Hafnium dioxide $\left(\mathrm{Hf}{\mathrm{O}}_2\right)$ is a promising ferroelectric (FE) material for achieving high-density nonvolatile memory and neuromorphic computing due to its compatibility with the mainstream integrated circuit technology and the surprisingly enhanced ferroelectricity by reduced thickness. The FE switching dynamics is essential to the device performance, but the complexity of $\mathrm{Hf}{\mathrm{O}}_2$ atomic structure causes unknown of various FE switching paths and domain-wall configurations. Here, we demonstrate that its low-barrier paths and domain walls can be comprehensively found and understood from a perspective of topological symmetry. By discussing pseudochirality and equivalent transformation relations in a crystal with first principles and lattice modes, we classify and analyze 4 low-barrier FE switching paths and 93 irreducible topology domain-wall configurations in $\mathrm{Hf}{\mathrm{O}}_2$. The anisotropic switching mechanism is inferred based on the investigation for 12 types of ${180}^{\circ }\text{-side}$ domain walls. This methodology is expected to be generally applicable to displacive ferroelectrics with low unit-cell point-group symmetries and lay a foundation for mechanism study of the switching dynamics.

Dirac points in the band structure of acoustic systems are essential features affording classical analogs of quantum condensed matter states. We show that measured dispersion curves near and at the Dirac point of an acoustic graphene analog can be suppressed by strong variations in the impedance boundary between free field and surface wave regimes under certain conditions. Increased Rayleigh scattering and diffractive excitation are shown to increase the dispersed surface wave pressure amplitude, circumventing the impedance-based wave suppression. The improved excitation and scattering conditions for observing acoustic Dirac points for two samples with two distinct operational frequency ranges are reported.

Recent inelastic neutron scattering (INS) experiments of the triangular antiferromagnet ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ revealed strong deviations from semiclassical theories. We demonstrate that key features of the INS data are well reproduced by a parton Schwinger boson theory beyond the saddle-point approximation. The measured magnon dispersion is well reproduced by the dispersion of two-spinon bound states (poles of the emergent gauge fields propagator), while the low-energy continuum scattering is reproduced by a quasifree two-spinon continuum, suggesting that a free spinon gas is a good initial framework to study magnetically ordered states near a quantum melting point.

${\mathrm{KV}}_3{\mathrm{Sb}}_5$ has recently attracted considerable attention due to its low-temperature superconducting properties, which are heralded by a charge-density wave. The apparent presence of a very weak magnetism does not result in long-range ordering. An explanation of the properties we present invokes higher-order terms in the vanadium magnetization density and a “hidden order” of Dirac (polar) multipoles. The Dirac dipole, known as an anapole or toroidal dipole, is one of a family of electronic multipoles visible in x-ray and magnetic neutron diffractions while undetectable with standard laboratory-based techniques. Actually, two viable magnetic structures, direct descendants of the established chemical structure, are studied with a view to testing their suitability in future experiments. One model structure is magnetoelectric and restricted to the linear type, whereas a second model cannot show a magnetoelectric effect of any type. The latter hosts a strange vanadium entity that is a true scalar and magnetic (time-odd), and associated in our paper with a fictitious charge distribution that is purely imaginary. Calculated x-ray and neutron-scattering amplitudes are symmetry-informed expressions of vanadium Dirac multipoles. Bragg diffraction patterns for the two models are found to be distinctly different, fortunately. Likewise, magnetochiral signals derived from our x-ray scattering amplitudes.

Coupled Majorana zero modes with nonzero energies are generally detrimental to the non-Abelian statistics due to the additional dynamic phase. Nevertheless, we show that a well-connected lead can introduce a local non-Hermitian dissipation term to shift the energies of both coupled Majorana modes to zero, and surprisingly turn the coupled Majorana mode far from the lead into a dark Majorana mode with exponentially small dissipation. This dark Majorana mode can conquer the drawback of the partially overlapped Majorana zero modes and possess the properties of true Majorana zero mode such as the perfect fractional Josephson effect and the non-Abelian statistics.

We consider a hybrid quantum Hall-superconductor system, where a superconducting finger with oblique profile is wedged into a two-dimensional electron gas in the presence of a perpendicular magnetic field, as considered by Lee et al., Nat. Phys. 13, 693 (2017). The electron gas is in the quantum Hall regime at filling factor $\nu =1$. Due to the Meissner effect, the perpendicular magnetic field close to the quantum Hall-superconductor boundary is distorted and gives rise to an in-plane component of the magnetic field. This component enables nonlocal crossed Andreev reflection between the spin-polarized chiral edge states running on opposite sides of the superconducting finger, thus opening a gap in the spectrum of the edge states without the need of spin-orbit interaction or nontrivial magnetic textures. We compute numerically the transport properties of this setup and show that a negative resistance exists as a consequence of nonlocal Andreev processes. We also obtain numerically the zero-energy local density of states, which systematically shows peaks stable to disorder. The latter result is compatible with the emergence of Majorana bound states.

The valley degeneracy in Si qubit devices presents problems for their use in quantum information processing. It is possible to lift this degeneracy by using the wiggle well architecture, in which an oscillatory Ge concentration couples the valleys. This paper presents the basic theory of this phenomenon together with model calculations using the empirical pseudopotential theory to obtain the overall magnitude of this effect and its dependence on the wavelength of the concentration oscillations. We derive an important selection rule which can limit the effectiveness of the wiggle well in certain circumstances.

We investigate shock-compressed copper in the warm dense matter regime by means of density functional theory molecular dynamics simulations. We use neural-network-driven interatomic potentials to increase the size of the simulation box and extract thermodynamic properties in the hydrodynamic limit. We show the agreement of our simulation results with experimental data for solid copper at ambient conditions and liquid copper near the melting point under ambient pressure. Furthermore, a thorough analysis of the dynamic ion-ion structure factor in shock-compressed copper is performed and the adiabatic speed of sound is extracted and compared with experimental data.

In this paper, we present a study of the temperature-dependent characteristics of electromagnetic fields at the atomic scale in multiferroic bismuth ferrite (${\mathrm{BiFeO}}_3$ or BFO). The study was performed using time differential perturbed angular correlation (TDPAC) spectroscopy on implanted ${}^{111}\mathrm{In}$ (${}^{111}\mathrm{Cd}$) probes over a wide temperature range. The TDPAC spectra show that substitutional ${}^{111}\mathrm{In}$ on the ${\mathrm{Fe}}^{3+}$ site experiences local electric polarization, which is otherwise expected to essentially stem from the ${\mathrm{Bi}}^{3+}$ lone pair electrons. Moreover, the TDPAC spectra show combined electric and magnetic interactions below the Néel temperature $T_N$. This is consistent with simulated spectra. X-ray diffraction (XRD) was employed to investigate how high-temperature TDPAC measurements influence the macroscopic structure and secondary phases. With the support of ab initio DFT simulations, we can discuss the probe nucleus site assignment and can conclude that the ${}^{111}\mathrm{In}$ (${}^{111}\mathrm{Cd}$) probe substitutes the Fe atom at the B site of the perovskite structure.

Using a BCS mean-field approach, we show how the interplay between low-momentum optical phonons and Jahn-Teller-type lattice distortions can open an attractive channel that allows the formation of pairs with the corresponding density exhibiting characteristic features of a pair-density wave. We demonstrate this numerically on a copper-oxide-type lattice.

Polar magnetism is compulsory when magnetic ions occupy sites that are not centers of inversion symmetry. Such magnetism is known to be visible in neutron diffraction, the technique of choice for magnetic structure determinations. Experiments in which the diffracted neutron polarization is analyzed are not a novelty. Symmetry-informed simulations of polarized neutron diffraction (PND) amplitudes for room-temperature hematite (α-${\mathrm{Fe}}_2{\mathrm{O}}_3$) illustrate the wealth of information on offer in future experiments. Two magnetic motifs, distinguished by the orientation of their bulk ferromagnetism and delineated by magnetic space groups $C2/c$ and $C{2}^{\prime }/c^{\prime }$, are current front-runners for room-temperature hematite. Both motifs are endowed with polar magnetism and iron Dirac (magnetoelectric) multipoles. The technique of resonant x-ray Bragg diffraction has previously been used to expose Dirac multipoles in room-temperature hematite. For unspecified reasons, the authors of a recent PND study of hamatite do not mention the compulsory polar magnetism, the published observation of Dirac multipoles, or the direct confirmation of neutron scattering by Dirac multipoles [H. Thoma et al., Phys. Rev. X 11, 011060 (2021) .]. The authors omission of polar magnetism in fits to their extensive neutron diffraction patterns calls for a reassessment of the claim to have determined the absolute direction of the Dzyaloshinskii-Moriya interaction.

Strain is an effective method to tune the electronic properties of two-dimensional (2D) materials and can induce novel phase transition. Recently, the 2D $M{A}_2{Z}_4$ family of materials has attracted interest because of their emerging topological, magnetic, and superconducting properties. Here, we investigate the impact of strain effects ($a/a_0$ = 0.96–1.04) on the physical properties of the Janus monolayer ${\mathrm{VSiGeN}}_4$ as a derivative of ${\mathrm{VSi}}_2{\mathrm{N}}_4$ or ${\mathrm{VGe}}_2{\mathrm{N}}_4$, which possesses dynamical, mechanical, and thermal stabilities. For out-of-plane magnetic anisotropy, with increasing strain, ${\mathrm{VSiGeN}}_4$ undergoes a transition between a ferrovalley semiconductor (FVS), half-valley metal (HVM), valley-polarized quantum anomalous Hall insulator, HVM, and FVS. These effects imply twice topological phase transitions, which are related to the sign-reversible Berry curvature and band inversion between $d_{xy}+d_{x^2-y^2}$ and $d_{z^2}$ orbitals for the $K$ or $-K$ valley. The band inversion also leads to transformation of valley splitting strength between the valence and conduction bands. However, for in-plane magnetic anisotropy, no special quantum anomalous Hall (QAH) states and valley polarization exist within the considered strain range. The actual magnetic anisotropy energy shows no special QAH and HVM states in monolayer ${\mathrm{VSiGeN}}_4$. Fortunately, these can easily be achieved by an external magnetic field, which adjusts the easy magnetization axis of ${\mathrm{VSiGeN}}_4$ from an in-plane one to an out-of-plane one. Our findings shed light on how strain can be employed to engineer the electronic states of ${\mathrm{VSiGeN}}_4$, which may lead to new perspectives on multifunctional quantum devices in valleytronics and spintronics.

We have built a theory of the spin-transfer torque (STT) effect in a conductive chiral helical magnet (CHM). It is shown that the STT effect induced by a spin current flowing through CHM leads to the rotation of the CHM magnetization spiral around its axis. The frequency of such rotation of the CHM magnetization is found. The former is expressed in terms of the parameters of the quantum-exchange Hamiltonian that specifies helical magnetic ordering in a conductive crystal. We have showcased that both the direction of rotation of the CHM magnetization and the direction of changes in the shape of the magnetic spiral are determined by the electron flow direction and the chirality of the magnet. The theory developed accounts for the generation of an electromagnetic field when rotating the magnetic spiral in the CHM subjected to an electric current flowing through the helimagnet.

Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at $T=0$, we study an extended Bose-Hubbard model in the limit of a large number of particles per site. Using a representation of this in terms of two coupled $XY$ models, we find, in addition to an insulating phase and a $(2+1)\mathrm{D}$ superfluid phase, two other phases. One phase is a 2D superfluid phase where a crossover from $(2+1)\mathrm{D}$ to 2D has taken place as a result of incipient charge ordering, signaled by $\theta$ disordering, and which is closely related to a supersolid phase. The other new phase is an edge metal state characterized by zero superfluid stiffness, zero charge ordering, and zero bulk compressibility. However, the edge compressibility of the system is nonzero. While we do not find any intermediate state with 2D metallic conductivity, we are able to connect these results to STM experiments on ${\mathrm{MoS}}_2$ showing brims of finite density of states around the entire edge of 2D ${\mathrm{MoS}}_2$ samples.

The field of two-dimensional ferromagnets has been reinvigorated by the discovery of ${\mathrm{VSe}}_2$ monolayer grown on van der Waals substrates, which is reported to be ferromagnetic with a Curie point higher than 330 K. However, the ferromagnetic and nonmagnetic states of pristine monolayer ${\mathrm{VSe}}_2$ are highly debated. Here, employing density functional theory, Wannier function calculations, and the band unfolding method, we explore the electronic structure of monolayer ${\mathrm{VSe}}_2$ with a $\sqrt{3}\times \sqrt{7}$ charge density wave (CDW). Certain qualitative aspects of the calculated unfolded band dispersion and unfolded Fermi surface of monolayer ${\mathrm{VSe}}_2$ with the $\sqrt{3}\times \sqrt{7}$ CDW in the nonmagnetic state agree well with previous angle-resolved photoemission spectroscopy results, albeit with uncertainty about whether these experiments probed single or multiple domains. Specifically, we find that an isolated CDW domain naturally induces a strong breaking of the threefold symmetry of the electronic structure. In addition we find that, relative to the undistorted structure, the CDW structure shows a strong competition between nonmagnetic and various magnetic states, with an energy difference less than 5 meV/f.u. For the CDW structure in the antiferromagnetic state, the band dispersions and Fermi surface are similar to those in the nonmagnetic state, while the unfolded bands of the ferromagnetic CDW state display a sizable exchange splitting. These results indicate the possibility of various antiferromagnetic fluctuations in ${\mathrm{VSe}}_2$ to coexist and compete with ferromagnetic order and the experimentally reported CDW order. Our calculations build insights for exploring the interplay between magnetism and CDW behaviors more generally in transition metal dichalcogenides.

Spin relaxation length is a fundamental material parameter that influences all aspects of spin dependent transport. The ability to tune the spin relaxation length leads to novel spintronic phenomena and functionalities. We explore the tunability of the spin relaxation length in the mesoscopic Cu channels of nonlocal spin valves by using the ionic gating technique via a ${\mathrm{Li}}^{+}$ containing solid polymer electrolyte. At 5 K, the Cu spin relaxation length ${\lambda }_{\mathrm{Cu}}$ is tuned reversibly between 670 and 410 nm and the Cu resistivity ${\rho }_{\mathrm{Cu}}$ is tuned by 9%. The strength of the Kondo effect due to the Fe impurities in Cu is tuned by one order of magnitude. At 295 K, ${\lambda }_{\mathrm{Cu}}$ is tuned between 380 and 300 nm and ${\rho }_{\mathrm{Cu}}$ is tuned by 7%. A gradual amplification of the tuning ranges by repeated gate cycling is observed and clearly suggests an electrochemical origin. Tunable spin relaxation in simple metals enriches functionalities in metal-based spintronics and shines light on fundamental spin relaxation mechanisms.

We show that short-range resonating valence bond correlations and long-range order can coexist in the ground state (GS) of a frustrated spin system. Our study comprises a comprehensive investigation of the quantum magnetism on the structurally disorder-free single crystal of ${\mathrm{Cu}}_2{\left(\mathrm{OH}\right)}_3{\mathrm{NO}}_3$, which realizes the $s$ = 1/2 Heisenberg model on a spatially anisotropic triangular lattice. Competing exchange interactions determined by fitting the magnetization measured up to 55 T give rise to an exotic GS wave function with the coexistence of the dominant short-range resonating valence bond correlations and weak long-range stripe order (ordered moment $M_0=\left|\langle s_i^z\rangle \right|\sim 0.02$). At low temperatures, a first-order spin-flop transition is visible at $\sim$1–3 T. As the applied field further increases, another two magnetic field induced quantum phase transitions are observed at $\sim$14–19 and $\sim$46–52 T, respectively. Simulations of the Heisenberg exchange model show semiquantitative agreement with the magnetic-field modulation of these unconventional phases, as well as the absence of visible magnetic reflections in neutron diffraction, thus supporting the GS of the spin system of ${\mathrm{Cu}}_2{\left(\mathrm{OH}\right)}_3{\mathrm{NO}}_3$ may be approximate to a quantum spin liquid. Our study establishes structurally disorder-free magnetic materials with spatially anisotropic exchange interactions as a possible arena for spin liquids.

In the new van der Waals Kondo-lattice ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, itinerant ferromagnetism and heavy fermionic behavior coexist. Both the key properties of such a system, namely, a spin-polarized Fermi surface and a low Fermi momentum, are expected to significantly alter Andreev-reflection-dominated transport at a contact with a superconducting electrode and display unconventional proximity-induced superconductivity. We observed interplay between Andreev reflection and Kondo resonance at mesoscopic interfaces between superconducting Nb and ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. Above the critical temperature ($T_c$) of Nb, the recorded differential conductance ($dI/dV$) spectra display a robust zero-bias anomaly which is described well by a characteristic Fano line shape arising from Kondo resonance. Below $T_c$, the Fano line mixes with Andreev-reflection-dominated $dI/dV$, leading to a dramatic, unconventional suppression of conductance at zero bias. As a consequence, an analysis of the Andreev reflection spectra within a spin-polarized model yields an anomalously large spin polarization which is not explained by the density of states of the spin-split bands at the Fermi surface alone. The results open up the possibilities of fascinating interplay between various quantum phenomena that may potentially emerge at the mesoscopic superconducting interfaces involving Kondo-lattice systems hosting spin-polarized conduction electrons.

We present a formulation of relativistic self-consistent $GW$ for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and nonrelativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully ab initio and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach an excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large computer simulations for anything beyond the simplest geometries. The inverse problem, determining the coefficients from a field on a boundary, is even more demanding, since traditional optimization requires a large number of forward problems to be solved sequentially. Here we show that the free-form inverse problem of wave equations can be solved with machine learning. First we show that deep neural networks can be used to predict the optical properties of nanostructured materials such as metasurfaces. Then we demonstrate the free-form inverse design of such nanostructures and show that constraints imposed by experimental feasibility can be taken into account. Our neural networks promise automated design in several technologies based on the wave equation.