A saddle point plus fluctuation analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly excited, generically nonthermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a nonequilibrium drive.

We present a symmetry-adapted real-space formulation of Kohn-Sham density functional theory for cylindrical geometries and apply it to the study of large X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham equations posed on all of space, we reduce the problem to the fundamental domain by incorporating cyclic and periodic symmetries present in the angular and axial directions of the cylinder, respectively. We develop a high-order finite-difference parallel implementation of this formulation, and verify its accuracy against established plane-wave and real-space codes. Using this implementation, we study the band structure and bending properties of X nanotubes and Xene sheets, respectively. Specifically, we first show that zigzag and armchair X nanotubes with radii in the range 1 to $5\mathrm{nm}$ are semiconducting, other than the armchair and zigzag type III carbon variants, for which we find a vanishingly small bandgap, indicative of metallic behavior. In particular, we find an inverse linear dependence of the bandgap with respect to the radius for all nanotubes, other than the armchair and zigzag type III carbon variants, for which we find an inverse quadratic dependence. Next, we exploit the connection between cyclic symmetry and uniform bending deformations to calculate the bending moduli of Xene sheets in both zigzag and armchair directions, while considering radii of curvature up to $5\mathrm{nm}$. We find Kirchhoff-Love type bending behavior for all sheets, with graphene and stanene possessing the largest and smallest moduli, respectively. In addition, other than graphene, the sheets demonstrate significant anisotropy, with larger bending moduli along the armchair direction. Finally, we demonstrate that the proposed approach has very good parallel scaling and is highly efficient, enabling ab initio simulations of unprecedented size for systems with a high degree of cyclic symmetry. In particular, we show that even micron-sized nanotubes can be simulated with modest computational effort. Overall, the current work opens an avenue for the efficient ab initio study of 1D nanostructures with large radii as well as 1D/2D nanostructures under uniform bending.

As a new class of condensed matter, topological insulators challenge the traditional wisdom of condensed matter physics. Doping topological insulators with magnetic elements can realize the quantum anomalous Hall state, a two-dimensional bulk insulator with nonzero Chern number. High harmonic generation (HHG) has emerged as a very promising tool to probe electronic properties. However, its application to magnetically doped topological insulators has not been realized. Here, we predict that high harmonics from six quintuple layers of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(6QL-${\mathrm{Bi}}_2{\mathrm{Se}}_3$) carry crucial information about its structure. HHG sensitively depends on crystal symmetry and laser polarization. While in the parent compound 6QL-${\mathrm{Bi}}_2{\mathrm{Se}}_3$ all the harmonic orders are odd, once it is doped with a magnetic Cr atom, selective even and odd harmonics appear, depending on whether the laser field is in-plane or out-of-plane. With spin-orbit coupling, both even and odd harmonics appear. We find that these seemingly complicated harmonics have a simple origin: microscopic interplay between symmetry operations and laser polarization. Our finding demonstrates the unexplored power of HHG in topological insulators and will have a broad impact on future research.

We study the quantum criticality of spinless fermions on a quasi-one-dimensional $\pi$-flux square lattice in cylinder geometry, by using the infinite density matrix renormalization group and Abelian bosonization. For a series of cylinder circumferences $L_y=4n+2=2,6,...$ with a periodic boundary condition, there are quantum phase transitions from gapped Dirac fermion states to charge density wave (CDW) states. We find that the quantum phase transitions for such circumferences are continuous and belong to the ($1+1$)-dimensional Ising universality class. On the other hand, when $L_y=4n=4,8,...$, there are gapless Dirac fermions at the noninteracting point and the phase transition to the CDW state is Gaussian. Both of these criticalities are described in a unified way by bosonization. We clarify their intimate relationship and demonstrate that a central charge $c=1/2$ Ising transition line arises as a critical state of an emergent Majorana fermion from the $c=2$ Gaussian transition point.

Using a large-$N$ theory in combination with the Keldysh nonequilibrium Green's function formalism, we investigate the current, differential conductance, zero-frequency shot noise, and Fano factor as measured by scanning tunneling shot-noise spectroscopy (STSNS) using a scanning tunneling microscope (STM) near single Kondo impurities and in Kondo lattices. We show that the Fano factor $F$ exhibits a characteristic bias dependence arising from Kondo screening that is similar to the Kondo resonance observed in the differential conductance. Moreover, the line shape of $F$ is strongly dependent on the ratio of the tunneling amplitudes for electron tunneling from the STM tip into the conduction band and electronic levels of the magnetic adatoms. We demonstrate that the Fano factor can be enhanced or suppressed due to interference effects and as such, is not only a sensitive probe for the correlation effects arising from Kondo screening, but also for quantum interference between tunneling electrons. We identify a correlation between the form of the differential conductance and the Fano factor that could be tested in future STSNS experiments.

The spin Hall effect due to skew scattering is studied by solving the Boltzmann equation in a bilayer electron system with attractive impurity potentials in one layer and repulsive ones in the other. In such an impurity configuration, directions of the spin Hall current in two decoupled layers are antiparallel. An analytical formula for the magnitude of the antiparallel spin Hall current is derived in the crossover from the decoupled bilayer to the strongly coupled one with no spin Hall current with increasing ${\mathrm{\Delta }}_{\mathrm{SAS}}$, the energy separation between the symmetric and antisymmetric states of the motion perpendicular to the layer. When the impurity potential is short ranged and ${\mathrm{\Delta }}_{\mathrm{SAS}}\ll {\varepsilon }_{\mathrm{F}}$, with ${\varepsilon }_{\mathrm{F}}$ being the Fermi energy, the normalized antiparallel spin Hall conductivity is found to be ${[1+{\left(\omega {\tau }_p\right)}^2]}^{-1}$, with $\omega ={\mathrm{\Delta }}_{\mathrm{SAS}}/\hslash$ and ${\tau }_p$ being the momentum relaxation time at ${\varepsilon }_{\mathrm{F}}$. This formula is explained by extending the dynamics for the Hanle effect, which was originally developed for spin, to the pseudospin (layer) degree of freedom. The present finding suggests that the Hanle effect will be useful in understanding the pseudospin dynamics as well as the spin dynamics.

Developing the nonequilibrium thermodynamics of friction is required for systematic design of low-friction surfaces for a broad range of technological applications. Intuitively, the thermodynamic work done by a material sliding along a surface is expected to be partially dissipated as heat and partially transformed into the change of the internal energy of the system. However, general nonequilibrium thermodynamic principles governing this separation are presently unknown. We develop a theoretical framework based on the transition state theory combined with the conventional Prandtl-Tomlinson model, allowing to set explicit expressions for evaluating the heat dissipation and internal energy change produced during the frictional stick-slip motion of a tip of a typical friction force microscope. We use the formalism to quantify the heat dissipation for a range of parameters relevant to materials in practical applications of nanoscale friction.

We discuss the quantum dynamics of the central spin model in a regime where the central spin and bath are slaved to each other. The exact solution is found when the bath is static and is compared with the effect of an external field, finding that they are inequivalent due to the quantum nature of the environment. When the bath has dynamics, we analyze the differences between the numerical simulation using time-dependent perturbation theory and the equation of motion technique, which shows better accuracy. We demonstrate that the use of dynamical renormalization group (dRG), simultaneously with the equation of motion technique, provides a suitable analytical tool to understand the physics, to capture the main physical processes, and a powerful method to eliminate secular terms. In addition, this approach allows to separate classical nonlinear behavior from corrections due to quantum correlations.

Perpendicular magnetic anisotropy (PMA) of magnetic materials has received much attention because of its potential application to spintronics devices. In general, the tensely strained $\left(001\right)\text{−}\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{S}{\mathrm{r}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ (LSMO) layer is easy plane. Here we demonstrate that the tensile LSMO layer will exhibit an out-of-plane magnetic anisotropy if it is sandwiched between two $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Co}{\mathrm{O}}_{2.5+\delta }$ (LSCO) layers. The most remarkable observation is that the PMA enhances with the increase of the Sr content in LSCO. It is $\sim 2.7\times {10}^6\mathrm{erg}/\mathrm{c}{\mathrm{m}}^3$ for $x=0.05$ and $\sim 4.3\times {10}^6\mathrm{erg}/\mathrm{c}{\mathrm{m}}^3$ for $x=0.5$. This value is two orders of magnitude greater than that obtained by compressively straining the LSMO film $(\sim {10}^4\mathrm{erg}/\mathrm{c}{\mathrm{m}}^3)$. Analysis of high resolution lattice image shows the formation of perovskite/brownmillerite-type interfaces in the multilayers: Brownmillerite-like lattice structure forms in the interfacial layers of LSCO, resulting in a coherent tilting of adjacent $\mathrm{Mn}{\mathrm{O}}_6$ octahedra. This in turn leads to, as evidenced by the analysis of x-ray linear dichroism, selective orbital occupation thus spin reorientation. There is evidence that the brownmillerite-structured LSCO is more easily formed when $x$ is high, which explains the growth of anisotropy constant with the increase of Sr content.

Frustrated spin-$\frac{1}{2}$ chains, despite the apparent simplicity, exhibit a remarkably rich phase diagram comprising vector-chiral (VC), spin-density-wave (SDW), and multipolar/spin-nematic phases as a function of the magnetic field. Here we report a study of $\beta \text{−}{\mathrm{TeVO}}_4$, an archetype of such compounds, based on magnetization and neutron diffraction measurements up to 25 T. We find the transition from the helical VC ground state to the SDW state at $\sim 3$ T for the magnetic field along the $a$ and $c$ crystal axes, and at $\sim 9$ T for the field along the $b$ axis. The high-field (HF) state, existing above $\sim 18$ T, i.e., above $\sim 1$/2 of the saturated magnetization, is an incommensurate magnetically ordered state and not the spin-nematic state, as theoretically predicted for the isotropic frustrated spin-1/2 chain. The HF state is likely driven by sizable interchain interactions and symmetric intrachain anisotropies uncovered in previous studies. Consequently, the potential existence of the spin-nematic phase in $\beta \text{−}{\mathrm{TeVO}}_4$ is limited to a narrow field range, i.e., a few tenths of a tesla bellow the saturation of the magnetization, as also found in other frustrated spin-$\frac{1}{2}$ chain compounds.

The dependence of the Hall conductivity on temperature and magnetic field in optimally doped ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4\pm \delta }$ $(x=0.105)$ thin films demonstrates that both the hole and the electron bands undergo Cooper pairing. The magnetic field suppresses the dominant hole band pairing more effectively, making the subdominant electron band pairing visible. Positively charged Cooper pairs dominate the Hall signal in the mixed state at a weak magnetic field near $T_c$, while at large field the negatively charged Cooper pairs take over. Sign reversals of the Hall conductivity induced by superconducting fluctuation occur in the transition and can be explained by a weakly coupled two-band Ginzburg-Landau-Lawrence-Doniach model.

We systematically investigated the pressure dependence of electrical transport and the crystal structure of topological insulator, $\mathrm{B}{\mathrm{i}}_{2-x}\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{3-y}\mathrm{S}{\mathrm{e}}_y$, which showed no superconductivity down to 2.0 K at ambient pressure. The $\mathrm{B}{\mathrm{i}}_{2-x}\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{3-y}\mathrm{S}{\mathrm{e}}_y$ crystal showed two structural phase transitions under pressure, from rhombohedral structure (space group No. 166, $R\overline{3}m$, termed phase I) to monoclinic structure (space group No. 12, $C2/m$, termed phase II), and from phase II to another monoclinic structure (space group No. 12, $C2/m$, termed phase III). Superconductivity appeared when applying pressure; actually the superconductivity of all $\mathrm{B}{\mathrm{i}}_{2-x}\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{3-y}\mathrm{S}{\mathrm{e}}_y$ samples emerged in phase I. The superconducting transition temperature, $T_{\mathrm{c}}$, increased against pressure in a pressure range of 0–15 GPa for all $\mathrm{B}{\mathrm{i}}_{2-x}\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{3-y}\mathrm{S}{\mathrm{e}}_y$ samples, and the maximum $T_{\mathrm{c}}$ was 5.45 K, recorded at 13.5 GPa in $\mathrm{B}{\mathrm{i}}_{2-x}\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{3-y}\mathrm{S}{\mathrm{e}}_y$ at $x=0$ and $y=1.0$. The magnetic field (H) dependence of the R–T plot for $\mathrm{B}{\mathrm{i}}_{2-x}\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{3-y}\mathrm{S}{\mathrm{e}}_y$ was measured to characterize the superconducting pairing mechanism of pressure-induced superconducting phase.

We introduce well-defined characterizations of prethermal states in realistic periodically driven many-body systems with unbounded chaotic diffusion of the kinetic energy. These systems, interacting arrays of periodically kicked rotors, are paradigmatic models of many-body chaos theory. We show that the prethermal states in these systems are well described by a generalized Gibbs ensemble based essentially on the average Hamiltonian. The latter is the quasiconserved quantity in the prethermal state and the ensemble is characterized by the temperature of the state. An explicit exact expression for this temperature is derived. Using also arguments based on chaos theory, we demonstrate that the lifetime of the prethermal state is exponentially long in the inverse of the temperature, in units of the driving frequency squared. Our analytical results, in particular those for the temperature and the lifetime of the prethermal state, agree well with numerical observations.

The $3d$ transition metal insulator ${\mathrm{Bi}}_2{\mathrm{CrAl}}_3{\mathrm{O}}_9$ forms with a quasi-one-dimensional structure characterized by linear chains of edge-sharing, Cr-and Al-centered, distorted octahedra. The UV/Vis spectrum of high-quality single crystals is marked by broad absorption edges corresponding to direct transitions across a 1.36-eV insulating gap. Measurements of dc magnetic susceptibility $\chi$ reveal a fluctuating moment of $2.60\pm 0.01{\mu }_B/\mathrm{Cr}$—reduced from the $3.87{\mu }_B/\mathrm{Cr}$ expected for ${\mathrm{Cr}}^{3+}$, while the Weiss temperature ${\mathrm{\Theta }}_W=-21\pm 1$ K implies that the prevailing local moment interactions are weakly antiferromagnetic in nature. Some 10% of the fluctuating moment is quenched, presumably due to the onset of an antiferromagnetic or spin glass phase at temperature $T^{★}=98\pm 3$ K, while measurements of magnetization versus field $H$ at $T\le 10$ K scale as $H/T^{0.68\left(4\right)}$, suggesting the presence of quantum fluctuations associated with a disordered phase. Density functional theory calculations carried out within the generalized gradient approximation are in excellent agreement with experimental results, asserting that short-range magnetic interactions remnant above $T^{★}$ stabilize the insulating state.

We demonstrate how the boundary-driven reconstruction of the superconducting order parameter can be employed to manipulate the zero-energy Majorana bound states (MBSs) occurring in a topological Josephson junction. We focus on an interface of two $p$-wave superconductors, which are described by a spin-vector order parameter $\mathit{d}$. Apart from the sensitivity of $\mathit{d}$ to external Zeeman/exchange fields, here, we show that the orientation of $\mathit{d}$ throughout the junction can be controlled by electrically gating the weak link. The remarkable local character of this knob is a manifestation of the edge reconstruction of the order parameter, which takes place whenever different $\mathit{d}$-vector configurations in each superconductor compete and are close in energy. As a consequence, the spin-dependent superconducting-phase difference across the junction is switchable from 0 to $\pi$. Moreover, in the regime where multiple edge MBSs occur for each superconductor, the Andreev bound state (ABS) spectra can be twisted by the application of either a charge- or spin-phase difference across the interface and give rise to a rich diversity of nonstandard ABS dispersions. Interestingly, some of these dispersions show band crossings protected by fermion parity, despite their $2\pi$-periodic character. These crossings additionally unlock the possibility of nontrivial topology in synthetic spaces, when considering networks of such 1D junctions. Lastly, the interface MBSs induce a distinct electronic spin polarization near the junction, which possesses a characteristic spatial pattern that allows the detection of MBSs using spin-polarized scanning tunneling microscopy. These findings unveil novel paths to mechanisms for ABS engineering and single-out signatures relevant for the experimental detection and manipulation of MBSs.

It is well known that competing phases can manifest within the core regions of superconducting vortices. In strong magnetic fields, neighboring vortices can overlap to give rise to long-ranged correlations in the competing phase. We show that the resulting textures can have topological character with similarities to skyrmion crystals in magnets. We illustrate this using the SO(3) theory of competing orders wherein a scalar charge-density-wave (CDW) order competes with superconductivity. We study this theory on a spherical surface enclosing a magnetic monopole, giving rise to two vortices on the surface. The lowest-energy solution has both vortex cores ordered in the same sense, with coherent CDW order developing over the entire sphere. This changes dramatically when a perturbation that breaks inversion symmetry is introduced. The CDW order becomes anticorrelated between vortices, resulting in a topologically stable configuration that is analogous to a skyrmion in a ferromagnet. We extend this idea to vortex lattices in the two-dimensional plane, modeled by the attractive Hubbard model with an orbital field. Upon introducing Rashba spin-orbit coupling (RSOC), we find spatially modulated textures with CDW order developing around vortex cores in a stripe-like anticorrelated fashion. In a wide parameter regime, RSOC lowers the energy cost for domain walls separating vortices with opposite CDW orders. As a consequence, the competing CDW order loses its rigidity and becomes short-ranged. We discuss implications for the underdoped cuprates where charge order develops without a sharp diffraction peak.

Realization of the anomalous refraction effects predicted by Huygens’ metasurfaces (HMS) has required tedious and time-consuming trial-and-error numerical full-wave computations. It is shown herein that these requirements can be alleviated for transverse magnetic propagation by a periodic dielectric-based HMS consisting of an electrically thick array of cascaded Fabry-Pérot etalons. This “Fabry-Pérot HMS” (FP-HMS) is easily designed to mimic the local scattering coefficients of a standard zero-thickness HMS (ZT-HMS) which, according to homogenization theory, should result in the desired anomalous refraction. To probe the characteristics of this practical FP-HMS, a method based on Floquet-Bloch (FB) analysis is derived for predicting the fields scattered from it for arbitrary angles of incidence. This method produces simple closed-form solutions for the FB wave amplitudes and the resulting fields are shown to agree well with full-wave simulations. These predictions and full-wave simulations verify the applicability of homogenization and scattering properties of ZT-HMSs to thick structures. They also verify the proposed semianalytical microscopic design procedure for such structures, offering an effective alternative path to implementation of theoretically envisioned intricate field manipulating devices.

We report results of terahertz Faraday and Kerr rotation spectroscopy measurements on thin films of ${\text{Bi}}_{1-x}{\text{Sb}}_x$, an alloy system that exhibits a semimetal-to-topological-insulator transition as the Sb composition $x$ increases. By using a single-shot time-domain terahertz spectroscopy setup combined with a table-top pulsed minicoil magnet, we conducted measurements in magnetic fields up to 30 T, observing distinctly different behaviors between semimetallic ($x<0.07$) and topological insulator ($x>0.07$) samples. Faraday and Kerr rotation spectra for the semimetallic films showed a pronounced dip that blueshifted with the magnetic field, whereas spectra for the topological insulator films were positive and featureless, increasing in amplitude with increasing magnetic field and eventually saturating at high fields ($>20$ T). Ellipticity spectra for the semimetallic films showed resonances, whereas the topological insulator films showed no detectable ellipticity. To explain these observations, we developed a theoretical model based on realistic band parameters and the Kubo formula for calculating the optical conductivity of Landau-quantized charge carriers. Our calculations quantitatively reproduced all experimental features, establishing that the Faraday and Kerr signals in the semimetallic films predominantly arise from bulk hole cyclotron resonances while the signals in the topological insulator films represent combined effects of surface carriers originating from multiple electron and hole pockets. These results demonstrate that the use of high magnetic fields in terahertz magnetopolarimetry, combined with detailed electronic structure and conductivity calculations, allows us to unambiguously identify and quantitatively determine unique contributions from different species of carriers of topological and nontopological nature in ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$.

We study the effect of resonances on the ability of prisms made of hyperbolic metamaterials in the canalization regime (such as wire array media) to couple evanescent high spatial frequencies (high-$k$ modes) to low spatial frequencies that propagate in the far-field zone. Using simple analytical models, we calculate the far-field propagation from the hyperprism. The resonant nature of the metal wire segments within the prism yields a transmission function identical to that of a grating, but with periodicity proportional to the wavelength, making the hyperprism function like a nondispersive grating. Numerically compensating the effect of resonances allows the hyperprism to be used as a one-dimensional imaging device able to resolve feature sizes below the diffraction limit if the host medium has a low refractive index. Furthermore, the hyperprism enables coupling of propagating plane waves to a range of high-$k$ modes that can be increased by increasing the angle of the prism. We quantify how this tunable, nondispersive excitation of high-$k$ modes opens up possibilities for new experimental approaches for coupling to plasmonic systems and for increased axial resolution in total internal reflection imaging, in particular in the terahertz spectrum.

The comprehensive analyses of exciton states and absorption spectra from freestanding monolayer transition metal dichalcogenides such as ${\mathrm{MoS}}_2, {\mathrm{MoSe}}_2, {\mathrm{MoTe}}_2, {\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$ are theoretically presented in the Wannier−Mott exciton theory. We propose an efficient and simple exact diagonalization method based on a variationally optimized two-dimensional (2D) modified Laguerre basis set, which has been successfully applied to calculate both the ground and excited states. The convergence of the method as a function of the basis set size was analyzed in detail. The modified Laguerre basis functions were very closely concentrated in space, and they led to a rather rapid convergence. Moreover, the convergence rate was faster under variational optimization. Our results regarding the exciton binding energies of a ground state with even a small number of basis states are in excellent agreement with those of the density-function theory calculations in the literature [I. Kylänpää and H.-P. Komsa, Phys. Rev. B 92, 205418 (2015)]. The exciton states appeared in an anomalous energy-level ordering of the orbital angular momentum caused by the dielectric screening effect. The exciton absorption spectra exhibited strong absorption lines of the nonhydrogenic exciton Rydberg series, which was dominated by the s-type exciton states. There were two prominent low-energy peaks of the A and B excitons, and the A exciton was slightly higher in intensity than the B exciton, which is in good agreement with the experimental observations. In general, our presented exact diagonalization method based on a variationally optimized 2D modified Laguerre basis set has proven to be applicable to more general cases of screened potentials in 2D materials and atomic physics, as well as providing a simple approach for investigating exciton properties.