The magnetic properties of tetragonal $\alpha \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$ spinel, its metastable high-pressure modification $\gamma \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$, and of an $\alpha \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$ modification with a high amount of lattice defects were investigated by direct current (dc) and alternating current (ac) magnetometry as well as by heat capacity measurements. An $\alpha \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$ phase modification with a high amount of lattice defects instead of the desired metastable high pressure $\gamma \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$ phase might unintentionally be obtained after the high-pressure application. The obtained results clarify strongly contradictory reports about the dc susceptibility data of $\gamma \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$ in the literature. Further, in situ low-temperature x-ray diffraction experiments from 150 to 275 K and Mn K-edge x-ray absorption spectroscopy experiments at 80 and 300 K do not indicate any structural transition to be coupled with the magnetic transition at 210 K for the given $\gamma \text{−}{\mathrm{Mn}}_3{\mathrm{O}}_4$ sample. This is in contradiction with what was concluded from powder neutron diffraction alone in the literature, where a coupled structural transition accompanied with large atomic displacements of a Mn species was claimed to be accompanied to the magnetic transition.

The Curie-Weiss law is widely used to estimate the strength of frustration in frustrated magnets. However, the Curie-Weiss law was originally derived as an estimate of magnetic correlations close to a mean-field phase transition, which—by definition—is absent in spin liquids. Instead, the susceptibility of spin liquids is known to undergo a Curie-law crossover between two magnetically disordered regimes. Here, we study the generic aspect of the Curie-law crossover by comparing a variety of frustrated spin models in two and three dimensions, using both classical Monte Carlo simulations and analytical Husimi tree calculations. Husimi tree calculations fit remarkably well the simulations for all temperatures and almost all lattices. We also propose a Husimi ansatz for the reduced susceptibility $\chi T$, to be used in complement to the traditional Curie-Weiss fit to estimate the Curie-Weiss temperature ${\theta }_{\mathrm{cw}}$. Applications to materials are discussed.

We study hard-core bosons on the honeycomb lattice subjected to anisotropic nearest-neighbor hopping along with anisotropic nearest-neighbor repulsion, using a quantum Monte Carlo technique. At half filling, we find a transition from strong topological interacting order to weak topological interacting order as a function of the hopping anisotropy. The strong topological phase is characterized by a finite topological entanglement entropy, while the weak topological order is identified with a nontrivial value of the bipartite entanglement entropy. Some of the order parameters and their derivatives demonstrate abrupt changes when varying the parameters controlling the lattice anisotropies, thus revealing the nature of this topological interacting phase transition.

Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting $N$ particles with multiple flavors in the interacting $\text{SU}\left(N\right)$ Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the $N$-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer $\mathcal{N}$, and increasing $\mathcal{N}$ monotonically approaches the exact solution. VDAT can be exactly evaluated in the $d=\infty$ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that $\mathcal{N}=3$ accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at $\mathcal{N}=3$, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at $\mathcal{N}=3$ to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using $\mathcal{N}=2$ and $\mathcal{N}=3$ for the $\text{SU}\left(2{\text{N}}_{\text{orb}}\right)$ Hubbard model in $d=\infty$ with ${\text{N}}_{\text{orb}}=2–8$, and compare to numerically exact dynamical mean-field theory solutions where available. The developments in this work will greatly facilitate the application of VDAT at $\mathcal{N}=3$ to strongly correlated electron materials.

Doping asymmetry is a notable phenomenon with semiconductors and a particularly long-standing challenge limiting the applications of most wide band-gap semiconductors, which are inherent of spontaneous heavy $n$- or $p$-type doping because of their extreme band edges. This study theoretically shows that by applying a proper external voltage on materials during their growth or doping processes, we can largely tune the band edges and consequently reverse the doping asymmetry in semiconductor thin films. We take zinc oxide as a touchstone and computationally demonstrate that this voltage-assisted doping approach efficiently suppresses the spontaneous $n$-type defects by around four orders under three distinct growth conditions and successfully generates $p$-type zinc oxide up to the lowest acceptor levels. The proposed approach is insensitive to materials, growth conditions, or defects origins, and thus offers a general solution to the doping asymmetry in semiconductor thin films.

We report a unified theory based on linear response, for analyzing the longitudinal optical conductivity (LOC) of materials with tilted Dirac cones. Depending on the tilt parameter $t$, the Dirac electrons have four phases: untilted, type I, type II, and type III; the Dirac dispersion can be isotropic or anisotropic; the spatial dimension of the material can be one, two, or three dimensions (1D, 2D, or 3D). The interband LOCs and intraband LOCs in $d$ dimension (with $d\ge 2)$ are found to scale as ${\sigma }_0{\omega }^{d-2}$ and ${\sigma }_0{\mu }^{d-1}\delta \left(\omega \right)$, respectively, where $\omega$ is the frequency and $\mu$ the chemical potential. The interband LOC vanishes in 1D due to lack of extra spatial dimension. In contrast, the interband LOCs in 2D and 3D are nonvanishing and share many similar properties. A universal and robust fixed point of interband LOCs appears at $\omega =2\mu$ no matter $d=2$ or $d=3$, which can be intuitively understood by the geometric structures of Fermi surface and energy resonance contour. The intraband LOCs and the carrier density for 2D and 3D tilted Dirac bands are both closely related to the geometric structure of Fermi surface and the cutoff of integration. The angular dependence of LOCs is found to characterize both spatial dimensionality and band tilting and the constant asymptotic background values of LOC reflect features of Dirac bands. The LOCs in the anisotropic tilted Dirac cone can be connected to its isotropic counterpart by a ratio that consists of Fermi velocities for both 2D and 3D. Most of the findings are universal for tilted Dirac materials and hence valid for a great many Dirac materials in the spatial dimensions of physical interest.

The most relevant characteristic of a topological insulator material is the presence of edge/surface states that are protected by the bulk topology, and therefore, insensitive to nonmagnetic disorder. However, if such disorder is induced by magnetic atoms or the topological insulator is subjected to an external magnetic field, the time-reversal symmetry is expected to break down, affecting the robustness of the edge/surface states. In this work, europium (Eu)-doped bismuth telluride thin films were grown by molecular beam epitaxy in order to analyze the effect of a small fraction of atoms with magnetic properties on topologically protected surface states. For films with different Eu concentrations, morphological and electronic characterizations were carried out using atomic force microscopy, scanning tunnelling microscopy, and scanning tunnelling spectroscopy (STS) techniques. The results show that, regardless of the Eu concentration, the layered structure characteristic of the ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ phase is maintained. However, large $(>2\%)$ Eu concentrations induce the appearance of protrusions and clusters on the surface of the films. The STS measurements show the presence of surface states for pure and low-content Eu:${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The suppression of surface states is indicated by STS spectra in regions with well-defined gaps for some locally limited regions of our samples with large concentration of Eu atoms. From density functional theory we are able to show that the Eu substitutional impurity at the Bi site is not the main mechanism responsible for the observed changes in the topological insulator band structure. Furthermore, the magnetic properties of europium are not the key factor dictating the different ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ local surface electronic properties experimentally observed by STS, which are mostly affected by alloying and atom replacement, which induce a chemical modification of the surface potential.

Weak spin-orbit coupling produces very limited current-induced spin accumulation in nonmagnetic semiconductor nanostructures. We demonstrate a possibility to parametrically increase spin polarization using the Kondo effect. As a model object we consider a quantum dot side coupled to a quantum wire, taking into account spin-dependent electron tunneling from the wire to the dot. Using the nonequilibrium Green functions, we show that the many-body correlations between the quantum dot and the quantum wire can increase the current-induced spin accumulation at low temperatures by almost two orders of magnitude for moderate system parameters. The enhancement is related to the Kondo peak formation in the density of states and the spin instability due to the strong Coulomb interaction. This effect may be useful to electrically manipulate the localized electron spins in quantum dots for their quantum applications.

We conduct an exhaustive investigation on the dependence of polaron migrations barriers on the fraction of Fock exchange, $\alpha$, in hybrid functionals. We analyze different the dependence of different physical quantities on $\alpha$, such as the band gap of the host material, the fundamental frequency of the polarons, and the polaron localization at the ground and transitions states. We demonstrate that for those systems in which polarons are more (less) localized at their ground state than at their transition state, the migration barriers increase (decrease) on increasing (decreasing) $\alpha$. By choosing the ${\text{V}}_k$ centers in alkali halides, a paradigmatic example of hole polarons, we show that the $\alpha$ values that reproduce the experimental band gap of the host materials give rise to migration barriers reasonably close to the experimental ones. Surprisingly, we observe that ${\text{V}}_k$ centers' localization behaves differently depending on halide ions. For alkali fluorides, polarons are more localized at the transition state, while for larger halides (Cl, Br, and I) the localization is larger at the ground state.

We study the anomalous Hall effect in a disordered Weyl semimetal. While the intrinsic contribution is expressed solely in terms of Berry curvature, the extrinsic contribution is given by a combination of the skew-scattering and side-jump terms. For the model of small-size impurities, we are able to express the skew-scattering contribution in terms of scattering phase shifts. We identify the regime in which the skew-scattering contribution dominates the side-jump contribution: the impurities are either strong or resonant and at dilute concentration. In this regime, the Hall resistivity ${\rho }_{xy}$ is expressed in terms of two scattering phases, analogous to the $s$-wave scattering phase in a nontopological metal. We compute the dependence of ${\rho }_{xy}$ on the chemical potential and show that ${\rho }_{xy}$ scales with temperature as $T^2$ in low temperatures and as $T^{3/2}$ in the high-temperature limit.

The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of the existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit's energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced spin-orbit interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a comodeling framework for double quantum dot (DQD) devices and their charge noise environments. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods, and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two-qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities $>97\%$ in the simulated Si-MOS devices at a typical TLF density of ${10}^{11}{\mathrm{cm}}^{-2}$. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to $91\%$ in the presence of the same density of TLFs. We further investigate the one- and two-qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities, which can compromise the device yields in scaled qubit technologies.

Topological classification of quantum solids often (if not always) groups all trivial atomic or normal insulators (NIs) into the same featureless family. As we argue here, this is not necessarily the case always. In particular, when the global phase diagram of electronic crystals harbors topological insulators with the band inversion at various time-reversal invariant momenta ${\mathbf{K}}_{\mathrm{inv}}^{\mathrm{TI}}$ in the Brillouin zone, their proximal NIs display noninverted band-gap minima at ${\mathbf{K}}_{\min }^{\mathrm{NI}}={\mathbf{K}}_{\mathrm{inv}}^{\mathrm{TI}}$. In such systems, once topological superconductors nucleate from NIs, the inversion of the Bogoliubov de Gennes bands takes place at ${\mathbf{K}}_{\mathrm{inv}}^{\mathrm{BdG}}={\mathbf{K}}_{\min }^{\mathrm{NI}}$, inheriting from the parent state. We showcase this (possibly general) proposal for two-dimensional time-reversal symmetry-breaking insulators. Then, distinct quantized thermal Hall conductivity and responses to dislocation lattice defects inside the paired states (tied with ${\mathbf{K}}_{\mathrm{inv}}^{\mathrm{BdG}}$ or ${\mathbf{K}}_{\min }^{\mathrm{NI}}$), in turn, unambiguously identify different parent atomic NIs.

A charge order-driven ferroelectricity, a novel mechanism completely different from conventional types such as lattice distortion observed in a typical ferroelectric, has been expected for a series of compounds $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ ($R=\mathrm{Ho}\sim \mathrm{Lu}$ and Y, In), but a real problem has been still unsolved whether or not the compounds are truly ferroelectric. Here, we demonstrate that $\mathrm{Tm}{\mathrm{Fe}}_2{\mathrm{O}}_4$, one of the $R{\mathrm{Fe}}_2{\mathrm{O}}_4$ family, is a true ferroelectric and piezoelectric compound with noncentrosymmetric structure (space group: $Cm$) at room temperature by using switching spectroscopy piezoelectric force microscopy, laser interferometry, scanning nonlinear dielectric microscopy, x-ray diffraction, selected-area electron diffraction, nano-beam electron diffraction, convergent-beam electron diffraction, and high-angle annular dark-field scanning transmission electron microscopy for single-crystalline $\mathrm{Tm}{\mathrm{Fe}}_2{\mathrm{O}}_4$. We have also found that $\mathrm{Tm}{\mathrm{Fe}}_2{\mathrm{O}}_4$ exhibits an electric field induced phase transition between ferroelectric and conductive states. We propose that the charge ordering of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions accompanied by an ordered displacement of ${\mathrm{Tm}}^{3+}$ ions lead to the ferroelectricity and piezoelectricity.

Ferroelectric control of two-dimensional magnetism is promising in fabricating electronic devices with high speed and low-energy consumption. The newly discovered layered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4{\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_n$ and their Sb counterparts exhibit $A$-type antiferromagnetism with intriguing topological properties. Here we propose to obtain tunable magnetic multistates in their thin films by ferroelectrically manipulating the interlayer magnetic couplings based on the Heisenberg model and first-principles calculations. Our strategy relies on the fact that interfacing the thin films with appropriate ferroelectric materials can switch on/off an interlayer hopping channel between Mn-$e_g$ orbitals as the polarizations reversed, thus resulting in a switchable interlayer antiferromagnetism-to-ferromagnetism transition. On the other hand, the interface effect leads to asymmetric energy barrier heights for the two polarization states. These properties allow us to build ferroelectrically switchable triple and quadruple magnetic states with multiple Chern numbers in thin films. Our study reveals that ferroelectrically switchable magnetic and topological multistates in the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ family can be obtained by rational design for multifunctional electronic devices, which can also be applied to other two-dimensional magnetic materials.

The spin dynamics in the block magnetic phase of the iron-based ladder compound ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ has been studied by means of single-crystal inelastic neutron scattering. Using linear spin-wave theory and Monte Carlo simulations, our analysis points to a magnetic Heisenberg model with effective frustrated antiferromagnetic couplings only, able to describe both the exotic block order and its dynamics. This new and purely antiferromagnetic picture offers a fruitful perspective to describe multiferroic properties, but also understand the origin of the stripelike magnetic instability observed under pressure as well as in other parent compounds with similar crystalline structure.

We study the effects of infinite-range (IR) interaction on the localization properties of one-dimensional disordered harmonic chains. Two kinds of disordered models are considered: one is with disordered masses, but constant spring coefficient (mass model), and the other is with disordered spring coefficient, but constant mass (spring model). It is found that the IR interaction induces a gap between the $\omega =0$ and the excited frequency band for both types of disordered models, and their gaps are both proportional to the IR interaction coefficient $\gamma$ for larger $\gamma$. In addition, the width of the excited frequency band of the mass model is also proportional to $\gamma$ for larger $\gamma$, while that of the spring model is independent of $\gamma$. By employing the normalized participation ratio, we find that the low-frequency modes of the mass model except for the lowest frequency change from extended to localized states, while the localized properties of the spring model modes remain unchanged. We also discuss the effects of IR interaction on the dynamic behaviors of the two kinds of disordered models.

We study magnon excitations and their interactions in honeycomb antiferromagnets with the Dzyaloshinskii-Moriya interaction. When an applied magnetic field is turned on, the classical ground state of the system is in noncollinear antiferromagnetic order. Therefore, it is crucial to consider the interactions between magnons. We find an exact and well-formed solution of the bosonic Bogoliubov–de Gennes Hamiltonian, which allows us to analytically study the topological properties and damping effects of the magnon bands. In particular, the formulas of the Berry phase and Berry curvature for the magnon bands are worked out analytically. The Mn-based trichalcogenide ${\mathrm{MnPS}}_3$ is taken as a candidate material realization to estimate the order of magnitude of the thermal Hall conductivity and its evolution with the temperature and the Dzyaloshinskii-Moriya interaction strength. We develop a nonlinear spin wave theory to study the damping effects of the topological magnons and find the different damping behaviors of the upper and lower topological magnon bands when tuning the applied magnetic field. In some parameter regions, the damping effects are so strong that the free magnon description breaks down. Finally, we discuss how to observe these effects in experiments.