In this paper, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of two-dimensional and three-dimensional (2D/3D) topological insulators and high-order topological insulators. We show that in the presence of either a two-fold-rotational symmetry or a mirror symmetry, a gauge-invariant quantity can be defined for arbitrary one-dimensional (1D) lines in the Brillouin zone. Such 1D quantities provide a new pathway to compute the $Z_2$ index of topological insulators. In contrast to the generic setup, where the $Z_2$ index generally involves 2D planes in the Brillouin zone with a globally defined smooth gauge, this 1D approach only involves some 1D lines in the Brillouin zone without requiring a global gauge. Such a simplified approach can be used in any time-reversal invariant insulators with a two-fold crystalline symmetry, which can be found in 30 of the 32 point groups. In addition, this 1D quantity can be further generalized to higher-order topological insulators to compute the magnetoelectric polarization $P_3$.

Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states. For the exploration of these, renormalization group methods are an appropriate, flexible tool that takes into account the mutual influence of competing tendencies. Here we show that, within reasonable, nontrivial approximations, the functional renormalization group known from simpler two-dimensional systems can be employed for the large-unit cell moiré superlattices with more than 10 000 bands, remedying the need to employ ad hoc restrictions to effective low-energy theories of a few bands and/or effective continuum theories. This provides a description on the atomic scale, allowing one to absorb available ab initio information on the model parameters and therefore lending the analysis a more concrete quantitative character. For the case of twisted bilayer graphene models, we explore the leading ordering tendencies, depending on the band filling and the range of interactions. The results indicate a delicate balance between distinct magnetically ordered ground states, as well as the occurrence of a charge modulation within the moiré unit cell for sufficiently nonlocal repulsive interaction.

We investigate the dynamical properties of a strongly disordered micropolar lattice made up of cubic block units. This phononic lattice model supports both transverse and rotational degrees of freedom, hence its disordered variant posseses an interesting problem as it can be used to model physically important systems like beamlike microstructures. Different kinds of single site excitations (momentum or displacement) on the two degrees of freedom are found to lead to different energy transports, both superdiffusive and subdiffusive. We show that the energy spreading is facilitated both by the low-frequency extended waves and a set of high-frequency modes located at the edge of the upper branch of the periodic case for any initial condition. However, the second moment of the energy distribution strongly depends on the initial condition and it is slower than the underlying one-dimensional harmonic lattice (with one degree of freedom). Finally, a limiting case of the micropolar lattice is studied where Anderson localization is found to persist and no energy spreading takes place.

Paradigmatic quantum spin liquid has been in the past closely linked to the high-temperature superconductivity. Here we focus on a layered 1T-${\mathrm{TaS}}_2$, which has recently emerged as a surprising candidate for a quantum spin liquid on a triangular lattice. Upon doping 1T-${\mathrm{TaS}}_2$ with Se, the ${}^{77}\mathrm{Se}$ nuclear magnetic resonance and ${}^{181}\mathrm{Ta}$ nuclear quadrupole resonance data show a remarkable robustness of the quantum spin liquid at low Se doping levels despite the growth of inhomogeneities in the electronic state. A dramatic change in the low-energy electronic excitations are observed in samples with a moderate Se content where the Mott insulating state gives way to a correlated metal and a low-temperature superconductivity. The effects of antiferromagnetic correlations can still be traced in the normal state above the superconducting critical temperature $T_{\mathrm{c}}=3.5\mathrm{K}$ and may, together with the underlying disorder, account for the large superconducting gap-to-$T_{\mathrm{c}}$ ratio $2\mathrm{\Delta }/k_{\mathrm{B}}{T}_{\mathrm{c}}\approx 7$ deduced from the scanning tunneling microscopy.

An in-depth analysis of Zn/Al-doped nickel ferrites grown by reactive magnetron sputtering is relevant due to their promising characteristics for applications in spintronics. The material is insulating and ferromagnetic at room temperature with an additional low magnetic damping. By studying the complex interplay between strain and cation distribution their impact on the magnetic properties, i.e., anisotropy, damping, and $g$-factor is unravelled. In particular, a strong influence of the lattice site occupation of ${\mathrm{Ni}}_{\text{Td}}^{2+}$ and cation coordination of ${\mathrm{Fe}}_{\text{Oh}}^{2+}$ on the intrinsic damping is found. Furthermore, the critical role of the incorporation of ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Al}}^{3+}$ is evidenced by comparison to a sample of altered composition. Specifically, the dopant ${\mathrm{Zn}}^{2+}$ is evidenced as a tuning factor for ${\mathrm{Ni}}_{\text{Td}}^{2+}$ and therefore unquenched orbital moment directly controlling the $g$-factor. A strain-independent reduction of the magnetic anisotropy and damping by adapting the cation distribution is demonstrated.

A fully oxygenated hexagonal 12-layer perovskite $\mathrm{BaFe}{\mathrm{O}}_3$ with nominal $\mathrm{F}{\mathrm{e}}^{4+}$ was obtained by high-pressure synthesis. The structure consists of face-sharing $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_9$ octahedral trimers and corner-sharing octahedra. A remarkable series of electronic transitions that relieve the electronic instability of $\mathrm{F}{\mathrm{e}}^{4+}$ are discovered on cooling; $2\mathrm{F}{\mathrm{e}}^{4+}\to \mathrm{F}{\mathrm{e}}^{3+}+\mathrm{F}{\mathrm{e}}^{5+}$ charge disproportionation and ordering over two sites accompanied by a structural distortion at 500 K; charge disproportionation of the remaining $\mathrm{F}{\mathrm{e}}^{4+}$ with magnetic order at 280 K; and an unprecedented charge interchange where $\mathrm{F}{\mathrm{e}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{5+}$ states are exchanged between two sites with spin orientation change at 50 K. These properties demonstrate the presence of multiple competing ground states in this complex, highly condensed network of corner- and face-sharing octahedra.

Two-dimensional van der Waals magnets with multiple functionalities are becoming increasingly important for emerging technologies in spintronics and valleytronics. Application of external pressure is one method to cleanly explore the underlying physical mechanisms of the intrinsic magnetism. In this paper, the magnetic, electronic, and structural properties of van der Waals-layered, Fe-deficient ${\mathrm{Fe}}_{3-x}\mathrm{Ge}{\mathrm{Te}}_2$ are investigated. Magnetotransport measurements show a monotonic decrease in the Curie temperature $\left(T_C\right)$ and the magnetic moment with increasing pressure up to 13.9 GPa. The electrical resistance of ${\mathrm{Fe}}_{3-x}\mathrm{Ge}{\mathrm{Te}}_2$ shows a change from metallic to a seemingly nonmetallic behavior with increasing pressure. High-pressure angle dispersive powder x-ray diffraction shows a monotonic compression of the unit cell and a reduction of the volume by $\sim 25\%$ with no evidence of structural phase changes up to 29.4(4) GPa. We suggest that the decrease in the $T_C$ due to pressure results from increased intralayer coupling and delocalization that leads to a change in the exchange interaction.

Nanomagnets with giant magnetic anisotropy energy and long coherence time are desired for various technological innovations such as quantum information procession and storage. Based on the first-principles calculations and model analyses, we demonstrate that a single uranium atom substituting Al on the ${\mathrm{Al}}_2{\mathrm{O}}_3\left(0001\right)$ surface may have high structural stability and large magnetic anisotropy energy up to 48 meV per uranium atom. As the magnetization resides in the localized $f$ shell and is not much involved in chemical bonding with neighbors, long coherence time up to $\sim 1.6\mathrm{mS}$ can be achieved for the quantum spin states. These results suggest a different strategy for the search of ultrasmall magnetic units for diverse applications in the quantum information era.

We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product $q_{T}l$ ($q_T$ is the wave vector of thermal phonons and $l$ is the elastic mean free path of electrons). In the temperature range 14–30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law $1/{\tau }_{\mathrm{e}\text{−}\mathrm{ph}}\sim T^{\mathrm{n}}$ with the exponents $n\approx 3.2–3.8$. We found that in this temperature range ${\tau }_{\mathrm{e}\text{−}\mathrm{ph}}$ and $n$ of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9–17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.

We report the atomic- and nanosecond-scale quantification of kinetics of a shock-driven phase transition in Zr metal. We uniquely make use of a multiple shock-and-release loading pathway to shock Zr into the $\beta$ phase and to create a quasisteady pressure and temperature state shortly after. Coupling shock loading with in situ time-resolved synchrotron x-ray diffraction, we probe the structural transformation of Zr in the steady state. Our results provide a quantified expression of kinetics of formation of $\beta$-Zr phase under shock loading: transition incubation time, completion time, and crystallization rate.

We theoretically study the nonlinear magnetic resonance driven by intense lasers or electromagnetic waves in a fully polarized frustrated magnet near a less-visible spin-nematic ordered phase. In general, both magnons and magnon pairs (two-magnon bound state) appear as the low-energy excitation in the saturated state of spin-nematic magnets. Their excitation energies are usually in the range between 10 GHz and 10 THz. Magnon pairs with angular momentum $2\hslash$ can be excited by the simultaneous absorption of two photons, and such multiphoton processes occur if the applied THz laser is strong enough. We compute laser-driven magnetic dynamics of a frustrated four-spin system with both magnon ($\hslash$) and magnon-pair ($2\hslash$)-like excitations, which is analogous to a macroscopic frustrated magnet with a spin-nematic phase. We estimate the required strength of the magnetic field of a laser for the realization of two-photon absorption, taking into account dissipation effects with the Lindblad equation. We show that an intense THz laser with an ac magnetic field of 0.1–1.0 T is enough to observe magnon-pair resonance.

We report structural and atomic transport properties of liquid Ti, which are poorly understood at high temperatures. The studies were performed using molecular dynamics (MD) simulation based on a potential model that accounts for the role of $d$ electrons. The interactions between ions are described by a pair potential built within the pseudopotential formalism obtained by an inverse scattering approach that consists of a repulsive core and long-range Friedel oscillations. The parameters determining the $s$- and $d$- electron contributions to the potential are deduced from the knowledge of liquid structure and diffusion coefficient at the melting temperature. The clear connection between local order and atomic transport in liquids emerges from the molecular dynamics simulation. The calculated pair correlation function and structure factor show very good agreement with recently available ab-initio molecular dynamics (AIMD) and experimental results, respectively. By comparing the temperature dependence of diffusion coefficient and viscosity, the effective pair potential based on the pseudopotential method provides a significantly important portion of the high temperature properties of liquid Ti and strongly validates the accuracy of the method. The activation energy of the liquid metals is obtained by fitting the Arrhenius formula. The approach presented herein gives a broader and deeper insight into the transition metal liquid state.

We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. Focusing on the role of spatially extended spin-spin correlations in determining the phases of the system, we characterize the spatial structure of the correlations in the steady state, as well as their temporal dynamics. In dimension one we use essentially exact matrix-product-operator simulations on large systems, and pushing these calculations to dimension two, we obtain accurate results on small cylinders. We also employ an approximation scheme based on solving the dynamics of the mean field dressed by the feedback of quantum fluctuations at leading order. This approach allows us to study the effect of correlations in large lattices with over one hundred thousand spins, as the spatial dimension is increased up to five. In dimension two and higher we find two new states that are stabilized by quantum correlations and do not exist in the mean-field limit of the model. One of these is a steady state with mean magnetization values that lie between the two bistable mean-field values and whose correlation functions have properties reminiscent of both. The correlation length of the new phase diverges at a critical point, beyond which we find emerging a new limit cycle state with the magnetization and correlators oscillating periodically in time.

Even though electron-phonon coupling is one of the most important parameters governing material evolution after ultrafast energy deposition it remains the most unexplored one. In this work we apply the dynamical coupling approach to calculate the nonadiabatic electron-ion energy exchange in nonequilibrium solids with the electronic temperature high above the atomic one. It is implemented into the tight-binding molecular dynamics code and used to study electron-phonon coupling in various elemental metals. The approach developed is a universal scheme applicable to electronic temperatures up to a few electron volts and to arbitrary atomic configurations and dynamics. We demonstrate that the calculated electron-ion (electron-phonon) coupling parameter agrees well with the available experimental data in the high-electronic-temperature regime, validating the model. The following materials are studied here: fcc metals Al, Ca, Ni, Cu, Sr, Y, Zr, Rh, Pd, Ag, Ir, Pt, Au, and Pb; hcp metals Mg, Sc, Ti, Co, Zn, Tc, Ru, Cd, Hf, Re, and Os; bcc metals V, Cr, Fe, Nb, Mo, Ba, Ta, and W; a diamond cubic lattice metal Sn; specific cases of Ga, In, Mn, Te, and Se; and additionally semimetal graphite and the semiconductors Si and Ge. For these materials, we provide an estimation of the electron-phonon coupling at elevated electron temperatures, which can be used in various models simulating ultrafast energy deposition in matter. We also discuss the dependence of the coupling parameter on atomic mass, temperature, and density.

Starting from a continuum-model description, we develop a microscopic weak-coupling theory for superconductivity in twisted double-bilayer graphene. We study both electron-phonon and entirely electronic pairing mechanisms. In each case, the leading superconducting instability transforms under the trivial representation $A$ of the point group $C_3$ of the system, while the subleading pairing phases belong to the $E$ channel. We explicitly compute the momentum dependence of the associated order parameters and find that the leading state has no nodal points for electron-phonon pairing but exhibits six sign changes on the Fermi surface if the Coulomb interaction dominates. On top of these system-specific considerations, we also present general results relevant to other correlated graphene-based moiré superlattice systems. We show that, irrespective of microscopic details, triplet pairing will be stabilized if the collective electronic fluctuations breaking the enhanced $\text{SU}{\left(2\right)}_{+}\times \text{SU}{\left(2\right)}_{-}$ spin symmetry of these systems are odd under time reversal, even when the main $\text{SU}{\left(2\right)}_{+}\times \text{SU}{\left(2\right)}_{-}$-symmetric part of the pairing glue is provided by phonons. Furthermore, we discuss the disorder sensitivity of the candidate pairing states and demonstrate that the triplet phase is protected against disorder on the moiré scale.

It was recently discovered that a conductive, metallic state is formed on the surface of some insulating oxides. First observed on ${\mathrm{SrTiO}}_3$ (001), it was then found in other compounds as diverse as anatase ${\mathrm{TiO}}_2$, ${\mathrm{KTaO}}_3$, ${\mathrm{BaTiO}}_3$, ZnO, and also on different surfaces of ${\mathrm{SrTiO}}_3$ (or other oxides) with different symmetries. The spatial extension of the wave function of this electronic state is of only a few atomic layers. Experiments indicate its existence is related to the presence of oxygen vacancies induced at or near the surface of the oxide. We present a simplified model aimed at describing the effect of its small spatial extension on measurements of its three-dimensional (3D) electronic structure by angular resolved photoemission spectroscopy. For the sake of clarity, we base our discussion on a simple tight-binding scheme plus a confining potential that is assumed to be induced by the oxygen vacancies. Our model parameters are, nevertheless, obtained from density functional calculations. With this methodology, we can explain, from a very simple concept of selective interference, the “wobbling,” i.e., the photoemission intensity modulation and/or apparent dispersion of the Fermi surface and spectra along the out-of-plane $\left(k_z\right)$ direction, and the “mixed 2D/3D” characteristics observed in some experiments. We conclude that the critical model parameters for such an effect are the relative strength of the electronic hopping of each band and the height/width aspect ratio of the surface confining potential. By considering recent photoemission measurements, in light of our findings, we can get relevant information on the electronic wave functions and the nature of the confining potential.

A graphene sheet biased with a drift electric current offers a unique opportunity to attain unidirectional, backscattering-immune, and subwavelength light propagation, as proposed by T. A. Morgado and M. G. Silveirinha [ACS Photonics 5, 4253 (2018)]. Here, we investigate in detail the impact of the intrinsic nonlocal response of graphene in the dispersion characteristics of the current-driven plasmons supported by single-layer and double-layer graphene systems. It is theoretically shown that even though the nonlocal effects weaken the spectral asymmetry of the plasmon dispersion, the studied platforms can support unidirectional backscattering-immune guided modes. Our analysis also confirms that the drift-current bias can effectively pump the graphene plasmons and enhance the propagation distance. Moreover, it is shown that the nonreciprocity and optical isolation can be boosted by pairing two drift-current-biased graphene sheets due to the enhanced radiation drag by the drifting electrons.

The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode structure and multipole content which determines the linear and nonlinear response of the resonator. Here, we develop the algorithm for the classification of eigenmodes in resonators of the simplest shapes depending on their symmetry group. For each type of mode, we find its multipole content bridging the gap between the modal and multipolar descriptions. As an illustrative example, we apply the developed formalism to the analysis of a dielectric triangular prism and demonstrate the formation of high-$Q$ resonances originating due to the suppression of scattering through the main multipole channel. The developed approach allows one to engineer, predict, and explain scattering phenomena and optical properties of resonators and meta-atoms based only on their symmetry without the need for numerical simulations, and it can be used for the design of photonic and microwave devices.

${\mathrm{In}}_2{\mathrm{O}}_3$ is an $n$-type transparent semiconducting oxide possessing a surface electron accumulation layer (SEAL) like several other relevant semiconductors, such as InAs, InN, ${\mathrm{SnO}}_2$, and ZnO. Even though the SEAL is within the core of the application of ${\mathrm{In}}_2{\mathrm{O}}_3$ in conductometric gas sensors, a consistent set of transport properties of this two-dimensional electron gas (2DEG) is missing in the present literature. To this end, we investigate high-quality single-crystalline as well as textured doped and undoped ${\mathrm{In}}_2{\mathrm{O}}_3$(111) films grown by plasma-assisted molecular beam epitaxy to extract transport properties of the SEAL by means of Hall effect measurements at room temperature while controlling the oxygen adsorbate coverage via illumination. The resulting sheet electron concentration and mobility of the SEAL are $\approx 1.5\times {10}^{13}{\mathrm{cm}}^{-2}$ and $\approx 150{\mathrm{cm}}^2/\mathrm{Vs}$, respectively, both of which are strongly reduced by oxygen-related surface adsorbates from the ambient air. Our transport measurements further demonstrate a systematic reduction of the SEAL by doping ${\mathrm{In}}_2{\mathrm{O}}_3$ with the deep compensating bulk acceptors Ni or Mg. This finding is supported by x-ray photoelectron spectroscopy (XPS) measurements of the surface band bending and SEAL electron emission. Quantitative analyses of these XPS results using self-consistent, coupled Schrödinger-Poisson calculations indicate the simultaneous formation of compensating bulk donor defects (likely oxygen vacancies), which almost completely compensate the bulk acceptors. Finally, an enhancement of the thermopower by reduced dimensionality is demonstrated in ${\mathrm{In}}_2{\mathrm{O}}_3$: Seebeck coefficient measurements of the surface 2DEG with partially reduced sheet electron concentrations between $3\times {10}^{12}$ and $7\times {10}^{12}{\mathrm{cm}}^{-2}$ (corresponding average volume electron concentration between $1\times {10}^{19}$ and $2.3\times {10}^{19}{\mathrm{cm}}^{-3}$) indicate a value enhanced by $\approx 80\%$ compared to that of bulk Sn-doped ${\mathrm{In}}_2{\mathrm{O}}_3$ with comparable volume electron concentration.