In the framework of the Landau-Ginzburg-Devonshire (LGD) approach we studied finite-size effects of the phase diagram and domain structure evolution in spherical nanoparticles of a uniaxial ferroelectric. The particle surface is covered by a layer of screening charge characterized by finite screening length. The phase diagram, calculated in coordinates particle radius and screening length has a wide region of versatile polydomain structures separating single-domain ferroelectric and nonpolar paraelectric phases. Unexpectedly, we revealed a region of irregular labyrinthine domains in the nanoparticles of uniaxial ferroelectric $\mathrm{CuIn}{\mathrm{P}}_2{\mathrm{S}}_6$ with the first-order paraelectric-ferroelectric phase transition. We established that the origin of labyrinthine domains is the mutual balance of LGD, polarization gradient, and electrostatic energies. The branching of the domain walls appears and increases rapidly when the polarization gradient energy decreases below the critical value. Allowing for the generality of the LGD approach, we expect that the gradient-induced morphological transition can be the source of labyrinthine domain appearance in many spatially confined ferroics with long-range order parameter, including relaxors, ferromagnetics, antiferrodistortive materials, and materials with incommensurate ferroic phases.

We report on electric dipoles induced by magnetic ion $\mathrm{C}{\mathrm{r}}^{3+}\left(3d^3\right)$ off-center displacement with potential strong magnetoelectric coupling in simple perovskite $\mathrm{DyCr}{\mathrm{O}}_3$ crystals. $\mathrm{DyCr}{\mathrm{O}}_3$ was found to show quantum paraelectric behavior and the existence of electrical dipoles, as revealed by the dielectric, Raman scattering, and x-ray absorption near-edge structure spectra experiments. The anomalous lattice volume decreasing rate at low temperatures might play an important role in the $\mathrm{C}{\mathrm{r}}^{3+}$ ion displacement induced polar instability in $\mathrm{DyCr}{\mathrm{O}}_3$ as predicted by previous theoretical calculations. Our results on $\mathrm{DyCr}{\mathrm{O}}_3$ provide important experimental evidence for non-$d^0$ transition-metal ion displacement induced electric dipoles, and they may lead to the exploration of multiferroics in a wider range of materials, especially magnetic perovskites.

We studied the effect of physical pressure on the electronic and magnetic properties of ferrimagnetic double perovskites $A_2{\mathrm{FeReO}}_6$ ($A=\mathrm{Ca}$, Ba) using Re $L_{2,3}$ edge x-ray absorption spectroscopy and powder diffraction measurements. Volume compression is shown to dramatically increase the magnetic coercivity ($H_c$) in polycrystalline samples of both compounds with $\mathrm{\Delta }{H}_c/\mathrm{\Delta }V\sim 150$–200 $\mathrm{Oe}/{\AA }^3$. A nearly eight-fold increase in $H_c$, from 0.2 to 1.55 T, is obtained in ${\mathrm{Ba}}_2{\mathrm{FeReO}}_6$ at $P=29$ GPa. While no signs of structural phase transitions are seen in either sample to $\sim 30$ GPa, the structural data points to a pressure-driven increase in tetragonal distortion of ${\mathrm{ReO}}_6$ octahedra. A sizable but pressure-independent Re orbital-to-spin magnetic moment ratio is observed, pointing to the critical role of spin-orbit interactions at Re sites. We present a $j_{\mathrm{eff}}$ description of the electronic structure that combines effects of crystal field and spin-orbit coupling on the Re $5d^2$ orbitals and use this description to provide insight into the pressure-induced enhancement of magnetic anisotropy.

We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the Néel state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular, we consider a long-range magnetically ordered state of interacting two-dimensional quantum spin-$1/2$ XY models using the Chern-Simons (CS) fermion representation of interacting spins. The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity which spontaneously violates the continuous $\mathrm{U}\left(1\right)$ symmetry generating a linearly dispersing gapless Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in high-precision agreement with magnons of the corresponding Néel antiferromagnet irrespective to the lattice symmetry. Using the fermion formulation of the system with frustration, we show that the competing interactions emerge in the form of long-range interaction vertices mediated by the CS gauge field, which are responsible for restoring the continuous symmetry at sufficiently strong frustration. We identify these new interaction vertices and discuss their implications for unconventional phase transitions. We also apply the proposed theory to a model of anyons that can be tuned continuously from fermions to bosons, and discuss the results.

To specify preferential occupation sites of Co substituents and to clarify charge and spin states of Co ions in (La, Co)-cosubstituted hexagonal magnetoplumbite-type (M-type) Sr ferrite ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{Fe}}_{12-y}{\mathrm{Co}}_y{\mathrm{O}}_{19}$ ($x,y\le 0.4$), ${}^{57}\mathrm{Fe}$ and ${}^{59}\mathrm{Co}$ nuclear magnetic resonance (NMR) spectra are measured under zero and external magnetic fields using powdered and single crystalline specimens. For comparison, NMR investigations of nondoped and La- or Co-doped M-type Sr ferrites are also performed. Ferrimagnetic M-type Sr ferrite contains the following five crystallographic Fe sites: the majority spin sites $12k$, $2a$, and $2b$, and the minority spin sites $4f_1$ and $4f_2$. Based on ${}^{57}\mathrm{Fe}$ and ${}^{59}\mathrm{Co}$ NMR, a plausible model of (La, Co)-codoped Sr ferrite is deduced. To a considerable degree, the charge compensation between ${\mathrm{La}}^{3+}$ and ${\mathrm{Co}}^{2+}$ works in the equal (La, Co)-codoped case, where more than half of the Co ions are considered to be present in the minority spin $4f_1$ sites at the center of the oxygen tetrahedra, with the $S=3/2$ state carrying a small orbital moment owing to spin-orbit interaction. The remaining small number of high-spin ${\mathrm{Co}}^{2+}$ ($S=3/2$, $L=1)$ ions with unquenched orbital moments would be distributed to the other octahedral $12k$, $2a$, and $4f_2$ sites.

We present a systematic study of the nonequilibrium steady states (NESS) in Mott insulators driven by dc or ac electric fields, based on the Floquet dynamical mean-field theory. The results are analyzed using a generalized tunneling formula for the current, which is reminiscent of the Meir-Wingreen formula and provides insights into the relevant physical processes. In the dc case, the spectrum of the NESSs exhibits Wannier-Stark (WS) states associated with the lower and upper Hubbard bands. In addition, there emerge WS sidebands from many-body states. Using the tunneling formula, we demonstrate that the tunneling between these WS states leads to peaks or humps in the induced dc current. In the ac case, we cover a wide parameter range of excitation frequencies and field strengths to clarify the crossover from field-induced tunneling behavior in the dc limit to nonequilibrium states dominated by multiphoton absorption in the ac limit. In the crossover regime, the single-particle spectrum is characterized by a coexistence of Floquet sidebands and WS peaks, and the current and double occupation exhibit a nontrivial dependence on the field strength. The tunneling formula works quantitatively well even in the ac case, and we use it to discuss the potential cooperation of tunneling and multiphoton processes in the crossover regime. The tunneling formula and its simplified versions also provide physical insights into the high-harmonic generation in Mott insulators.

Using scattering-vector ($\mathit{q}$)-dependent electron-energy-loss spectroscopy (EELS), we found anisotropy of Li $1s\to 2p$ excitation for $\mathrm{LiCo}{\mathrm{O}}_2$. To achieve this, EELS spectra for $\mathrm{LiCo}{\mathrm{O}}_2$ (i.e., Li K edge overlapped with $\mathrm{Co}{M}_{2,3}$ edge) were compared with those of $\mathrm{Co}{M}_{2,3}$ edge for $\mathrm{N}{\mathrm{a}}_{0.72}\mathrm{Co}{\mathrm{O}}_2$ under dipole transition conditions. Then, first-principles calculations of loss functions and the Bethe-Salpeter equation of Li K edge were applied for $\mathrm{LiCo}{\mathrm{O}}_2$. We also demonstrate that crystallographic orientation-dependent EELS for $\mathrm{LiCo}{\mathrm{O}}_2$ reflects the anisotropy of Li $1s\to 2p$ excitation.

The interaction of solid-state electronic spins with deformations of their host crystal is an important ingredient in many experiments realizing quantum information processing schemes. Here, we theoretically characterize that interaction for a nitrogen-vacancy (NV) center in diamond. We derive the symmetry-allowed Hamiltonian describing the interaction between the ground-state spin-triplet electronic configuration and the local strain. We numerically calculate the six coupling-strength parameters of the Hamiltonian using density functional theory, and propose an experimental setup for measuring those coupling strengths. The importance of this interaction is highlighted by the fact that it enables to drive spin transitions, both magnetically allowed and forbidden, via mechanically or electrically driven spin resonance. This means that the ac magnetic field routinely used in a wide range of spin-resonance experiments with NV centers could in principle be replaced by ac strain or ac electric field, potentially offering lower power requirements, simplified device layouts, faster spin control, and local addressability of electronic spin qubits.

Relativistic Dirac fermions are ubiquitous in condensed-matter physics. Their mass is proportional to the material energy gap and the ability to control and tune the mass has become an essential tool to engineer quantum phenomena that mimic high-energy particles and provide novel device functionalities. In topological insulator thin films, new states of matter can be generated by hybridizing the massless Dirac states that occur at material surfaces. In this paper, we experimentally and theoretically introduce a platform where this hybridization can be continuously tuned: the $\mathrm{P}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{S}{\mathrm{n}}_{\mathrm{x}}\mathrm{Se}$ topological superlattice. In this system, topological Dirac states occur at the interfaces between a topological crystalline insulator $\mathrm{P}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{S}{\mathrm{n}}_{\mathrm{x}}\mathrm{Se}$ and a trivial insulator, realized in the form of topological quantum wells (TQWs) epitaxially stacked on top of each other. Using magnetooptical transmission spectroscopy on high-quality molecular-beam epitaxy grown $\mathrm{P}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{S}{\mathrm{n}}_{\mathrm{x}}\mathrm{Se}$ superlattices, we show that the penetration depth of the TQW interface states and therefore their Dirac mass are continuously tunable with temperature. This presents a pathway to engineer the Dirac mass of topological systems and paves the way towards the realization of emergent quantum states of matter using $\mathrm{P}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{S}{\mathrm{n}}_{\mathrm{x}}\mathrm{Se}$ topological superlattices.

Using a periodic train of Lorentzian voltage pulses, which generates solitonlike electronic excitations called levitons, we investigate the charge density backscattered off a quantum point contact in the fractional quantum Hall regime. We find a regular pattern of peaks and valleys, reminiscent of analogous self-organization recently observed for optical solitons in nonlinear environments. This crystallization phenomenon is confirmed by additional side dips in the Hong-Ou-Mandel noise, a feature that can be observed in present-day electron quantum optics experiments.

The quantum anomalous Hall effect (QAHE) hosts the dissipationless chiral edge states associated with the nonzero Chern number, providing potentially significant applications in future spintronics. The QAHE usually occurs in a two-dimensional system with time-reversal symmetry breaking. In this Rapid Communication, we propose that the QAHE can exist in three-dimensional (3D) ferromagnetic insulators. By imposing inversion symmetry, we develop the topological constraints dictating the appearance of a 3D QAHE based on a parity analysis at the time-reversal invariant points in reciprocal space. Moreover, using first-principles calculations, we identify that 3D QAHE can be realized in a family of intrinsic ferromagnetic insulating oxides, including layered and nonlayered compounds that share a centrosymmetric structure with space group $R\overline{3}m$ (No. 166). The Hall conductivity is quantized to be $-\frac{3e^2}{hc}$ with the lattice constant $c$ along the $c$ axis. The chiral surface sheet states are clearly visible and uniquely distributed on the surfaces that are parallel to the magnetic moment. Our findings open a promising pathway to realize the QAHE in 3D ferromagnetic insulators.

The conserved bulk spin current [Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], defined as the time derivative of the spin displacement operator, ensures automatically the Onsager relation between the spin Hall effect (SHE) and the inverse SHE. Here, we reveal another desirable property of this conserved spin current: the Mott relation linking the SHE and its thermal counterpart, the spin Nernst effect (SNE). According to the Mott relation, the SNE is known once the SHE is understood. In a two-dimensional Dirac-Rashba system with a smooth scalar disorder potential, we find a sign change of the spin Nernst conductivity when tuning the chemical potential.

Probing the optical Stark effect at the single-molecule or atomic scale is crucial for understanding many photoinduced chemical and physical processes on surfaces. Here, we report a study about the optical Stark effect of single atomic defects on a $\mathrm{Ti}{\mathrm{O}}_2\left(110\right)$ surface with photoassisted scanning tunneling spectroscopy. When a laser is coupled into the tunneling junction, the midgap state of the $\mathrm{OH}\text{−}{\mathrm{O}}_2$ defects changes remarkably in differential conductance spectra. As the laser power gradually increases, the energy of the midgap state shifts away from the Fermi level with an increase in intensity and a broadening of the peak width. The observation can be explained as an optical Stark effect with the Autler-Townes formula. This large optical Stark effect is due to a tip enhancement and a strong dipole moment in the transient charged state during electron tunneling. Our study provides different aspects in exploring electron-photon interactions at the microscopic scale.

We introduce the method of stochastic lists to deal with a multivariable positive function, defined by a self-consistent equation, typical for certain problems in physics and mathematics. In this approach, the function's properties are represented statistically by lists containing a large collection of sets of coordinates (or “walkers”) that are distributed according to the function's value. The coordinates are generated stochastically by the Metropolis algorithm and may replace older entries according to some protocol. While stochastic lists offer a solution to the impossibility of efficiently computing and storing multivariable functions without a systematic bias, extrapolation in the inverse of the number of walkers is usually difficult, even though in practice very good results are found already for short lists. This situation is reminiscent of diffusion Monte Carlo and is hence generic for all population-based methods. We illustrate the method by computing the lowest-order vertex corrections in Hedin's scheme for the Fröhlich polaron and the ground-state energy and wave function of the Heisenberg model in two dimensions.

Here we report the evolution of bulk band structure and surface states in rare-earth monobismuthides with partially filled $f$ shell. Utilizing synchrotron-based photoemission spectroscopy, we determined the three-dimensional bulk band structure and identified the bulk band inversions near the X points, which, according to the topological theory, could give rise to nontrivial band topology with an odd number of gapless topological surface states. Near the surface $\overline{\mathrm{\Gamma }}$ point, no clear evidence for a predicted gapless topological surface state is observed due to its strong hybridization with the bulk bands. Near the $\overline{M}$ point, the two surface states, because of projections from two inequivalent bulk band inversions, interact and give rise to two peculiar sets of gapped surface states. The bulk band inversions and corresponding surface states can be tuned substantially by varying rare-earth elements, in good agreement with density-functional theory calculations assuming local $f$ electrons. Our study therefore establishes rare-earth monobismuthides as an interesting class of materials possessing tunable electronic properties and magnetism, providing a promising platform to search for various properties in potentially correlated topological materials.

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.

A Dyakonov plasmon surface wave (DPSW), which is a special case of Dyakonov surface wave (DSW), is studied theoretically at the interface of an isotropic plasma and a uniaxial rutile ${\mathrm{TiO}}_2$ in the terahertz (THz) frequencies. DPSW has the combination of properties of both DSW and surface plasmon polariton (SPP) such as directionality (of DSW) and high localization degree (of SPP). The existence conditions for propagation of the DPSW in this structure are found to be extremely relaxed compared to DSW existing in dielectric media. DPSWs in comparison to common SPPs are composed of four evanescent waves: transverse electric and transverse magnetic in the isotropic plasma cover, and ordinary and extraordinary waves in the uniaxial rutile ${\mathrm{TiO}}_2$ crystal substrate. Frequency tunability, localization degree, directionality, and hybridization factor of the DPSWs for three cases of THz frequencies are investigated. It is also demonstrated that the presence of the plasma medium with tunable permittivity can lead to novel applications of DPSWs in such structures.

Brownian microparticles diffusing in optical potential-energy landscapes constitute a generic test bed for nonequilibrium statistical thermodynamics and have been used to emulate a wide variety of physical systems, ranging from Josephson junctions to Carnot engines. Here we demonstrate that it is possible to scale down this approach to nanometric length scales by constructing a tilted washboard potential for the rotation of plasmonic gold nanorods. The potential depth and tilt can be precisely adjusted by modulating the light polarization. This allows for a gradual transition from continuous rotation to discrete stochastic jumps, which are found to follow Kramers dynamics in excellent agreement with stochastic simulations. The results widen the possibilities for fundamental experiments in statistical physics and provide insights into how to construct light-driven nanomachines and multifunctional sensing elements.

The two-dimensional Holstein-Hubbard model is studied by means of continuous-time quantum Monte Carlo simulations. Using renormalization-group-invariant correlation ratios and finite-size extrapolation, the critical temperature of the charge-density-wave transition is determined as a function of coupling strength, phonon frequency, and Hubbard repulsion. The phase transition is demonstrated to be in the universality class of the two-dimensional Ising model and detectable via the fidelity susceptibility. The structure of the ground-state phase diagram and the possibility of a bipolaronic metal with a single-particle gap above $T_c$ are explored.