In this paper, we employ the generalized Bloch theory to rediscover the generalized Brillouin zone theory and follow this way to obtain the Green's function of the non-Hermitian system. We focus on a classical chiral model and give the exact expression of the Green's function for a finite-size system and the formal expression of the Green's function suitable for infinite size. Based on these results, we further derive the correlation matrix and validate it numerically against direct calculations for a system of size 40. The numerical results show the accuracy of our exact expression and the high fidelity of our formal expression.

As a nondestructive regulation method, applying external electric field to regulate thermal transport has become one of the most effective reversible strategies. However, to date, using external electric fields to regulate thermal transport in van der Waals (vdW) heterostructures has been rarely reported, despite the great significance to engineering heat-transfer applications in electronics. Herein, based on the state-of-the-art first-principles calculations, we investigate the external electric field engineered thermal transport in BAs/MoSSe vdW twins heterostructures (i.e., BAs/MoSSe-I and BAs/MoSSe-II), which are constructed from monolayer BAs and Janus MoSSe. The thermal conductivity of different stacked BAs/MoSSe shows similar response to positive electric field. However, with negative electric field applied, the thermal conductivity of BAs/MoSSe-II is 22.4 times higher than that of BAs/MoSSe-I under the strength of $-0.2\mathrm{V}{\AA }^{-1}$. Detailed analysis reveals that the renormalization of phonons driven by the electric field mainly affects the phonon anharmonicity, which is induced by the electric field enhanced or weakened interlayer interaction, finally leading to the different response of the thermal conductivity for the two stacked BAs/MoSSe. The highly effective regulation of thermal transport in vdW heterostructures driven by the external electric fields as shown in this study is valuable for physical and engineering applications in electronics, thermoelectric, and thermal management.

Van der Waals multiferroic tunnel junctions (vdW-MFTJs) with multiple nonvolatile resistive states are highly suitable for new physics and next-generation storage electronics. However, currently reported vdW-MFTJs are based on two types of materials, i.e., vdW ferromagnetic and ferroelectric materials, forming a multiferroic system. This undoubtedly introduces additional interfaces, increasing the complexity of experimental preparation. Herein, we engineer vdW intrinsic MFTJs utilizing bilayer ${\mathrm{VS}}_2$. By employing the nonequilibrium Green's function combined with density functional theory, we systematically investigate the influence of three types of electrodes (including non-vdW pure metal Ag/Au, vdW metallic $1\mathrm{T}\text{−}{\mathrm{MoS}}_2/2\mathrm{H}\text{−}{\mathrm{PtTe}}_2$, and vdW ferromagnetic metallic ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2/{\mathrm{Fe}}_3{\mathrm{GeTe}}_2$) on the electronic transport properties of ${\mathrm{VS}}_2$-based intrinsic MFTJs. We demonstrate that these MFTJs manifest a giant electrode-dependent electronic transport characteristic effect. Comprehensively comparing these electrode pairs, the ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2/{\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ electrode combination exhibits optimal transport properties, the maximum TMR (TER) can reach 10949% (69%) and the minimum resistance-area product (RA) is 0.45 $\mathrm{\Omega }$ $\mu {\mathrm{m}}^2$, as well as the perfect spin filtering and negative differential resistance effects. More intriguingly, TMR (TER) can be further enhanced to 34 000% (380%) by applying an external bias voltage, while RA can be reduced to 0.16 $\mathrm{\Omega }$ $\mu {\mathrm{m}}^2$ under the influence of biaxial stress. Additionally, considering the impact of surface dangling bonds of pure metal electrodes on the multiferroicity of ${\mathrm{VS}}_2$, we introduce a graphene interlayer between them. This strategy effectively preserves the intrinsic properties of ${\mathrm{VS}}_2$ and significantly amplifies the TMR (TER) of the MFTJ composed of Ag/Au electrode pairs by an order of magnitude. Our proposed concept of designing vdW-MFTJs using intrinsic multiferroic materials points towards new avenues in experimental exploration.

Motivated by the recent reports of high-$T_c$ superconductivity in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under pressure, we analyzed theoretically the magnetic excitations in the normal and the superconducting state in this compound, which can be measured by inelastic neutron scattering or resonant inelastic x-ray scattering. We show that the bilayer structure of the spin response allows us to elucidate the role of the interlayer interaction and the nature of the Cooper pairing in a very efficient way. In particular, we demonstrate the key difference between the potential $s_{\pm }$- and $d$-wave gaps, proposed recently, by comparing the corresponding response in the even and odd channels of the spin susceptibility. We show that the mostly interlayer driven bonding-antibonding $s_{\pm }$ Cooper pairing produces a single large spin resonance peak in the odd channel only near the $X$ point, whereas spin resonances in both the odd and the even channel are predicted for the $d$-wave scenario.

Highly entangled excitations such as Majorana fermions of Kitaev quantum spin liquids have been proposed to be utilized for future quantum science and technology, and a deeper understanding of such excitations has been strongly desired. Here we demonstrate that Majorana fermion's mass and associated topological quantum phase transitions in the Kitaev quantum spin liquids may be manipulated by using electric fields in sharp contrast to the common belief that an insulator is inert under weak electric fields due to charge energy gaps. Using general symmetry analysis with perturbation and exact diagonalization, we uncover the universal phase diagrams with electric and magnetic fields. We also provide distinctive experimental signatures to identify Kitaev quantum spin liquids with electric fields, especially in connection with the candidate materials such as $\alpha \text{−}{\mathrm{RuCl}}_3$.

Quantum anomalous Hall (QAH) insulators exhibit chiral edge channels characterized by vanishing longitudinal conductance and quantized Hall conductance of ${Ce}^2$/$h$, wherein the Chern number C is an integer equal to the number of the parallel chiral edge channels. These chiral edge channels conduct dissipationless transport in QAH insulators, making them pivotal for applications in low-consumption electronics and topological quantum computing. While the QAH effect with multiple chiral edge channels (i.e., C > 1) has been demonstrated in multilayers consisting of magnetic topological insulators and normal insulators, the channel number remains fixed for a given sample. Here, we unveil the tunability of the number of chiral edge channels within a single QAH insulator device. By tuning the magnetization of individual layers within the multilayer system, Chern insulating states with different Chern numbers are unveiled. The tunable Chern number was corroborated by our theoretical calculations. Furthermore, we conducted layer-dependent calculations to elucidate the contribution of the Chern number from different layers in the multilayer. Our findings demonstrate an extra degree of freedom in manipulating the chiral edge channels in QAH insulators. This tunability offers an extra dimension for the implementation of the QAH-based multichannel dissipationless transport.

In this work, we establish a theoretical analysis of the emergence of layer-contrasted Nernst response perpendicular to the direction of the temperature gradient in twisted moiré layers, called layer Nernst effect (LNE). This phenomenon arises from the trigonal warping of the Fermi surface along with a layer-contrasted pseudomagnetic field. Interestingly, the Fermi surface's warping explicitly breaks intravalley inversion symmetry, which leads to an imbalance between left- and right-moving carriers, thus resulting in a nonvanishing LNE. We then validate our theoretical scheme by applying it to twisted bilayer graphene (TBG). Importantly, we find that the LNE coefficient in TBG can reach values as high as ${10}^3$ $\mathrm{A}/(\mathrm{m}·\mathrm{K})$, surpassing those of previously known materials by at least one order of magnitude. These results provide a theoretical foundation for utilizing TBG and other twisted moiré layers as promising platforms to explore layer caloritronics and develop thermoelectric devices.

Progress toward a first-principles theory of plasticity and work hardening is currently impeded by an insufficient description of dislocation kinetics, that is, of the dynamic effect of driving forces in a given dislocation theory. Current continuum theories of dislocation kinetics are often incapable of treating the short-range interaction of dislocations. This work presents a kinetic theory of continuum dislocation dynamics in a vector density framework which takes into account the short-range interactions by means of suitably defined correlation functions. The weak line bundle ensemble of dislocations is defined, whereby the treatment of dislocations by a vector density is justified. It is then found by direct averaging of the dislocation transport equation that additional driving forces arise which are dependent on the dislocation correlations. A combination of spatial coarse graining and statistical averaging of discrete dislocation systems is then used to evaluate the various classes of tensorial dislocation correlations which arise in the line bundle kinetic theory. A chiral classification of slip-system interactions in face-centered-cubic crystals is introduced in order to define proper and improper rotations by which correlation functions corresponding to six interaction classifications can be evaluated. The full set of these six dislocation correlations are evaluated from discrete data. Only the self-correlations (for densities of like slip system) are found to be highly anisotropic. All six classes of correlation functions are found to be of moderate range, decaying within two to four times the coarse-graining distance. The correlations corresponding to the coplanar interactions are found to be negligible. Implications of the evaluated correlations for the implementation of vector density continuum dislocation dynamics are discussed, especially in terms of an additional correlation component of the driving force and a gesture toward a coarse-grained dislocation mobility.

Lead zirconate titanate $\left(\mathrm{PbZ}{\mathrm{r}}_{1-x}\mathrm{T}{\mathrm{i}}_x{\mathrm{O}}_3,\mathrm{PZT}\right)$ exhibits excellent piezoelectric properties in the morphotropic phase boundary (MPB) region of its temperature-composition phase diagram. However, the microscopic origin of its high piezoelectric response remains controversial. Here, we develop a machine-learning-based deep potential (DP) model of PZT using the training data set from first-principles density functional theory calculations. Based on DP-assisted large-scale atomic simulations, we reproduce the temperature-composition phase diagram of PZT, in good agreement with the experiment except for the absence of structural transition from R3c to R3m. We find that the rhombohedral phase maintains R3c symmetry with slight oxygen octahedral tilting with increase of temperature, instead of exhibiting R3m symmetry. This discrepancy could trace back to the lack of experimental measurements to identify such slight octahedral tilting. More importantly, we clarify the atomic-level feature of PZT at the MPB, which exhibits the competing coupling of ferroelectric nanodomains with various polarization orientations. The high piezoelectric response is driven by the polarization rotation of nanodomains induced by an external electric field.

The bismuth halide ${\mathrm{Bi}}_4{\mathrm{I}}_4$ undergoes a structural transition around $T_P\sim 300\mathrm{K}$, which separates a high-temperature $\beta$ phase ($T>T_P$) from a low-temperature $\alpha$ phase ($T<T_P$). $\alpha$ and $\beta$ phases are suggested to host electronic band structures with distinct topological classifications. Rapid quenching was reported to stabilize a metastable $\beta \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ at $T<T_P$, making possible a comparative study of the physical properties of the two phases in the same low-temperature range. In this work, we present a structural investigation of ${\mathrm{Bi}}_4{\mathrm{I}}_4$ before and after quenching together with electrical resistivity measurements. We found that rapid cooling does not consistently lead to a metastable $\beta \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$, and a quick transition to $\alpha \text{−}{\mathrm{Bi}}_4{\mathrm{I}}_4$ is observed. As a result, the comparison of putative signatures of different topologies attributed to a specific structural phase should be carefully considered. The observed phase instability is accompanied by an increase in iodine vacancies and by a change in the temperature dependence of electrical resistivity, pointing to native defects as a possible origin of our finding. Density functional theory (DFT) calculations support the scenario that iodine vacancies, together with bismuth antisites and interstitials are among the defects that are more likely to occur in ${\mathrm{Bi}}_4{\mathrm{I}}_4$ during the growth.

We study a Lindbladian generalization of the Anderson model of localization that describes disordered free fermions coupled to a disordered environment. From finite-size scaling of both eigenvalue statistics and the participation ratio, we identify localization transitions in both the non-Hermitian Lindbladian spectrum, which governs transient relaxation dynamics, and the Hermitian stationary state density matrix. These localization transitions occur at different critical values of the Hamiltonian and dissipative disorder strength, implying the existence of unconventional phases with a mixture of localized and delocalized features. We find that this phenomenon is robust to changes in the value of the dissipative spectral gap.

We study the fate of a two-dimensional quadratic band crossing topological phases under a one-dimensional quasiperiodic modulation. By employing numerically exact methods, we fully characterize the phase diagram of the model in terms of spectral, localization, and topological properties. Unlike in the presence of regular disorder, the quadratic band crossing is stable to the application of the quasiperiodic potential, and most of the topological phase transitions occur through a gap closing and reopening mechanism, as in the homogeneous case. For sufficiently high quasiperiodic potential, the quadratic band crossing point splits into Dirac cones, enabling transitions into gapped phases with Chern numbers $C=\pm 1$, which are absent in the homogeneous limit. This behavior stands in sharp contrast to the disordered case, where gapless $C=\pm 1$ phases can arise by perturbing the band crossing with any amount of disorder. In the quasiperiodic case, we find that the $C=\pm 1$ phases can become gapless only for higher potential strength. Only in this regime do the subsequent quasiperiodic-induced topological transitions into the trivial phase mirror the well-known “levitation and annihilation” mechanism in the disordered case.

Magnetic tunnel junctions (MTJs) are key components of spintronic devices, such as magnetic random-access memories. Normally, MTJs consist of two ferromagnetic (FM) electrodes separated by an insulating barrier layer. Their key functional property is tunneling magnetoresistance (TMR), which is a change in MTJ's resistance when magnetization of the two electrodes alters from parallel to antiparallel. Here, we demonstrate that TMR can occur in MTJs with a single FM electrode, provided that the counterelectrode is an antiferromagnetic (AFM) metal that supports a spin-split band structure and/or a Néel spin current. Using $\mathrm{Ru}{\mathrm{O}}_2$ as a representative example of such antiferromagnet and $\mathrm{Cr}{\mathrm{O}}_2$ as a FM metal, we design all-rutile $\mathrm{Ru}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2/\mathrm{Cr}{\mathrm{O}}_2$ MTJs to reveal a nonvanishing TMR. Our first-principles calculations predict that magnetization reversal in $\mathrm{Cr}{\mathrm{O}}_2$ significantly changes conductance of the MTJs stacked in the (110) or (001) planes. The predicted giant TMR effect of about 1000% in the (110)-oriented MTJs stems from spin-dependent conduction channels in $\mathrm{Cr}{\mathrm{O}}_2$ (110) and $\mathrm{Ru}{\mathrm{O}}_2$ (110), whose matching alters with $\mathrm{Cr}{\mathrm{O}}_2$ magnetization orientation, while TMR in the (001)-oriented MTJs originates from the Néel spin currents and different effective $\mathrm{Ti}{\mathrm{O}}_2$ barrier thickness for two magnetic sublattices that can be engineered by the alternating deposition of $\mathrm{Ti}{\mathrm{O}}_2$ and $\mathrm{Cr}{\mathrm{O}}_2$ monolayers. Our results demonstrate a possibility of a sizable TMR in MTJs with a single FM electrode and offer a practical test for using the antiferromagnet $\mathrm{Ru}{\mathrm{O}}_2$ in functional spintronic devices.

The van der Waals (vdW) ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ (FGT) has recently attracted much attention due to its fruitful physical phenomena. In this paper, by varying the thickness of FGT nanoflakes, the relationship between anomalous Hall conductivity (AHC) ${\sigma }_{\text{AH}}$ and the sheet electric conductivity ${\sigma }_{xx}$ in FGT is found to follow ${\sigma }_{\text{AH}}\propto {\sigma }_{xx}^{\gamma }$, where $\gamma$ varies from 1.4 to 2.2 as the temperature increases from 2 K to the Curie temperature of 200 K. The scaling relation is found to be near the transition between the intrinsic and dirty regimes, suggesting a dual origin involving the intrinsic Berry curvature and the strong scattering. Moreover, an upturn of the sheet resistivity <20 K is caused by the electron-electron interaction due to Fe vacancies and the quantum correction to the AHC is negligible. This paper is beneficial to the further understanding of the physics of the AHC in vdW ferromagnets.

The recent discovery of high-temperature superconductivity in hydrogen-based compounds under pressure has fueled the hope for the exploration of hydrides with high critical temperatures ($T_c$). In this work, we systematically investigated pressure-stabilized ternary C-Se-H and C-Te-H compounds using the state-of-the-art structure prediction approach in combination with first-principles calculations. As a result, our simulations identified two cubic phases ($\mathrm{CSe}{\mathrm{H}}_6$ and ${\mathrm{C}}_2\mathrm{Te}{\mathrm{H}}_8$) with a metastable stability feature. $Fd\text{−}3m$-structured $\mathrm{CSe}{\mathrm{H}}_6$ adopted a diamond-type host Se framework with an embedded guest $\mathrm{C}{\mathrm{H}}_6$ covalent octahedron, and ${\mathrm{C}}_2\mathrm{Te}{\mathrm{H}}_8$ with $Fm\text{−}3m$ symmetry adopted a face-centered cubic arrangement of ${\mathrm{H}}_8$ cubes, which are interlinked by a molecular unit $\mathrm{C}{\mathrm{H}}_4$ tetrahedron. Electron-phonon coupling simulations reveal that $\mathrm{CSe}{\mathrm{H}}_6$ has high-temperature superconductivity with a $T_c$ of 80.6 K at 250 GPa. This high superconductivity could be attributed to the fact that the C $2p$, Se $4p$, and H $1s$ electron states near the Fermi energy couple with high-frequency H-associated phonons. Furthermore, ${\mathrm{C}}_2\mathrm{Te}{\mathrm{H}}_8$ was estimated to have an even higher $T_c$ of 151.4 K at 300 GPa due to the large average phonon frequency and the strong coupling between C- and H-derived optical phonons and electrons (C $2p$, Te $5p$, and H $1s$) near the Fermi level. The present results shed light on the future exploration of high-temperature superconductivity among multinary hydrides.

We investigate the impacts of the quantum geometry of Bloch states, specifically through the band-resolved quantum-metric tensor, on Cooper pairing and flat-band superconductivity in a three-dimensional pyrochlore-Hubbard model. First we analyze the low-lying two-body spectrum exactly, and show that the pairing order parameter is uniform in this four-band lattice. This allows us to establish direct relations between the superfluid weight of a multiband superconductor and (i) the effective mass of the lowest-lying two-body branch at zero temperature, (ii) the kinetic coefficient of the Ginzburg-Landau theory in proximity to the critical temperature, and (iii) the velocity of the low-energy Goldstone modes at zero temperature. Furthermore, we perform a comprehensive numerical analysis of the superfluid weight and Goldstone modes, exploring both their conventional and geometric components at zero temperature.

Phonon-driven $s$-wave superconductivity is fundamentally antagonistic to uniform magnetism, and field-induced suppression of the critical temperature is one of its canonical signatures. Examples of the opposite are unique and require fortuitous cancellations and very fine parameter tuning. The recently discovered Ising superconductors violate this rule: An external magnetic field applied in a certain direction does not suppress superconductivity in an ideal, impurity-free material. We propose a simple and experimentally accessible system where the effects of spin-conserving and spin-flip scattering can be studied in a controlled way, namely ${\mathrm{NbSe}}_2$ monolayers dosed with magnetic $3d$ atoms. We predict that the critical temperature is slightly increased by an in-plane magnetic field in ${\mathrm{NbSe}}_2$ dosed with Cr. Due to the band spin splitting, magnetic spin-flip scattering requires a finite momentum transfer, while spin-conserving scattering does not. If the magnetic anisotropy is easy-axis, an in-plane field reorients the impurity spins and transforms spin-conserving scattering into spin-flip. The critical temperature is enhanced if the induced magnetization of ${\mathrm{NbSe}}_2$ has a substantial long-range component, as is the case for Cr ions.

The mechanical properties of materials at high pressures determine their applications in extreme conditions. Vanadium, a rare-earth metal, exhibits abnormal strength softening at high pressures. However, the mechanism of this remarkable softening is still open to debate up to now. In the present study, the dislocation density, elastic modulus, and lattice distortion effects on the strength of vanadium at high pressure are investigated systematically. The in situ dislocation density of vanadium as a function of pressure is measured. It is demonstrated that the softening mechanism of vanadium is multifaceted: the elastic modulus softening, the anomalous decrease of dislocation density, and the body-centered-cubic lattice distortion all contribute to the strength softening of vanadium. Among these factors, the elastic modulus softening is the dominant one and the abrupt drop of dislocation density has a moderate influence, while the body-centered-cubic lattice distortion has an inappreciable contribution to the anomalous strength softening of vanadium. This work highlights the general factors that affect the strengthening and softening mechanism of materials under extreme conditions.

In a statistical physics context, inverse problems consist of determining microscopic interactions such that a system reaches a predefined collective state. A complex collective state may be prescribed by specifying the overlap distribution between microscopic configurations, a notion originally introduced in the context of disordered systems like spin glasses. We show that in spite of the absence of disorder, nonequilibrium spin models exhibiting spontaneous magnetization oscillations provide a benchmark to prescribe a nontrivial overlap distribution with continuous support, qualitatively analogous to the ones found in disordered systems with full replica symmetry breaking. The overlap distribution can be explicitly tailored to take a broad range of predefined shapes by monitoring the spin dynamics. The presence of a nontrivial overlap distribution is traced back to an average over infinitely many pure states, a feature shared with spin glasses, although the structure of pure states is here much simpler.

We study the metallic phase of the Anderson model in a random-regular graph, specifically the degree of ergodicity of the high-energy wave functions. We use the multifractal formalism to analyze numerical data for unprecedented large system sizes, obtaining a set of correlated volumes $N_q$ which control the finite-size effects of the wave function $q$ moment. Those volumes grow very fast, $ln[ln\left(N_q\right)]\sim W,$ with disorder strength but show no tendency to diverge, at least in an intermediate metallic regime. Close to the Anderson transitions, we characterize the crossover to system sizes much smaller than the first correlated volume. Once this crossover has taken place, we obtain evidence of a scaling in which the derivative of the first fractal dimension behaves critically with an exponent $\nu =1.$