Layered $\mathrm{N}{\mathrm{b}}_{3}M{X}_7$ ($M=\mathrm{Se},\mathrm{S},\mathrm{Te}$; $X=\mathrm{I},\mathrm{Br}$) compounds with a noncentrosymmetric kagome lattice structure constitute a promising candidate for exhibiting optical anisotropy and nonlinearity. Nevertheless, there has been limited research on their nonlinear optical properties both theoretically and experimentally. In this paper, we systematically study the linear and nonlinear optical responses of the bulk $\mathrm{N}{\mathrm{b}}_{3}M{X}_7$ ($M=\mathrm{Se},\mathrm{S},\mathrm{Te}$; $X=\mathrm{I},\mathrm{Br}$) family. Previously, two distinct stacking sequences (i.e., AA and AB stacking) in $\mathrm{N}{\mathrm{b}}_{3}M{X}_7$ compounds had been identified in experiments. Therefore, the influence of the stacking sequence and the isoelectronic substitution on the linear and nonlinear optical response of the $\mathrm{N}{\mathrm{b}}_{3}M{X}_7$ compounds are investigated. It reveals that all four materials (AB-$\mathrm{N}{\mathrm{b}}_3\mathrm{Te}{\mathrm{I}}_7$, AA-$\mathrm{N}{\mathrm{b}}_3\mathrm{Te}{\mathrm{I}}_7$, AB-$\mathrm{N}{\mathrm{b}}_3\mathrm{Se}{\mathrm{I}}_7$, and AA-$\mathrm{N}{\mathrm{b}}_3\mathrm{SB}{\mathrm{r}}_7$) exhibit significant second-harmonic generation and linear electro-optic effects. Notably, the second-harmonic generation coefficient (${\chi }_{zzz}^{\left(2\right)}$) of AB-$\mathrm{N}{\mathrm{b}}_3\mathrm{Te}{\mathrm{I}}_7$ reaches 3081 pm/V at 0.91 eV, which is nearly 14 times as large as that of the known nonlinear optical material GaN. Furthermore, AB-$\mathrm{N}{\mathrm{b}}_3\mathrm{Te}{\mathrm{I}}_7$ exhibits a large linear electro-optic coefficient $r_{zzz}$(0) of 5.94 pm/V, which outperforms that of GaN by almost tenfold. The prominent nonlinear optical responses observed in the $\mathrm{N}{\mathrm{b}}_{3}M{X}_7$ compounds are attributed to the intralayer directional covalent bonding. Our findings indicate that the $\mathrm{N}{\mathrm{b}}_{3}M{X}_7$ materials would have potential applications in nonlinear optical and linear electro-optic devices.

Magneto-oscillations in two-dimensional systems with spin-orbit interaction (SOI) are typically characterized by fast Shubnikov–de Haas (SdH) oscillations and slower spin-orbit-related beatings. The characterization of the full SdH oscillatory behavior in systems with both SOI and Zeeman coupling requires a time-consuming diagonalization of large matrices for many magnetic field values. By using the Poisson summation formula, we can explicitly separate the density of states into fast and slow oscillations, which determine the corresponding fast and slow parts of the magneto-oscillations. We introduce an efficient scheme of partial diagonalization of our Hamiltonian, where only states close to the Fermi energy are needed to obtain the SdH oscillations, thus reducing the required computational time. This allows an efficient method for numerically fitting the SdH data, using the inherent separation of the fast and slow oscillations. We compare systems with only Rashba SOI and both Rashba and Dresselhaus SOI with and without an in-plane magnetic field. The energy spectra are characterized in terms of symmetries, which have direct and visible consequences in the magneto-oscillations. To highlight the benefits of our methodology, we use it to extract the spin-orbit parameters by fitting realistic transport data.

We theoretically investigate the electronic properties of finite-sized (e.g., triangular and diamond-shaped) Kane-Mele-type topological insulator nanoflakes on top of an $s$-wave superconductor. We find that the second-order topological superconductor can be generated when the magnetism is only applied on the system boundaries, which host two Majorana corner states located at the corners of two neighboring boundaries. By tuning the applied boundary magnetism, we observe that two isolated Majorana corner states can be adiabatically moved along the system boundaries. Furthermore, we show the possibility of performing topological quantum braiding of the Majorana corner states towards the far-reaching implications of quantum information and quantum computation.

In the ultrathin regime, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ films feature two surfaces (with each surface being a two-dimensional Dirac-fermion system) with complicated spin textures and a tunneling term between them. We find in this regime that the quasiparticle scattering is completely different compared with the thick-film case and even behaves differently at each thickness. The thickness-dependent warping effect and tunneling term are found to be the two main factors that govern the scattering behaviors. The interband backscattering that signals the existence of a tunneling term is found to disappear at four quintuple layers by the step-edge reflection approach. A four-band model is presented that captures the main features of the thickness-dependent scattering behaviors. Our work clarifies that the prohibition of backscattering guaranteed by symmetry in topological insulators breaks down in the ultrathin regime.

Electronic states near surface regions can be distinct from bulk states, which are paramount in understanding various physical phenomena occurring at surfaces and in applications in semiconductors, energy, and catalysis. Here, we report an abnormal surface region band enhancement effect in angle-resolved photoemission spectroscopy on kagome superconductor ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$, by depositing noble gases with fine control. In contrast to conventional surface contamination, the intensity of the surface region Sb band can be enhanced more than three times with noble-gas adsorption. In the meantime, a hole-doping effect is observed for the enhanced surface region band, with other bands hardly changing. The doping effect is more pronounced with heavier noble gases. We propose that noble-gas atoms selectively fill alkali metal vacancy sites on the surface, which improves the surface condition, boosts surface region bands, and effectively dopes it with the Pauli repulsion mechanism. Our results provide a unique and reversible way to improve surface conditions and tune surface region bands by controlled surface noble-gas deposition.

There has been a growing interest in hybrid quantum Hall–superconductor devices, driven by the prospect to realize exotic ground states and excitations with non-Abelian exchange statistics. While the existing experiments clearly demonstrate Andreev coupling between the edge states and the superconductors, the question remains whether the quantum coherence could propagate between several superconducting contacts via chiral channels. To answer this question, we have first extended the Landauer-Büttiker (LB) formalism to samples with one superconducting contact and found a remarkable agreement within a series of measurements related to each other via LB-type formulas. We have then switched to the case of multiple superconducting contacts, and found that we can describe the measurements self-consistently if we neglect the superconducting phase coherence between multiple contacts. We interpret this result as a negative answer to the question posed above: the phase correlations between multiple superconducting contacts are not established via $\mu \text{m}$-long quantum Hall edge states. Looking forward, our approach may find applications in the broader field of topological superconductivity and proximal structures. Possible violations of the self-consistency tests presented here may be used as an indication that superconducting phase coherence is induced in the quantum Hall edges.

Density functional theory predicted that the ground state of ${\mathrm{U}}_2\mathrm{Ti}$ should undergo a Peierls-like doubling of its unit cell along the $c$ axis on cooling from high temperature [G. Kaur et al., J. Alloys Compd. 730, 36 (2018)]. We report x-ray diffraction, heat capacity, and resistivity measurements showing that with decreasing temperature the transition from the parent hexagonal structure occurs in two steps, via an incommensurate state below $T_{\mathrm{ICDW}}=71\left(1\right)$ K which then undergoes a lock-in transition to the predicted commensurate Peierls-like state at $T_{\mathrm{CCDW}}=46\left(3\right)$ K. The signatures of the upper transition in thermodynamic and transport measurements are weak, meaning that similar incommensurate charge density waves (ICDWs) preceding CDWs might occur more widely in other systems but elude detection. The collinear nature of both the ICDW and Peierls-like states we report is much simpler than more complex incommensurate states seen in $\alpha \text{−}\mathrm{U}$, which may in time provide greater insight into the mechanism for ICDW formation.

$1T\text{−}{\mathrm{TiSe}}_2$ has been intensely investigated for its intriguing charge density wave (CDW) phase, which competes with emerging superconductivity. However, the mechanism of the CDW transition has been elusive with the possibility of strong excitonic interaction. Here, we investigate, using angle-resolved photoelectron spectroscopy and density functional theory calculations, the evolution of the CDW band structure upon electron doping into the surface layer by alkali metal adsorbates. Alkali metal adsorption induces substantial electron donation into the Ti $3d$ conduction band with strong band renormalization while the Se $4p$ valance band is contrastingly intact. The density functional theory calculations reveal that only the spectator-type Ti $3d$ band is selectively doped with the CDW band gap largely intact. This result indicates that the CDW formation is not critically related to the metallic electron density and, in turn, to the excitonic coupling due to its unique multiband configuration.

We show that the interplay between spin-orbit coupling and cubic symmetry breaking in ${\mathrm{SrTiO}}_3$ results in a highly anomalous Zeeman effect of conduction electrons substantially different among the three conduction subbands and strongly dependent on their splitting. This effect can be measured via electrically driven spin resonance enabled by the interplay between electron hopping and spin-orbit coupling, and enhanced by the near degeneracy of the conduction subbands. The proposed effects can provide a unique insight into the electronic properties of ${\mathrm{SrTiO}}_3$ and its heterostructures.

We have investigated the electronic structure of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7-\delta }$ $(\delta \approx 0.07)$ by means of hard x-ray photoemission spectroscopy (HAXPES). Although the nominal Ni valence is close to $+2.5$, the Ni $2p$ HAXPES spectra show an absence of ${\mathrm{Ni}}^{2+}/{\mathrm{Ni}}^{3+}$ charge disproportionation. The Ni $2p$ spectral shape including the main peak and the charge-transfer satellite indicate that oxygen $2p$ holes are heavily involved in the transport properties. The spectral weight suppression at the Fermi level indicates that the carriers of O $2p$ character (mixed with Ni $3d$) are affected by electronic correlation which would be associated with the density wave transition and the superconductivity controlled by pressure.

Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.

The shape of the Fermi surface influences many physical phenomena in materials and a growing interest in how the spin-dependent properties are related to the fermiology of crystals has surged. Recently, a novel current-dependent nonlinear magnetoresistance effect, known as bilinear magnetoelectric resistance (BMR), has been shown to be not only sensitive to the spin texture in spin-polarized nonmagnetic materials, but also dependent on the convexity of the Fermi surface in topological semimetals. In this paper, we show that the temperature dependence of the BMR signal strongly depends on the crystal axis of the semimetallic ${\mathrm{MoTe}}_2$. For the $a$ axis, the amplitude of the signal remains fairly constant, while for the $b$ axis it reverses sign at about $100\mathrm{K}$. We calculate the BMR efficiencies at $10\mathrm{K}$ to be ${\chi }_J^A=173\left(3\right)\mathrm{n}{\mathrm{m}}^2{\mathrm{T}}^{-1}{\mathrm{A}}^{-1}$ and ${\chi }_J^B=-364\left(13\right)\mathrm{n}{\mathrm{m}}^2{\mathrm{T}}^{-1}{\mathrm{A}}^{-1}$ for the $a$ and $b$ axis, respectively, and we find that they are comparable to the efficiencies measured for ${\mathrm{WTe}}_2$. We use density-functional theory calculations to compute the Fermi surfaces of both phases at different energy levels and we observe a change in convexity of the outermost electron pocket as a function of the Fermi energy. Our results suggest that the BMR signal is mostly dominated by the change in the Fermi-surface convexity.

Topology-related ideas might lead to noise-resilient quantum computing. For example, it is expected that the slow spatial exchange (“braiding”) of Majorana zero modes in superconductors yields quantum gates that are robust against disorder. Here, we report our numerical experiments, which describe the dynamics of a Majorana qubit built from quantum dots controlled by time-dependent gate voltages. Our protocol incorporates nonprotected control, braiding-based protected control, and readout of the Majorana qubit. We use the Kitaev chain model for the simulations, and we focus on the case when the main source of errors is quasistatic charge noise affecting the hybridization energy splitting of the Majorana modes. We provide quantitative guidelines to suppress both diabatic errors and disorder-induced qubit dephasing, such that a fidelity plateau is observed as the hallmark of the topological quantum gate. Our simulations predict realistic features that are expected to be seen in future braiding experiments with Majorana zero modes and other topological qubit architectures.

Herein, we achieve giant Goos-Hänchen (GH) shifts driven by Fabry-Perot quasibound states in the continuum (quasi-BICs) in double-layer gratings. Based on the hybrid coupling model, the linewidths of two resonant modes in a double-layer grating are determined entirely by the far-field coupling strength. When the vertical distance between two single-layer gratings satisfies the Fabry-Perot resonant condition, the linewidth of one of the resonant modes vanishes, giving rise to a Fabry-Perot BIC. The $Q$ factor of the Fabry-Perot quasi-BIC can be tuned over a wide range by the vertical distance between single-layer two gratings. Driven by the angle-sensitive and ultrastrong resonant properties of the Fabry-Perot quasi-BIC, the GH shift can be significantly enhanced to the order of ${10}^3\lambda$, together with high reflection. Compared with the reported works on giant GH shifts assisted by momentum-mismatch-driven quasi-BICs in dimerized gratings [Phys. Rev. Appl. 12, 014028 (2019); Phys. Rev. A 104, 023518 (2021)], the proposed scheme greatly reduces the difficulty in experiments. Our work not only provides a feasible recipe to observe quasi-BIC-driven giant GH shifts, but also facilitates the development of high-performance sensors and optical switches.

We propose a method to intrinsically realize the nonvolatile electrical control of noncollinear antiferromagnetism, and translate our idea to concrete van der Waals $\mathrm{V}{\mathrm{I}}_2$ bilayers from the first-principles calculations. In $\mathrm{V}{\mathrm{I}}_2$ bilayer systems, we unravel that the sliding ferroelectricity couples strongly to the spin spiral chirality of each $\mathrm{V}{\mathrm{I}}_2$ monolayer, which we refer to as the spin spiral chirality–sliding ferroelectricity locking effect. In this view, a flexibly electrical switch of the noncollinear antiferromagnetism can be realized via interlayer sliding. Our work therefore opens a different direction for the study of type-II multiferroic materials in two dimensions.

Exploration of exotic quantum physics in magnetic systems of reduced dimensionality is among the central themes of condensed matter physics. Here we investigate the nature of magnetic couplings, topological excitations, and critical phenomena in monolayer $\mathrm{MnPS}{\mathrm{e}}_3$, a representative two-dimensional antiferromagnet. We first establish, based on first-principles calculations, that the $\mathrm{S}=5/2\mathrm{M}{\mathrm{n}}^{2+}$ ions possess single-ion anisotropy, favoring in-plane magnetization, and exhibit isotropic antiferromagnetic pairwise couplings. Next, our atomistic magnetics simulations identify antiferromagnetically coupled meron pairs to be the characteristic topological excitations, whose size, polarity, and dynamics can be delicately tuned by an external magnetic field. Significantly, a critical temperature of $\sim 30$ K is indicated in both the susceptibility and specific heat, and detailed scaling analyses on the spin correlations and stiffness unambiguously attribute the critical behavior to the Berezinskii-Kosterlitz-Thouless universality class. Our findings thereby provide an ideal candidate antiferromagnetic counterpart of the recently identified monolayer XY ferromagnet of $\mathrm{CrC}{\mathrm{l}}_3$, the former may harbor distinct topological excitations and multicriticality.

The claims that a copper-substituted lead apatite, denoted as ${\mathrm{CuPb}}_9{\left({\mathrm{PO}}_4\right)}_6{\left(\mathrm{OH}\right)}_2$, could be a room-temperature superconductor have led to intense research activity. While other research groups did not confirm these claims, and the hope of realizing superconductivity in this compound has all but vanished, other findings have emerged which motivate further work on this material. In fact, density functional theory calculations indicate the presence of two nearly flat bands near the Fermi level, which are known to host strongly correlated physics. To facilitate the theoretical study of the intriguing physics associated with these two flat bands, we propose a minimal tight-binding model which reproduces their main features. We then calculate the orbital magnetic susceptibility of our two-band model and find a large diamagnetic response which arises due to the multiorbital nature of the bands and which could provide an explanation for the strong diamagnetism reported in experiments.

In recent breakthrough experiments, twisted moiré layers of transition-metal dichalcogenides are found to manifest both integer and fractional quantum anomalous Hall effects in zero applied magnetic field because of the underlying flat-band topology and spontaneous breaking of the time-reversal invariance. In the current Letter, we critically analyze the experimental values of the quantized conductance in each case to emphasize the role of disorder in the problem, pointing out that obtaining accurate quantized conductance in future experiments would necessitate better contacts and lower disorder.

${\mathrm{CeRh}}_6{\mathrm{Ge}}_4$ is unusual in that its ferromagnetic transition can be suppressed continuously to zero temperature, i.e., to a ferromagnetic quantum-critical point (QCP), through the application of modest hydrostatic pressure. This discovery has raised the possibility that the ferromagnetic QCP may be of the Kondo-breakdown type characterized by a jump in Fermi volume, to which thermopower $S$ measurements should be sensitive. Though $S/T$ changes both sign and magnitude around the critical pressure ${\mathrm{P}}_c\approx 0.8$ GPa, these changes are not abrupt but extend over a pressure interval from within the ferromagnetic state up to ${\mathrm{P}}_c$. Together with temperature and pressure variations in electrical resistivity and previously reported heat capacity, thermopower results point to the near coincidence of two sequential effects near ${\mathrm{P}}_c$, delocalization of $4f$ degrees of freedom through orbital-selective hybridization followed by quantum criticality of itinerant ferromagnetism.

We report on a realistic and rather general scheme where noncollinear magnetic textures proximitized with the most common $s$-wave superconductor can appear as the alternative to $p$-wave superconductor—the prime proposal to realize two-dimensional (2D) Kitaev model for topological superconductors (TSCs) hosting Majorana flat edge mode (MFEM). A general minimal Hamiltonian suitable for magnet/superconductor heterostructures reveals robust MFEM within the gap of Shiba bands due to the emergence of an effective “$p_x+p_y$”-type $p$-wave pairing, spatially localized at the edges of a 2D magnetic domain of spin spiral. We finally verify this concept by considering Mn (Cr) monolayer grown on an $s$-wave superconducting substrate Nb(110) under strain [Nb(001)]. In both 2D cases, the antiferromagnetic spin-spiral solutions exhibit robust MFEM at certain domain edges that is beyond the scope of the trivial extension of one-dimensional (1D) spin-chain model in 2D. This approach, particularly when the MFEM appears in the TSC phase for such heterostructure materials, offers a perspective to extend the realm of the TSC in 2D.