The Kane-Mele model has been modified to achieve versatile topological phases. Previous work [T. Frank et al., Phys. Rev. Lett. 120, 156402 (2018)] introduced a staggered intrinsic spin-orbit coupling effect to generate pseudohelical edge states, with Rashba spin-orbit coupling facilitating spin flips in alternating sublattices. Our study demonstrates that, in the absence of Rashba spin-orbit coupling, the modified Kane-Mele model with staggered intrinsic spin-orbit coupling evolves into a $Z_2$ class topological metal, specifically a two-dimensional Weyl nodal-line semimetal. In a nanoribbon geometry, we predict the emergence of antihelical edge states, which support spin-polarized currents flowing in the same direction along parallel boundaries. Unlike pseudohelical edge states, antihelical edge states can be viewed as a superposition of two antichiral edge states related by time-reversal symmetry. However, the spin Hall conductance from antihelical edge states is not quantized due to the presence of gapless bulk states. Additionally, we examine the robustness of helical, pseudohelical, and antihelical edge states in the presence of nonmagnetic disorders, highlighting the particular fragility of antihelical edge states. Our findings enhance the understanding of the modified Kane-Mele model, providing new insights into its topological properties.

Graphene nanostructures, renowned for their exceptional electronic and transport properties, hold great promise for stretchable electronics. Zigzag graphene nanoribbons (ZGNRs) further intrigue with their intrinsic edge magnetism, unlocking new potentials in spintronic devices. In this paper, we integrate mechanical behavior with $\pi$ magnetism to establish a robust platform for mechanical spin splitting in ZGNRs. Our findings reveal fully spin-polarized states in a large energy window, exhibiting significant magnetic moments and tunable spin gaps in helicoidal ZGNRs. Substantial spin splitting occurs when helical morphologies lead to different bond lengths at one zigzag edge relative to the other. The spin-splitting and spin-gap characteristics within the bipolar spin-semiconducting phase can be precisely controlled by varying helical configurations and the magnitude of strain induced by deformation. This mechanical control over electronic and magnetic properties positions ZGNRs as a promising candidate for stretchable spintronic devices.

The formation of a class of self-organized, one-dimensional nanostructures in the ternary material system Au/Co/Ge(001) is reported. These “nanorods” form after the subsequent deposition of Co and Au on the clean Ge(001) surface, followed by thermal annealing. The local structural and electronic properties were probed using scanning tunneling microscopy and spectroscopy. Various types of nanorods exist and their distribution and mean length are controlled by the amount of deposited Co and the annealing temperature. Differential tunneling conductance measurements indicate the existence of four dominant peaks near the Fermi energy and an anomalous suppression of the differential tunneling conductance at the Fermi level, resulting in a zero-bias anomaly.

In magnetic fields, thermal gradient-induced effects such as the Nernst and thermal Hall effects are significantly influenced by phonon drag, which works in conjunction with the force on electrons in a magnetic field. We introduce a method to calculate Nernst and thermal Hall conductivities influenced by phonon drag using linear response theory to treat the magnetic field as a first-order perturbation. Our formula is general enough to apply to various systems in which the Green's functions of electrons and phonons are given. We apply the obtained general theory to the recent experiments of dilute metal ${\mathrm{SrTiO}}_{3-\delta }$, known for strong Nernst and thermal Hall effects because of phonon drag. We find good agreement even quantitatively. This is notable as all model parameters are derived from experimental data without adjustable parameters.

We carry out a systematic study of the electronic and magnetic structure of the ambient-pressure bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Employing the hybrid exchange-correlation functional, we show that the exchange correlation pushes the bonding $d_{z^2}$ bands below the Fermi level to be fully occupied. The calculated Fermi surfaces and the correlation normalized band structure match well with the experimental findings at ambient pressure. Moreover, the electronic susceptibility calculated for this band structure features nesting-induced peaks near the wave vector $Q=(\pi /2,\pi /2)$, suggesting a possible density wave instability in agreement with recent experiments. Through a mean-field study and $\text{DFT}+U$ calculation introducing a Hubbard U interaction within conventional density functional theory, we confirm the spin-charge intertwined double-stripe order is the magnetic ground state. Our results provide a faithful description for the low-pressure ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ electronic structure.

The recently reported nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under pressure provides a new platform for exploring unconventional superconductivity. The oxygen vacancies (${\mathrm{V}}_{\mathrm{O}}$'s) are inevitably introduced during the sample preparation, as confirmed by experimental observations. While it is believed the ${\mathrm{V}}_{\mathrm{O}}$'s could play a key role in influencing the superconductivity of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, their basic structural and electronic properties remain to be clarified. Here, combining the cluster expansion method and first-principles calculations, we successfully identify eight intermediate ground states of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7–x}$ with variable $x$. Contrary to the general assumption of a random distribution, surprisingly, we find the ${\mathrm{V}}_{\mathrm{O}}$'s eventually form exotic one-dimensional chain structures along the in-plane direction in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7–x}$. These recently discovered ${\mathrm{V}}_{\mathrm{O}}$ chains significantly change the electronic properties with redistributed electrons and altered orbital interactions. The $d_{z2}$ orbitals of Ni atoms adjacent to the ${\mathrm{V}}_{\mathrm{O}}$ chain become fully occupied, with a decreased proportion around the Fermi level ($E_{\mathrm{F}}$). Importantly, a flat $d_{x2-y2}$ orbital that emerges above $E_{\mathrm{F}}$ enhances the transition dipole moment, leading to a prominent peak in optical conductivity perpendicular to the chain, which is ready to be detected experimentally. Furthermore, Wannier downfolding analysis demonstrates significant variations in orbital interactions caused by the ${\mathrm{V}}_{\mathrm{O}}$ chains, particularly the sign changes in intrabilayer $d_{z2}$ hopping. Our study provides the benchmark structures of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7–x}$ and develops a deeper insight into the fundamental electronic and optical properties of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7–x}$.

Spin fluctuations play pivotal roles in condensed matter physics. Motivated by the discovery of valence bond order (VBO) -based fluctuations in superconductors and spin-liquid candidates, we investigated VBO within a molecule-based triangular lattice exhibiting antiferromagnetic order (AFO) in ${\beta }^{\prime }\text{−}\mathrm{EtM}{\mathrm{e}}_3\mathrm{As}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$ using vibrational spectroscopy. The two triangular lattice layers of dimer $\left({\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2^{-}\right)$ units in the unit cell, separated by cationic $\mathrm{EtM}{\mathrm{e}}_3\mathrm{A}{\mathrm{s}}^{+}$ layers, are crystallographically independent below the cation ordering temperature $T_{\mathrm{cat}}=230$ K. Below $T_{\mathrm{cat}}$, part of the triangular lattice in both layers exhibits VBO fluctuations with inhomogeneous charges. At approximately 50 K, between $T_{\mathrm{cat}}$ and the antiferromagnetic transition temperature $T_{\mathrm{AF}}=23$ K, the VBO fluctuations in one layer freeze and coexist with frustrating 1/2 spins in the dimers. Conversely, the VBO fluctuations in the other layer cease simultaneously with the antiferromagnetic transition. In both layers, the frozen VBO (nonmagnetic tetramers) and spin-1/2 dimers coexist below $T_{\mathrm{AF}}$. The results of this study reveal that hidden VBOs coexist in the AFO state.

We employ a “real-time” excitation scheme to calculate the excitation spectra of a two-dimensional electron system in a square array of quantum dots placed in a circular cylindrical far-infrared photon cavity subjected to a perpendicular homogeneous external magnetic field. The Coulomb interaction of the electrons is handled via spin density functional theory and the para- and the diamagnetic parts of the electron-photon coupling are updated according to a configuration interaction method in each iteration of the density functional calculation. The results show that an excitation scheme built on using the symmetry of the lateral square superlattice of the dots and the cylindrical cavity produces both para- and diamagnetic resonance peaks with oscillator strengths that can be steered by the excitation pulse parameters. The excitation method breaks the conditions for the generalized Kohn theorem and allows for insight into the subband structure of the electron system and can be used both inside and outside the linear response regime.

Bounded excitons in transition metal dichalcogenides monolayers lead to numerous opto-electronic applications, which require a detailed understanding of the exciton dynamics. The dynamical properties of excitons with finite momentum transfer $\mathbf{Q}$ can be investigated experimentally using electron energy-loss (EEL) spectroscopy. The EEL spectrum depends on the response function of the material which in turn is determined by the exciton energies and eigenvectors in the exciton band structure. In this work, we utilize ab initio density-functional theory plus Bethe-Salpeter equation ($\mathrm{DFT}+\mathrm{BSE}$) approach to explore the exciton band structure and also $\mathbf{Q}$-resolved EEL spectrum in monolayer ${\mathrm{WSe}}_2$. In particular, we carefully examine the discrepancies and connections among the existing EEL spectrum formulas for quasi-two-dimensional (2D) systems, and establish a proper definition of the EEL spectrum, which is then used to calculate the EEL spectra of monolayer ${\mathrm{WSe}}_2$. We find that remarkably, the dispersion of the calculated lowest-energy EELS peaks for the in-plane momentum transfer follows almost precisely the nonparabolic upper band of the lowest bright A exciton, and also agrees well with the previous experiment. Furthermore, we show that only the bright exciton with its electric dipole being parallel to the direction of the transferred momentum is excited, i.e., EEL spectroscopy selectively probes bright exciton bands. This explains why only the upper band of the A exciton, which is a longitudinal exciton with an in-plane dipole moment, was observed in the previous experiment. Our findings will stimulate further EEL experiments to measure other branches of the exciton band structure, such as the parabolic lower band of the A exciton, and hence will lead to a better understanding of the exciton dynamics in quasi-2D materials.

Volkov-Pankratov states are nontopological massive bound states which generally arise across the smooth interface between two adjacent regions of a two-band semimetal, over which a gap parameter changes sign smoothly. In this work, we show that these modes can be engineered even for a generic smooth interface without any sign inversion. We consider threefold and twofold topological semimetals in which two adjacent regions are illuminated by light with different phases. We show that the interface can exhibit an asymmetric Rosen-Morse potential well for a certain parameter regime even without any sign change of the gap term. Such a quantum well can host a number of Volkov-Pankratov states. We also note that even in a two-band two-dimensional semimetal like graphene, the Volkov-Pankratov states can emerge if one induces a momentum shift rather than opening a gap. Finally, we discuss the transport signatures over those interfacial quantum wells. We note that although the Ramsauer-Townsend effect appears over the symmetric-type Pöschl-Teller potential well, this effect is absent over an asymmetric Rosen-Morse potential well. We reveal that a transition from a unit transmission to a unit reflection can be achieved by just controlling light parameters in a periodically driven graphene. We observe that the unit reflection phenomenon is direction sensitive; i.e., only incoming electrons from one particular side (left or right) can be perfectly reflected back without any transmission.

Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous non-Abelian symmetries) is known to be superdiffusive, with anomalous transport properties displaying remarkable robustness to isotropic integrability-breaking perturbations. Using a discrete-time classical model, we numerically study the crossover to conventional diffusion resulting from both noisy and Floquet isotropic perturbations of strength $\lambda$. We identify an anomalously-long crossover timescale $t_{★}\sim {\lambda }^{-\alpha }$ with $\alpha \approx 6$ in both cases. We discuss our results in terms of a kinetic theory of transport that characterizes the lifetimes of large solitons responsible for superdiffusion.

Antiferromagnets (AFM) with a nonrelativistic spin splitting (NSS) of electronic bands expand the range of spin-dependent phenomena and their applications. A crucial understanding for both of them pertains to the inherent spin dynamics. We demonstrate that the $d$-wave NSS gives rise to extremely anisotropic spin dynamics of carriers driven by the relaxation induced by motional narrowing. In contrast to the lack of relaxation of the spin polarization along the Neel vector, the dynamics of perpendicular spin components greatly varies from a long relaxation for a weak NSS to the fast-decaying oscillations for a strong NSS, a regime relevant to AFM with the $d$-wave NSS. The extreme anisotropy of the spin relaxation is transformed by the external magnetic field, which triggers the relaxation of the parallel spin component and also suppresses all the relaxation rates at larger magnitudes. The predicted spin dynamics of the $d$-wave NSS, known also from altermagnets, can be used as their experimental fingerprints and guide future applications.

The first quantum fractal discovered in physics is the Hofstadter butterfly. It stems from large external magnetic fields. We discover instead a class of non-Hermitian quantum fractals (NHQFs) emerging in coupled Hatano-Nelson models on a tree lattice in the absence of any fields. Based on analytic solutions, we are able to rigorously identify the self-similar recursive structures in the energy spectrum and wave functions. We prove that the complex spectrum of NHQFs bears a resemblance to the Mandelbrot set in fractal theory. The self-similarity of NHQFs is rooted in the interplay between the iterative lattice configuration and non-Hermiticity. Moreover, we show that NHQFs exist in generalized non-Hermitian systems with iterative lattice structures. Our findings open another avenue for investigating quantum fractals in non-Hermitian systems.

We study non-Hermitian Josephson junctions formed by superconductors with a finite phase difference under non-Hermiticity, which naturally appears due to coupling to normal reservoirs. Depending on the structure of non-Hermiticity, captured in terms of retarded self-energies, the low-energy spectrum hosts topologically stable exceptional points either at zero or finite real energies as a function of the superconducting phase difference. Interestingly, the corresponding phase-biased supercurrents may acquire divergent profiles at such exceptional points. This instance is a natural and unique non-Hermitian effect that signals a possible way to enhance the sensitivity of Josephson junctions. Our work opens a way for realizing unique non-Hermitian phenomena due to the interplay between non-Hermitian topology and the Josephson effect.

The high-pressure temperature phase diagram and transport properties of materials are of broad interest to planetary sciences and high-energy-density sciences and applications. Alumina $\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)$ or its various forms (e.g., solutions with other oxides or silicates) are important constituents in Earth's and super-Earths' mantles, common window materials in dynamic compression experiments, and standard pressure calibrators in diamond-anvil-cell experiments. Its structures and transport properties are of particular importance but have not been well studied at above 100 GPa pressures. Based on extensive first-principles molecular dynamics calculations, we obtain atomic level insights on structural differences and accurate results on electrical conductivity $\left({\sigma }_{\mathrm{dc}}\right)$, thermal conductivity $\left(\kappa \right)$, and reflectivity of ${\mathrm{Al}}_2{\mathrm{O}}_3$ in several phases at pressures of $\sim 130-1300\mathrm{GPa}$ and temperatures of 4000–20 000 K. We find the solid-to-liquid state changes of ${\mathrm{Al}}_2{\mathrm{O}}_3$ are accompanied by an insulator-to-semimetal transition with enhanced ${\sigma }_{\mathrm{dc}}$ and $\kappa$, which is similar to other silicates and oxides and can facilitate magnetic field generation in deep interiors of rocky planets. We also find the solid-to-solid transition [from ${\mathrm{Rh}}_2{\mathrm{O}}_3\left(\mathrm{II}\right)$ to ${\mathrm{CaIrO}}_3]$ is accompanied by negligible changes in ${\sigma }_{\mathrm{dc}}$ and $\kappa$ at 160 GPa, contrary to previous expectations, whereas another higher pressure phase transition (${\mathrm{CaIrO}}_3$ to ${\mathrm{U}}_2{\mathrm{S}}_3$ at 450 GPa) is associated with increases in ${\sigma }_{\mathrm{dc}}$ and $\kappa$. Furthermore, we show the transport properties can be enhanced by oxygen vacancy in ${\mathrm{Al}}_2{\mathrm{O}}_3$, but are not significantly affected by forming solutions with ${\mathrm{MgSiO}}_3$, particularly when in the solid states.