. Second, we extend the modified work-heat equivalence principle to deduce the melting quantities from the Holzapfel equation-of-state parameters up to 10 TPa. Our steep melting lines accord fully with the state-of-the-art static measurements, dynamic experiments, and ab initio simulations. In particular, we observe that the melting gradient of hcp iron is always higher than the adiabatic slope of liquid iron. This difference has a profound geophysical implication for the core solidification and the magnetic-field generation of super-Earths. Finally, we perform numerical calculations for the Hugoniot and isentropic profiles. Our theoretical predictions would facilitate designing future multishock and ramp-wave studies to uncover the mystery of extrasolar worlds.

The discovery of room-temperature monolayer ferroelectrics (FEs) holds significant promise for advancing the development of nanoscale functional devices. Although the ab initio calculations have demonstrated the strain-induced ferroelectricity of two-dimensional (2D) PbTe, the structural and thermodynamic characteristics of this ferroelectric phase transition at larger temporal and spatial scales remain unexplored. Molecular dynamics (MD) is an effective tool to use to address this question. However, the lack of an appropriate force field has hindered progress. Here, we have developed an interatomic potential for 2D PbTe based on the deep potential framework, enabling MD simulations with ab initio-level accuracy to investigate the FE phase transition. Our MD results demonstrate robust ferroelectricity at room temperature in adequately strained 2D PbTe, which remains paraelectric at lower temperatures. Structural analyses indicate that the FE transitions are displacive, highlighting the strong coupling between the strain condition and the polarization state. Furthermore, we established a phase diagram of 2D PbTe in the temperature-strain space, guiding the tunable phase transition temperature with the aid of prestrains. Finally, the second-order transition nature of FE transition in 2D PbTe is observed, suggesting the potential utilization of a new room-temperature, nonhysteresis 2D ferroelectric material.

An efficient and general strategy of metadynamics (MetaD) for investigating interstitial diffusion in a crystal is proposed by exploiting crystallographic symmetry. Assuming complete ignorance of the diffusion phenomenon of interest, the three-dimensional coordinates of the interstitial atom with the periodic boundaries are chosen as the collective variables (CVs). Multiple potential hills are simultaneously deposited at all crystallographically equivalent positions on the free-energy surface (FES) defined in the CV space. As a result, the proposed multihill strategy highly accelerates atomic jumps in comparison with the single-hill strategy in conventional MetaD. The key features are that the FES estimated from the final bias potential is exactly satisfied with the symmetry of the host crystal and that all elementary processes of interstitial diffusion are obtained by the single MetaD simulation without any prior knowledge of the diffusion mechanism. The high efficiency and efficacy of the multihill strategy are demonstrated, taking the proton diffusion in barium zirconate with the cubic perovskite structure as a model case.

Electric manipulation of skyrmions in two-dimensional (2D) magnetic materials has garnered significant attention due to the potential in energy-efficient spintronic devices. In this work, using first-principles calculations and Monte Carlo simulations, we report the electric-field-tunable magnetic skyrmions in $\mathrm{Mn}{\mathrm{In}}_2{\mathrm{Te}}_4$ monolayer. By adjusting the magnetic parameters, including the Heisenberg exchange interaction, Dzyaloshinskii-Moriya interaction, and magnetic anisotropy, through applying an electric field, the formation or annihilation of skyrmions can be achieved. Our work suggests a platform for experimental realization of the electric-field-tunable magnetic skyrmions in 2D magnets.

Spin-orbit torque (SOT) driven magnetization switching, assisted by spin-transfer torque (STT), enables field-free switching in ferromagnetic nanostructures and is expected to be a writing method for next-generation spintronic nonvolatile memory. The role of STT is to shift the magnetization pointing in an in-plane direction via the SOT to a different direction and ensure the switching. Here, we study the dependence of the switching probability on the STT strength using a numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation. While a monotonic increase of the switching probability with increasing STT strength is found in a relatively weak STT region, we find an unexpected increase in the error rate in a relatively large STT current close to a critical current. Based on the statistical analysis of the magnetization dynamics and solving the LLG equation analytically, we reveal that the origin of the switching error is the presence of an inactive region in the Bloch sphere where the magnetization dynamics becomes very slow compared with conventional SOT switching. Since this region exists far away from the initial state of the magnetization, a strong STT is necessary to reach the region. Accordingly, the switching error increases in a strong STT region. We also show that the issue can be solved by reducing the time only the STT is applied and/or enhancing the SOT strength.

We present a detailed theoretical investigation of the linear and nonlinear optical response in a model system for a disordered $d$-wave superconductor. By evaluating the quasiparticle contribution (BCS response) we show that for both quantities the gap symmetry considerably changes the paradigm of the optical response as compared to the conventional $s$-wave case. For what concerns the linear response our findings agree with previous work showing that in strongly disordered $d$-wave superconductors a large fraction of uncondensed spectral weight survives below $T_c$, making the optical absorption around the gap-frequency scale almost unchanged with respect to the normal state. Our numerical results are in excellent quantitative agreement with experiments in overdoped cuprates. In the nonlinear regime we focus on the third-harmonic generation (THG), finding that, as already established for the $s$-wave case, in general a large THG is triggered by disorder-activated paramagnetic processes. However, in the $d$-wave case the BCS response is monotonously increasing in frequency, losing any signature of THG enhancement when the THz pump frequency $\omega$ matches the gap maximum $\mathrm{\Delta }$, a hallmark of previous experiments in conventional $s$-wave superconductors. Our findings, along with the mild polarization dependence of the response, provide an explanation for recent THG measurements in cuprates, setting the framework for the theoretical understanding of nonlinear effects in unconventional cuprates.

The random transverse-field Ising ferromagnet (RTFIF) is a highly disordered quantum system which contains randomness in the coupling strengths as well as in the transverse-field strengths. In one dimension, the critical properties are governed by an infinite-randomness fixed point (IRFP), and renormalization-group studies argue that the two-dimensional (2D) model is also governed by an IRFP. However, even the location of the critical point remains unsettled among quantum Monte Carlo (QMC) studies. In this work, we perform extensive QMC simulations to locate the quantum critical point and attempt a finite-size scaling analysis to observe the critical behavior. We estimate the critical field strength of the 2D RTFIF as ${\mathrm{\Gamma }}_c=7.52\left(2\right)$, together with critical exponents such as $\beta =1.5\left(3\right), \nu =1.6\left(3\right)$, and $z=3.3\left(3\right)$ or $\psi =0.50\left(3\right)$. We have also considered the McCoy-Wu model, which has randomness in the ferromagnetic coupling strengths but not in the transverse-field strength. Our QMC calculation shows that the critical behavior of the 2D McCoy-Wu model is closer to that of the 2D transverse-field Ising spin glass than to that of the 2D RTFIF. These numerical findings enhance our understanding of disordered 2D quantum systems.

We experimentally demonstrate the coherent propagation of magnon polarons, the hybridized excitations formed by the coupling of spin waves and Rayleigh/Love surface acoustic waves, in a heterostructure consisting of ferroelectric ${\mathrm{BaTiO}}_3$ and ferromagnetic ${\mathrm{La}}_{0.67}{\mathrm{Sr}}_{0.33}{\mathrm{MnO}}_3$. By systematically adjusting external magnetic field strengths and angles with respect to the wave vector, the wavelengths of coherent magnon polarons can be precisely controlled and maintained over distances of up to $80\mu \mathrm{m}$. Their excitation was obtained using nanoscale interdigital transducer antennas. Our theoretical model, based on effective interlayer magnetoelastic coupling, reproduces the experimental transmission spectra, in particular the anticrossing features, allowing us to estimate the magnetoelastic coupling strength in this system to be of the order of $2\times {10}^5\mathrm{J}/{\mathrm{m}}^3$. Our findings provide valuable insights into the coherent properties of magnon polarons and open up possibilities for the design of functional devices in the fields of spintronics and magnonics.

In previous theoretical studies of phonon-mediated superconductors, the electron-phonon coupling is treated by solving the Migdal-Eliashberg equations under the bare vertex approximation, whereas the effect of Coulomb repulsion is incorporated by introducing one single pseudopotential parameter. These two approximations become unreliable in low carrier density superconductors in which the vertex corrections are not small and the Coulomb interaction is poorly screened. Here, we go beyond these two approximations and employ the Dyson-Schwinger equation approach to handle the interplay of the electron-phonon interaction and Coulomb interaction in a self-consistent way. We first derive the exact Dyson-Schwinger integral equation of the full electron propagator. Such an equation contains several unknown single-particle propagators and fermion-boson vertex functions, and thus seems to be intractable. To solve this difficulty, we further derive a number of identities satisfied by all the relevant propagators and vertex functions and then use these identities to show that the exact Dyson-Schwinger equation of the electron propagator is actually self-closed. This self-closed equation takes into account not only all the vertex corrections, but also the mutual influence between electron-phonon interaction and Coulomb interaction. Solving it by using proper numerical methods leads to the superconducting temperature $T_c$ and other quantities. As an application of the approach, we compute the $T_c$ of the interfacial superconductivity realized in the one-unit-cell $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$ system. We find that $T_c$ can be strongly influenced by the vertex corrections and the competition between phonon-mediated attraction and Coulomb repulsion.

Motivated by the recent discovery of superconductivity in the kagome ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{K}, \mathrm{Rb}, \mathrm{Cs})$ metals, we perform a theoretical study of the symmetry-allowed superconducting orders on the two-dimensional kagome lattice with focus on their response to disorder. We uncover a qualitative difference between the robustness of intraband spin-singlet (even-parity) and spin-triplet (odd-parity) unconventional superconductivity to atomic-scale nonmagnetic disorder. Due to the particular sublattice character of the electronic states on the kagome lattice, disorder in spin-singlet superconducting phases is only weakly pair-breaking despite the fact that the gap structure features sign changes. By contrast, spin-triplet condensates remain fragile to disorder on the kagome lattice. We demonstrate these effects in terms of the absence of impurity bound states and an associated weak disorder-induced $T_c$ suppression for spin-singlet order. We also discuss the consequences for quasiparticle interference and their inherent tendency for momentum-space anisotropy due to sublattice effects on the kagome lattice. For unconventional kagome superconductors, our results imply that any allowed spin-singlet order, including for example $d+id$-wave superconductivity, exhibits a disorder-response qualitatively similar to standard conventional $s$-wave superconductors.

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest nontrivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($\omega \sim -i{k}^4$) characteristic of “fracton hydrodynamics” with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($\omega \sim \pm k^2-i{k}^4$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which, depending on parameters, may be either purely diffusive ($\omega \sim -i{k}^2$) or quadratically propagating and quadratically relaxing ($\omega \sim \pm k^2-i{k}^2$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.