We study the growth of entanglement entropy and bond dimension with time in density matrix renormalization group simulations of the periodically driven single-impurity Anderson model. The growth of entanglement entropy is found to be related to the ordering of the bath orbitals and to the relation of the driving period $T$ to the convergence radius of the Floquet-Magnus expansion. Ordering the bath orbitals by their Floquet quasienergy is found to reduce the exponential growth rate of the computation time at intermediate driving periods, suggesting new ways to optimize matrix product state calculations of driven systems.

Global symmetry (0-symmetry) acts on the whole space while higher $k$-symmetry acts on all the codimension-$k$ closed subspaces. The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries (unless we engineer fine-tuned toy models). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that the emergent spontaneously broken higher symmetries are nothing but a kind of topological order. Thus the study of emergent spontaneously broken higher symmetries is a study of topological order. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possible phases induced by certain types of excitations in topological orders. (Anomalous) higher symmetry can also emerge in gapless systems if the gapless excitations contain gapless gauge fields. In particular, EM condensed matter systems that include the dynamical EM field have an emergent anomalous $U\left(1\right)$-1-symmetry below the energy gap of the magnetic monopoles. So EM condensed matter systems can realize some physical phenomena of anomalous higher symmetry. In particular, any gapped liquid phase of an EM condensed matter system (induced by arbitrary fluctuations and condensations of electric charges and photons) must have a nontrivial bosonic topological order.

A triangular domain structure within hexagonal monolayer ${\mathrm{WS}}_2$ is found to be induced by edge polarization. Based on density-functional theory calculations, the local electrostatic potential over ${\mathrm{WS}}_2$ is investigated, and with the S-adatom and ${\mathrm{S}}_2$-addimer reconstructions at the W edges, the domains facing the W edges are found to be lower by up to 1.8 eV in the electrostatic potential than those facing the S edges. The edge-induced band bending in the terminated two-dimensional system is a two-dimensional analogy of the surface band bending effect in the terminated three-dimensional system. The largest potential difference is found to be comparable to the electronic gap of ${\mathrm{WS}}_2$, and near the edges, the W and S domains can be $n$- and $p$-type doped, respectively, by which the hexagonal monolayer ${\mathrm{WS}}_2$ can be applied to a bipolar electronic junction device.

Using femtosecond nonlinear photoemission electron microscopy (PEEM) we provide a detailed characterization of slow light in a small-size asymmetric photonic crystal structure. We show that PEEM is capable of providing a unique description of the light propagation in such structures by direct imaging of the guided mode. This noninvasive characterization technique allows modal properties such as effective index, phase velocities, and group velocities to be determined. Combining experimental results with finite element method simulation calculations, we study slow light phenomena in a photonic crystal defect mode, and we produce a comprehensive picture of the mechanisms behind it. Our results illustrate the usefulness of electron microscopy in exploring nano-optical applications.

We investigate topological characteristics of the photon-dressed band structure of the $\alpha \text{−}{\mathcal{T}}_3$ lattice on being driven by off-resonant circularly polarized radiation. We obtain exact analytical expressions of the quasienergy bands over the first Brillouin zone. The broken time-reversal symmetry caused by the circularly polarized light lifts the triple point degeneracy completely at both the Dirac points. The gaps become unequal at $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ (except at $\alpha =0$ and 1), which reveals the absence of inversion symmetry in the system. At $\alpha =1/\sqrt{2}$, the gap between the flat and valence bands closes at $\mathbf{K}$, while that between the conduction and flat bands closes at ${\mathbf{K}}^{\prime }$, thereby restoring a semimetalic phase. At the gap closing point ($\alpha =1/\sqrt{2}$) which is independent of the radiation amplitude, there is a reappearance of low-energy Dirac cones around $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points. Under the influence of the circularly polarized radiation, the $\alpha \text{−}{\mathcal{T}}_3$ lattice is transformed from semimetal to a Haldane-like Chern insulator characterized by nonzero Chern number. The system undergoes a topological phase transition from $\mathcal{C}=1(-1)$ to $\mathcal{C}=2(-2)$ at $\alpha =1/\sqrt{2}$, where $\mathcal{C}$ is the Chern number of the valence (conduction) band. This sets an example of a multiband system having larger Chern number. These results are supported by the appearance of chiral edge states in an irradiated $\alpha \text{−}{\mathcal{T}}_3$ nanoribbon.

We analyze spin and orbital angular momenta in monochromatic acoustic wave fields in a homogeneous medium. Despite being purely longitudinal (curl-free), inhomogeneous acoustic waves generically possess nonzero spin angular momentum density caused by the local rotation of the vector velocity field. We show that the integral spin of a localized acoustic wave vanishes in agreement with the spin-0 nature of longitudinal phonons. We also show that the helicity or chirality density vanishes identically in acoustic fields. As an example, we consider nonparaxial acoustic Bessel beams carrying well-defined integer orbital angular momentum, as well as nonzero local spin density, with both transverse and longitudinal components. We describe the nontrivial polarization structure in acoustic Bessel beams and indicate a number of observable phenomena, such as nonzero energy density and purely circular transverse polarization in the center of the first-order vortex beams.

The magnetic structure of a monolayer-thick $\mathrm{GdA}{\mathrm{u}}_2$ surface alloy on Au(111) has been investigated down to the atomic level by spin-polarized scanning tunneling microscopy. Spin-resolved tunneling spectroscopy combined with density-functional theory calculations reveal the local spin polarization of both Gd and Au atomic sites within the surface alloy. Moreover, the impact of dislocation lines on the atomic-scale magnetic structure as well as on the local coercive field strength is demonstrated.

We quantitatively evaluated oxygen octahedral distortions in epitaxial thin films of the itinerant ferromagnet, ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Co}{\mathrm{O}}_3$ (LSCO), and investigated their impact on strucure-property relationships. The compressively strained film on a $\mathrm{LaAl}{\mathrm{O}}_3$ substrate has a lower electrical resistivity and higher ferromagnetic transition temperature than the tensilely strained film on a ${\mathrm{La}}_{0.30}{\mathrm{Sr}}_{0.70}{\mathrm{Al}}_{0.65}{\mathrm{Ta}}_{0.35}{\mathrm{O}}_3$ substrate. The magnetic anisotropy is also found to depend on the type of strain, with perpendicular magnetic anisotropy induced in the compressively strained film and in-plane magnetization seen in the tensilely strained film. Our synchrotron x-ray-diffraction measurements and quantitative analysis reveal distinct oxygen octahedral distortions accommodated in these films and show that the out-of-plane and in-plane Co–O bond lengths of the compressively strained film are comparable to the in-plane and out-of-plane bond lengths of the tensilely strained film. These results indicate that the bond-length changes in LSCO modify hybridization between Co $3d$ and O2p orbitals, leading to the strain-dependent properties. These results highlight the significant role of octahedral distortions for structure-property relationships in the strained LSCO films.

Experiments on planar Josephson-junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a one-dimensional channel in the junction of a two-dimensional electron gas (2DEG) proximitized by two spatially separated superconductors. The channel, which is below the break between the superconductors, is not in direct contact with the superconducting leads, so that proximity coupling is expected to be weaker and less well controlled than in the simple nanowire configuration widely discussed in the literature. This provides a strong incentive for this paper which investigates the nature of proximitization in these Josephson-junction architectures. At a microscopic level we demonstrate how and when it can lead to topological phases. We do so by going beyond simple tunneling models through solving self-consistently the Bogoliubov-de Gennes equations of a heterostructure multicomponent system involving two spatially separated $s$-wave superconductors in contact with a normal Rashba spin-orbit-coupled 2DEG. Importantly, within our self-consistent theory we present ways of maximizing the proximity-induced superconducting gap by studying the effect of the Rashba spin-orbit coupling, chemical potential mismatch between the superconductor and 2DEG, and sample geometry on the gap. Finally, we note (as in experiment) a Fulde-Ferrell-Larkin-Ovchinnikov phase is also found to appear in the 2DEG channel, albeit under circumstances which are not ideal for the topological superconducting phase.

Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static. Time dependence naturally arises, however, when flux is modulated or when flux noise is considered. In this case, application of the existing quantization procedure can lead to inconsistencies. To resolve these, we generalize circuit quantization to incorporate time-dependent external flux.

The superconducting ground state of recently discovered ZrIrSi is probed by means of muon spin rotation and relaxation ($\mu \mathrm{SR}$) and resistivity measurements. The occurrence of superconductivity at $T_{\mathrm{C}}=1.7$ K is confirmed by resistivity measurements. Zero field $\mu \mathrm{SR}$ study revealed that below $T_{\mathrm{C}}$ there is no spontaneous magnetic field in the superconducting state, which indicates time-reversal symmetry is preserved in the case of ZrIrSi. From transverse field $\mu \mathrm{SR}$ measurement, we have estimated the superfluid density as a function of temperature, which is described by an isotropic $s$-wave model with a superconducting gap $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_{\mathrm{C}}=5.10\left(2\right)$ and indicates the presence of strong coupling superconductivity. Ab initio electronic structure calculation indicates that there are four bands passing through the Fermi level, forming four Fermi surface pockets. We find that the low-energy bands are dominated by the $4d$ orbitals of the transition metal Zr, with substantially less weight from the $5d$ orbitals of the Ir atoms.

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here, we show that the confinement of quasiparticles can also suppress transport even if the dynamics are generated by nondisordered Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields, prepared in a paradigmatic state with a domain wall and thus with a spatially varying energy density. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from “hot” to “cold” regions of the chain is suppressed for all accessible times. We argue that this phenomenon is general, as it relies solely on the emergence of confinement of excitations.

We report the hydrostatic pressure induced two topological phase transitions in strong spin-orbit coupled material $\mathrm{TlBi}{\mathrm{S}}_2$ at room temperature. Frequencies of the ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{E}}_{\mathrm{g}}$ phonons are observed to increase monotonically up to $\sim 4.0\mathrm{GPa}$, but with a clear slope change in ${\mathrm{A}}_{1\mathrm{g}}$ mode at $\sim 1.8\mathrm{GPa}$. Interestingly, there are two clear anomalies noticed in phonon linewidths of ${\mathrm{E}}_{\mathrm{g}}$ mode at pressures $\sim 0.5$ and $\sim 1.8\mathrm{GPa}$. Such anomalies are evidence of isostructural electronic transitions associated with unusual electron-phonon coupling. The high-pressure synchrotron powder diffraction and Raman show a first-order phase transition above 4 GPa. First-principles density functional theory-based calculations of electronic band structure, topological invariant ${\mathbb{Z}}_2$ and mirror Chern number $n_M$ reveal that the phonon anomalies at $\sim 0.5$ and $\sim 1.8\mathrm{GPa}$ are linked to the band inversions at $\mathrm{\Gamma }$ and $F$ points of the Brillouin zone respectively. The first band inversion at $\mathrm{\Gamma }$ point at $\sim 0.5$ GPa changes the ${\mathbb{Z}}_2$ from 0 to 1 leading to the transition of $\mathrm{TlBi}{\mathrm{S}}_2$ system into a topological insulator. The second band inversion at $F$ point at $\sim 1.8\mathrm{GPa}$ results in $n_M=2$, revealing a transition to a topological crystalline insulating state. Therefore the applied pressure systematically tunes the electronic states of $\mathrm{TlBi}{\mathrm{S}}_2$ from a normal semiconductor to a topological insulator and finally into a topological crystalline insulator at two distinct pressures of $\sim 0.5$ and $\sim 1.8\mathrm{GPa}$ respectively, before undergoing a structural phase transition at $\sim 4\mathrm{GPa}$.

We investigate elastic-wave propagation in a spatially dispersive multilayered, totally passive metamaterial system. At oblique incidence a longitudinal (acoustic) wave can convert to transverse in the solid material comprising the layers, but when the incident wave enters the multilayer from a solid as opposed to a liquid medium, the incident transverse component supported by the solid medium indirectly causes the longitudinal transmission response to be greatly modified, with a similar result for the transverse wave exiting the multilayer into a solid medium in response to an incident longitudinal wave. The conversion between longitudinal and transverse waves is found to lead to the emulation of a characteristic nonreciprocal phenomenon at some frequencies: a directionality in the transmission response, sometimes simultaneously with the reflection response. The directionality can be exploited, for example, in the construction of antiseismic structures or breakwater structures. The inclusion of gain and loss elements can strongly enhance the directionality. Periodicity-breaking defects can cause a great variability in the response, enabling the use of devices based on this phenomenon as sensors.

We report the effects of cobalt doping on the magnetic properties of two-dimensional van der Waals ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. Single crystals of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_3{\mathrm{GeTe}}_2$ with $x=0–0.78$ were successfully synthesized and characterized with x-ray diffraction, energy dispersive x-ray spectroscopy, and magnetization measurements. Both the Curie-Weiss temperature and ferromagnetic (FM) ordered moment of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ are gradually suppressed upon Co doping. A kink in the zero-field-cooling low field $M\left(T\right)$ curve which is previously explained as an antiferromagnetic transition is observed for samples with $x=0–0.58$. Our detailed magnetization measurements and theoretical calculations strongly suggest that this kink is originated from the pinning of magnetic domain walls. The domain pinning effects are suddenly enhanced when the doping concentration of cobalt is around 50%, both the coercive field $H_c$ and the magnetic remanence to saturated magnetization ratio $M_R/M_S$ are largely improved and a hard magnetic phase emerges in bulk single crystal samples. The strong doping dependent magnetic properties suggest more spintronic applications of ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$.

We study spin eigenexcitation of a skyrmion in a collinear uniaxial antiferromagnet by means of analytical and numerical methods. We found a discrete spectrum of modes which are localized on the skyrmion. Based on a qualitatively different dependence of the mode eigenfrequencies on the skyrmion radius $R_0$, we divided all localized modes into two branches. Modes of the low-frequency branch are analogous to the localized magnon modes of a ferromagnetic skyrmion, their frequencies scale as $R_0^{-2}$ for the large radius skyrmions, while the modes of the high-frequency branch have no direct ferromagnetic counterpart and do not demonstrate the significant radius dependence and are compactly situated at the magnon continuum. All the modes, except the radially symmetrical one, are doubly degenerated with respect to the sense of rotation around the skyrmion center: clockwise or counterclockwise. An out-of-plane magnetic field removes the degeneracy (for all modes except translational), resulting in a frequency splitting, which for the small fields is linear in field. The possibility of excitation of the modes by means of the external ac magnetic fields is discussed. To explain our numerical results for the low-frequency modes, we introduce a string model for an antiferromagnetic domain wall representing boundary of the large radius skyrmion.

We report the discovery of superconductivity in high-quality single crystals of transition-metal pnictides WP grown by chemical vapor transport method. Bulk superconductivity is observed at $T_{\text{c}}\sim 0.8\mathrm{K}$ at ambient pressure by electrical resistivity, ac magnetic susceptibility, and specific-heat measurements. The effects of magnetic field on the superconducting transitions are studied, leading to a large anisotropy parameter around 2 with the in-plane and out-of-plane upper critical fields of ${\mu }_0{H}_{\text{c}2,\parallel }=17.2\mathrm{mT}$ and ${\mu }_0{H}_{\text{c}2,\perp }=8.5\mathrm{mT}$, respectively. The low value of electron-phonon coupling estimated from the normal-state resistivity and specific-heat measurements suggest that WP is a weak-coupling BCS superconductor. Our finding demonstrates that WP is the first superconductor among $5d$–transition metal pnictides with MnP-type structure at ambient pressure, which will help in the search for new superconductors in transition-metal pnictides.

Antiferromagnetism and $d$-wave superconductivity are the most important competing ground-state phases of cuprate superconductors. Using cellular dynamical mean-field theory for the Hubbard model, we revisit the question of the coexistence and competition of these phases in the one-band Hubbard model with realistic band parameters and interaction strengths. With an exact diagonalization solver, we improve on previous works with a more complete bath parametrization which is carefully chosen to grant the maximal possible freedom to the hybridization function for a given number of bath orbitals. Compared with previous incomplete parametrizations, this general bath parametrization shows that the range of microscopic coexistence of superconductivity and antiferromagnetism is reduced for band parameters for ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ (NCCO) and confined to electron doping with parameters relevant for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ (YBCO).

An essential ingredient in many model Hamiltonians, such as the Hubbard model, is the effective electron-electron interaction $U$, which enters as matrix elements in some localized basis. These matrix elements provide the necessary information in the model, but the localized basis is incomplete for describing $U$. We present a systematic scheme for computing the manifestly basis-independent dynamical interaction in position representation, $U(\mathbf{r},{\mathbf{r}}^{\prime };\omega )$, and its Fourier transform to time domain, $U(\mathbf{r},{\mathbf{r}}^{\prime };\tau )$. These functions can serve as an unbiased tool for the construction of model Hamiltonians. For illustration we apply the scheme within the constrained random-phase approximation to the cuprate parent compounds ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$ within the commonly used one- and three-band models, and to nonsuperconducting ${\mathrm{SrVO}}_3$ within the $t_{2g}$ model. Our method is used to investigate the shape and strength of screening channels in the compounds. We show that the $\mathrm{O}2p_{x,y}-\mathrm{Cu}3d_{x^2-y^2}$ screening gives rise to regions with strong attractive static interaction in the minimal (one-band) model in both cuprates. On the other hand, in the minimal ($t_{2g}$) model of ${\mathrm{SrVO}}_3$ only regions with a minute attractive interaction are found. The temporal interaction exhibits generic damped oscillations in all compounds, and its time integral is shown to be the potential caused by inserting a frozen point charge at $\tau =0$. When studying the latter within the three-band model for the cuprates, short time intervals are found to produce a negative potential.

We observe optical second harmonic generation (SHG) on the $1S$ exciton resonance of the yellow exciton series in ${\mathrm{Cu}}_2\mathrm{O}$ in four crystal directions ([001], $\left[\overline{1}10\right],\left[11\overline{2}\right]$, and [111]). For light with the $k$-vector parallel [001] and $\left[\overline{1}10\right]$, SHG is symmetry forbidden in an ideal crystal according to band structure. We explain the observation of SHG signals in the forbidden geometries by local strain inducing splitting and mixing of the $1S$ components. Experimental data and a microscopic theory confirm that this effect observed on the $1S$ exciton requires a relatively long exciton lifetime. The SHG signals of excitons with principal quantum number $n\ge 2$ are compliant with selection rules derived by group theory from the symmetry of an unstrained crystal.