Utilizing a tunneling spectroscopy approach based on the energy-dependent inverse decay length, our research unveils distinct dispersion characteristics of germanene's topological edge states. We observe a pronounced variance in Fermi velocity, with armchair edges exhibiting a velocity higher than zigzag edges by about an order of magnitude. This difference highlights the influence of edge termination on the energy-momentum dispersion relation of one-dimensional topological edge states in two-dimensional topological insulators, aligning with the theoretical framework of a Kane-Mele topological insulator.

We study the time evolution of the Rényi entanglement entropies following a quantum quench in a two-dimensional (2D) free fermion system. By employing dimensional reduction, we effectively transform the 2D problem into decoupled chains, a technique applicable when the system exhibits translational invariance in one direction. Various initial configurations are examined, revealing that the behavior of entanglement entropies can often be explained by adapting the one-dimensional quasiparticle picture. However, intriguingly, for specific initial states the entanglement entropy saturates to a finite value without the reduced density matrix converging to a stationary state. We discuss the conditions necessary for a stationary state to exist and delve into the necessary modifications to the quasiparticle picture when such a state is absent.

Understanding the interplay of properties in two-dimensional (2D) multiferroic materials is of paramount importance for crafting the blueprint of cutting-edge functional devices in the next generation. In the present study, we report a family of stable multiferroics $\mathrm{Al}\mathit{XY}$ ($X=\mathrm{S},\mathrm{Se}$; $Y=\mathrm{Cl},\mathrm{Br},\mathrm{I}$) with the coexistence of ferroelectricity and ferroelasticity, using density functional theory (DFT) calculations. The $\mathrm{Al}\mathit{XY}$ monolayers (MLs) exhibit large in-plane ferroelectric polarization ($P_y$) ranging from 148 to 177 pC/m with a moderate switching barrier of 0.102–0.192 eV/atom. The polarization in these MLs owes its origin to the repositioning of Al atoms, actuated by soft $B_{2u}$ phonon mode in the paraelectric phase (Pmmn). These MLs exhibit robust ferroelasticity with a large reversible strain of 38%–45.1% and moderate switching barriers of 0.175–0.213/eV/atom. The ferroelectric and ferroelastic (FA) phases differ in the electric polarization direction by ${90}^{\circ }$ rotation. Besides a strong anisotropy in mechanical properties, in-plane piezoelectricity and carrier mobilities are observed in the $\mathrm{Al}\mathit{XY}$ MLs. Moreover, FA switching provides a highly effective way for finely tuning these anisotropic properties of $\mathrm{Al}\mathit{XY}$ MLs. Complementing these findings, we devised an empirical predictive model built on descriptors derived from linear regression analysis, linking atomic polarizability, Bader charge, lattice constant ($b$), layer thickness ($h$), bandgap, and effective mass of electron in order to estimate polarization ($P_y$) and in-plane piezoelectric constants ($d_{22},d_{21}$) of $\mathrm{Al}\mathit{XY}$ MLs, which is in excellent agreement ($R^2=0.95-0.98$) with results obtained from DFT.

The conductance at the band edges of one-dimensional fermionic wires, with $N$ sites, has been shown to have subdiffusive $(1/N^2)$ behavior. We investigate this issue in two-dimensional fermionic wires described by a hopping model on an $N_x\times N_y$ rectangular lattice comprised of vertical chains with a Hermitian intrachain and interchain hopping matrices given by $H_0$ and $H_1$, respectively. We study particle transport using the nonequilibrium Green's function formalism, and we show that the asymptotic behavior of the conductance, $T\left(\omega \right)$, at the Fermi level $\omega$, is controlled by the spectrum of a dimensionless matrix $A\left(\omega \right)=(-\omega +H_0)H_1^{-1}$. This gives three simple conditions on the spectrum of $A\left(\omega \right)$ for observing ballistic, subdiffusive, and exponentially decaying $T\left(\omega \right)$ with respect to $N_x$. We show that certain eigenvalues of $A\left(\omega \right)$ give rise to subdiffusive contributions in the conductance, and correspond to the band edges of the isolated wire. We demonstrate that the condition for observing the subdiffusive behavior can be satisfied if $A\left(\omega \right)$ has nontrivial topology. In that case, a transition from ballistic behavior to subdiffusive behavior of the conductance is observed as the hopping parameters are tuned within the topological regime. We argue that at the transition point, different behaviors of the conductance can arise as the trivial bulk bands of $A\left(\omega \right)$ also contribute subdiffusively. We illustrate our findings in a simple model by numerically computing the variation of the conductance with $N_x$. Our numerical results indicate a different subdiffusive behavior ($1/N_x^3$) of the conductance at the transition point. We find the numerical results to be in good agreement with the theoretical predictions.

Quantum computing demands innovative approaches for realizing qubits, and one promising avenue involves leveraging gated hybridized van der Waals (vdW) vertical heterostructures, referred to as vdW qubits. The two-level system that characterizes the vdW qubit comes from the layer-dependent orbital character of the charge carrier. This paper investigates the potential of gated vdW heterostructures for quantum computing. We study how gate fields affect the orbital composition of bands, enabling spatial superposition of electrons across layers of two-dimensional materials. Our ab initio calculations assess 20 transition metal dichalcogenides, identifying layers with slight energy offsets as vdW qubit candidates. Our investigation extends to the heterostructures formed based on the layered materials meeting these criteria. To simulate these qubits within large quantum circuits efficiently, we employ the tight-binding approach with maximally localized Wannier functions, validated against full ab initio calculations. At zero field, we confirm the existence of highly hybridized states that manifest as a qubit state exhibiting an approximately equal distribution between $|0\rangle$ and $|1\rangle$. The electric field application serves as a modulator for adjusting the contribution of these states. This phenomenon is general and is explored in the context of four distinct heterostructures. In addition, our study identified 222 possible combinations matching different layers on the conduction or the valence as promising host heterostructures for implementing vdW qubits.

Here we study nonmonotonic features which appear both in magnetoresistivity and anomalous Hall resistivity during the simple magnetization process, by systematically measuring type-II magnetic Weyl semimetal ${\mathrm{EuCd}}_2{\mathrm{Sb}}_2$ films over a wide carrier density range. We find that a positive magnetoresistivity hump can be explained as manifestation of a field-linear term in the generalized magnetoconductivity formula including the Berry curvature. As also confirmed by model calculation, the term can be negative and pronounced near the Weyl point energy in the case that the Weyl cones are heavily tilted. Our findings demonstrate extensive effects of the Berry curvature on various magnetotransport in magnetic Weyl semimetals beyond the anomalous Hall effect.

In x-ray photoelectron spectroscopy (XPS), the injected hole interacts with the electronic polarization cloud induced by the hole itself, ultimately resulting in a lower binding energy. Such a polarization effect can shift the core-level energy by more than 1 eV, as shown here by embedded many-body perturbation theory for the paradigmatic case of noble-gas clusters made of Ar, Kr, or Xe. The polarization energy is almost identical for the different core orbitals of a given atom, but it strongly depends on the position of the ionized atom in the cluster. An analytical formula is derived from classical continuum electrostatics, providing an effective and accurate description of polarization effects, which permits to achieve an excellent agreement with available experiments on noble-gas clusters at a modest computational cost. Moreover, the analytical formula is transferable to other insulating systems, as demonstrated by carbon $1s$ in the diamond cluster. Electronic polarization provides a crucial contribution to the core-level absolute energies and chemical shifts.

Due to the interplay of multicomponent order parameters [e.g., a twisted bilayer superconductor with interlayer Josephson coupling or a frustrated $(n\ge 3)$-band superconductor], a superconductor can possess a $\text{U}\left(1\right)\times {\mathbb{Z}}_2$ symmetry, corresponding to the superconducting $T_c$ and time-reversal symmetry breaking transition $T_{\text{TRSB}}$, respectively. It was then conjectured that in this class of Hamiltonians, there exists a vast parameter regime $\mathcal{O}$ such that the system exhibits vestigial TRSB, i.e., $T_{\text{TRSB}}>T_c$, while at the boundary $\partial \mathcal{O}$, the system possesses a single phase transition $T_{\text{TRSB}}=T_c$. In this paper, we provide evidence towards this conjecture by mathematically eliminating the possibility of a floating phase, i.e., $T_{\text{TRSB}}<T_c$, for the strong coupling regime. More specifically, we prove that the correlation functions of $U\left(1\right)$ spins are bounded above by that of ${\mathbb{Z}}_2$ spins for all temperatures and lattice structures (e.g., ${\mathbb{Z}}^d$ for all $d$). In particular, this guarantees the existence of high-$T_c$ TRSB (and consequently topological) superconductivity in a large class of Hamiltonians. Note that the same property can also be proven for a certain parameter regime $(\mathrm{\Delta }\ge 4/5)$ of the generalized XY model on any lattice structure, despite belonging to an entirely distinct class of $\text{U}\left(1\right)\times {\mathbb{Z}}_2$ Hamiltonians.

We undertake a theoretical analysis to probe the Kerr spectrum within the superconducting phase of strontium ruthenate, where the Kerr rotation experiments demonstrate the existence of a superconducting state with broken time-reversal symmetry. We find that spin-orbit coupling changes the hybridization along the Fermi surface's diagonal zone mainly affects Hall transport. We show that the dominant Hall response arises mainly from the quasi-1D orbitals $d_{yz}$ and $d_{xz}$, linked to their hybridization, while other contributions are negligible. This shows that breaking of time-reversal symmetry of quasi-1D orbitals can account for the existence of the Kerr angle, irrespective of the order symmetry specific to the $d_{xy}$ orbital. Moreover, the optical Hall conductivity and Kerr angle estimated for the hypothesized superconducting orders also closely match the experimental findings, providing important insight on the role of the spin-orbit coupling, hybridization, and emergent order.

In this paper, we use a perturbation strategy to show that the band tails in the density of states (DOS) distribution of amorphous semiconductors form due to the existence of excess delocalized charges. These charges satisfy a Gaussian distribution with a mean of zero and vary slowly in space due to the short- and medium-range order of amorphous materials. The charges exist due to the bond angle and bond length distortion. They induce an extra potential energy distribution that leads to energy band fluctuation in the energy-space diagram and consequently gives rise to localized states. A $150\times 150\times 7.5$ nm large-scale finite-element excess charge model for hydrogenated amorphous silicon ($a$-Si:H) is developed using a moving average smoothing that filters a Gaussian array of random charge values. Thanks to the analytical and computational simplicity of the theory in this paper (compared with conventional approaches considering atomistic details and complex electron-electron interactions), this large-scale model is calculated in only 90 s and reproduces the typical exponential and linear features found in the conduction band tail of $a$-Si:H and other amorphous semiconductors. Through a satisfactory fitting to experimental $a$-Si:H DOS data in the literature, model parameters are semiquantitatively determined. Unlike previous analytical and computational efforts, this large-scale model is physically unambiguous, computationally tractable, and satisfactorily accurate. The large-scale modeling capability allows reliable insights into the geometric features of localized and extended states, which are visualized in a nonschematic manner. This further leads to reinvestigations of several established concepts and conclusions. First, calculations in this paper challenge the description that the wave function envelope of a localized state decays away from its center in an exponential manner and that the spread of this exponential decay varies with energy in a power-law manner. Second, impurity states and/or extended states are critical to enable band tail hopping. Third, low-energy states are spatially included inside high-energy states, so the existing concept of average spatial separation of localized states is meaningless. Fourth, the mobility edge obtained from conductivity activation energy measurements turns out to be higher than the actual critical energy $E_{ct}$ that demarcates extended states from localized states; this judgment is supported by the electron mobility-energy relation that is inferred from the geometry of states, which validates a continuous increase of energy-specific mobility as electron energy increases from $E_{ct}$.

Second-order topological insulators possess unique boundary states beyond the conventional bulk-boundary correspondence, which provides opportunities for multidimensional wave manipulation in electronic and acoustic systems. This paper develops an acoustic second-order topological insulator by sonic crystals, hosting multiple corner states at different frequency ranges within one complete bandgap. The topologically protected multifrequency corner states provide robust control of acoustic waves with good immunity against defects. The one-dimensional sound propagation and zero-dimensional sound localization at different frequencies are experimentally observed. We also find these multifrequency corner states are susceptible to the bandgap size of sonic crystals, which could be systematically tunned through topology optimization. The reported results expand the boundaries of constructing second-order topological insulators and exploring multifrequency localized wave modes.

Recently, the vanadium-based kagome metals ${\mathrm{RV}}_6{\mathrm{Sn}}_6$ $(\mathrm{R}=\text{rare-earth})$ have attracted wide attention due to their novel magnetism and nontrivial topological properties. In this paper, the ${\mathrm{DyV}}_6{\mathrm{Sn}}_6$ and ${\mathrm{HoV}}_6{\mathrm{Sn}}_6$ single crystals were successfully synthesized and the magnetotransport measurements were performed to explore the physical properties. The magnetism along different directions in $\mathrm{Dy}/{\mathrm{HoV}}_6{\mathrm{Sn}}_6$ were studied via magnetic susceptibility and magnetization measurements, which reveals ferromagnetic interaction along the $c$ axis with magnetic transition temperature $T_m=3.3$ K/2.7 K and antiferromagnetic interaction within the $\mathit{ab}$ plane. Negative magnetoresistance was observed at small field and low temperature, which is attributed to the suppression of spin scattering. The nonlinear behavior of the Hall resistivity above $T_m$ indicates that Dy/${\mathrm{HoV}}_6{\mathrm{Sn}}_6$ are multiband systems while the S-shaped feature at low field and linear behavior at high filed below $T_m$ imply the possible existence of anomalous Hall effect.

It is a matter of current debate whether the gate-tunable superconductivity in twisted bilayer graphene is phonon mediated or arises from electron-electron interactions. The recent observation of the strong coupling of electrons to so-called $K$-phonon modes in angle-resolved photoemission spectroscopy experiments has resuscitated early proposals that $K$ phonons drive superconductivity. We show that the bandwidth-enhancing effect of interactions drastically weakens both the intrinsic susceptibility towards pairing as well as the screening of Coulomb repulsion that is essential for the phonon attraction to dominate at low temperature. This rules out purely $K$-phonon-mediated superconductivity with the observed transition temperature of $\sim 1$ K. We conclude that the unflattening of bands by Coulomb interactions challenges any purely phonon-driven pairing mechanism, and must be addressed by a successful theory of superconductivity in moiré graphene.

Quantum systems with geometrical frustration remain an outstanding challenge for numerical simulations due to the infamous numerical sign problem. Here, we overcome this obstruction via complex path integration in a geometrically frustrated ladder of interacting bosons at finite density. This enables studies of the many-body ground state properties, otherwise inaccessible with standard quantum Monte Carlo methods. Specifically, we study a chemical potential tuned quantum phase transition, along which we track the emergence of quasi-long-range order and critical softening of the single particle gap. We chart future methodological improvements and applications in generalized geometrically frustrated lattice models.

We provide the plasmon spectrum and related properties of the three-dimensional (3D) Dirac semimetals ${\mathrm{Na}}_3\mathrm{Bi}$ and ${\mathrm{Cd}}_3{\mathrm{As}}_2$ based on the random-phase approximation. The necessary one-electron eigenvalues and eigenfunctions are obtained from an effective $\mathbf{k}·\mathbf{p}$ Hamiltonian. Below the energy at which the velocity $v_z$ along the $k_z$ axis vanishes, the density of states differs drastically from that of a 3D electron gas (3DEG) or graphene. The dispersion relation is anisotropic for wave vectors parallel ($q$) and perpendicular ($q_z$) to the $(x,y)$ plane and is markedly different than that of graphene or a 3DEG. The same holds for the energy-loss function. Both depend sensitively on the position of the Fermi energy $E_F$ relative to the region of the Berry curvature of the bands. For $E_F$ below the energy at which $v_z$ vanishes, the range of the relevant wave vectors $q$ and $q_z$ shrinks, for $q_z$ by about one order of magnitude.

Damping of phonon momentum suppresses the lattice thermal conductivity (${\kappa }_{\mathrm{l}}$) through low-energy acoustic-optical phonon interactions. We studied the thermal transport properties and underlying mechanism of phonon interactions in the large unit cell $\mathrm{C}{\mathrm{u}}_{26}{\mathrm{V}}_2\mathrm{S}{\mathrm{n}}_6\mathrm{S}{\mathrm{e}}_{32}$. The large number of atoms in the unit cell results in low acoustic phonon cutoff frequency, flat phonon branches, low-frequency Raman active modes, localized rattlerlike vibrations and strong crystalline anharmonicity. The crystal structure complexity disrupts the phonon propagation through weak bonded Cu atoms, bosonlike peak and poor phonon velocity. The sulfur at selenium sites ($\mathrm{C}{\mathrm{u}}_{26}{\mathrm{V}}_2\mathrm{S}{\mathrm{n}}_6\mathrm{S}{\mathrm{e}}_{30}{\mathrm{S}}_2$) distort the crystal lattice by offering additional scattering mechanism at the anionic sites, thereby increasing the power factor and decreasing the ${\kappa }_{\mathrm{l}}$. This strategic manipulation of phonon scattering towards ultralow ${\kappa }_{\mathrm{l}}$ not only results in improved thermoelectric performance but also offers insights into the fundamental understanding of heat transport in complex structured, large unit cell compounds.

Quantum anomalous Hall (QAH) effect with dissipationless edge channels offers innovative insight for designing the next-generation low-power electronic devices. Based on first-principles calculations and the tight-binding (TB) model, we predict rich QAH states with a tunable Chern number in single-layer ferromagnetic cerium monohalides $\mathrm{Ce}X$ ($X$ = Cl, Br, I). These stable ferromagnetic single-layer materials have isotropic magnetocrystalline anisotropy in the $x\text{−}y$ plane, which favors the adjustment of the topological state with an external magnetic field. A distinct Weyl nodal loop exists in the band structure of the $\mathrm{Ce}X$ single layers without spin-orbit coupling (SOC). When SOC is included and all mirror symmetries are broken, QAH state can be realized. Intriguingly, QAH states with varying Chern number ($C=\pm 1$), two-dimensional Weyl semimetals and band gap periodically manifest as the magnetization direction rotates in the $x\text{−}y$ plane. Furthermore, A TB model based on Slater-Koster framework is constructed to explain the origin of nontrivial band structure in $\mathrm{Ce}X$ single layers. The $\mathrm{Ce}X$ single layers exhibit remarkable topological states, providing an excellent platform for exploring low-power spintronic devices.

Remarkable recent experiments have observed fractional quantum anomalous Hall effects at zero field and unusually high temperatures in twisted semiconductor bilayer $t{\mathrm{MoTe}}_2$, hence realizing the first genuine fractional Chern insulators. Intriguing observations in these experiments, such as the absence of integer Hall effects at twist angles where a fractional Hall effect is observed, do however remain unexplained. The experimental phase diagram as a function of twist angle remains to be established. By a comprehensive numerical study, including entanglement spectroscopy, we show that band mixing has large qualitative and quantitative effects on the energetics of competing states and their energy gaps throughout the twist angle range $\theta \le 4^{\circ }$. This lays the foundation for a detailed realistic study of a rich variety of strongly correlated moiré superlattices and an understanding of the phase diagram of these fascinating systems.

The self-energy corrections to phonons have mostly been observed for modes with zone-center ($q=0$) wave vectors. Here, we investigated the self-energy corrections to phonons in ionic-liquid-gated semiconductors, i.e., monolayer and bilayer ${\mathrm{WS}}_2$, experimentally. Apart from the previously observed $A_{1g}\left(\mathrm{\Gamma }\right)$ mode renormalization by Raman spectroscopy, we additionally discovered that the zone-edge longitudinal acoustic (LA($M$)) phonon also softened under finite electron doping. This observed renormalization effect arises from the LA($M$) phonon-assisted electron scattering between the $\mathbf{K}$ and $\mathbf{Q}$ valleys in the conduction bands, indicating the nonadiabatic self-energy corrections dominate, different from the $A_{1g}\left(\mathrm{\Gamma }\right)$ mode. The self-energy corrections of the two modes both depend on layer configurations. Our findings suggest that ${\mathrm{WS}}_2$ and other similar two-dimensional materials are intriguing playgrounds to study the electron-phonon interactions and valley-related physics.