We numerically investigate the quantum phase transitions induced by Anderson disorder in a topological superconductor (TSC), which is composed of a quantum anomalous Hall insulator (QAHI) and a proximity coupled $s$-wave superconductor (SC). From the transport phenomena presented, we deduce that with the increase of Anderson disorder strength, the topological quantum phase changes from Chern number $\mathcal{N}=0$ to $\mathcal{N}=1$ and finally to $\mathcal{N}=2$. Then we use the effective-medium theory to verify our numerical results and conclude that the phase transitions should ascribe to the negative correction of topological mass.

Twisted bilayer graphene with tiny rotation angles have drawn significant attention due to the observation of the unconventional superconducting and correlated insulating behaviors. In this paper, we employ a full tight-binding model to investigate collective excitations in twisted bilayer graphene near the magic angle. The polarization function is obtained from the tight-binding propagation method without diagonalization of the Hamiltonian matrix. With the atomic relaxation considered in the simulation, both damped and undamped plasmon modes are discovered near the magic angle under both room temperature and superconductivity transition temperature. In particular, an undamped plasmon mode in narrow bands can be directly probed in magic angle twisted bilayer graphene at superconductivity transition temperature. The undamped plasmon mode is tunable with angles and gradually fades away with both temperature and chemical potential. In practice, the flat bands in twisted bilayer graphene can be detected by exploring the collective plasmons from the measured energy loss function.

A semiclassical theory for the orbital magnetization due to adiabatic evolutions of Bloch electronic states is proposed. It renders a unified theory for the periodic-evolution pumped orbital magnetization and the orbital magnetoelectric response in insulators by revealing that these two phenomena are the only instances where the induced magnetization is gauge invariant. This theory also accounts for the electric-field-induced intrinsic orbital magnetization in two-dimensional metals and Chern insulators. We illustrate the orbital magnetization pumped by microscopic local rotations of atoms, which correspond to phonon modes with angular momentum, in toy models based on honeycomb lattice, and the results are comparable to the pumped spin magnetization via strong Rashba spin-orbit coupling. We also show the vital role of the orbital magnetoelectricity in validating the Mott relation between the intrinsic nonlinear anomalous Hall and Ettingshausen effects.

The electronic properties of antimonene, single-layer Sb, are attracting great attention. In this paper, spin transport in armchair antimonene nanoribbon (ASbNR) is investigated. Following the tight-binding model, we calculate both the transmission probability and the conductance by means of the nonequilibrium Green's function (NEGF) method. The effects of an external electric field vertical to the ribbon plane are explored. Our results indicate that the spin-flip rate increases with the vertical electric field. Disorder effects on the spin transport are addressed by considering the presence of charged impurities. It is found that charged impurities also enhance the spin-flip rate but to a lesser extent than the out-of-plane electric field.

The layered two-dimensional material ${\mathrm{MoTe}}_2$ in the $T_d$ crystal phase is a semimetal which has theoretically been predicted to possess topologically nontrivial bands corresponding to Weyl fermions. Clear experimental evidence by angle-resolved photoemission spectroscopy (ARPES) is, however, lacking, which calls for a careful examination of the relation between ground state band structure calculations and ARPES intensity plots. Here we report a study of the near-Fermi-energy band structure of ${\mathrm{MoTe}}_2\left(T_d\right)$ by means of ARPES measurements, density functional theory, and one-step-model ARPES calculations. Good agreement between theory and experiment is obtained. We analyze the orbital character of the surface bands and its relation to the ARPES polarization dependence. We find that light polarization has a major effect on which bands can be observed by ARPES. For $s$-polarized light, the ARPES intensity is dominated by subsurface Mo $d$ orbitals, while $p$-polarized light reveals the bands mainly derived from Te $p$ orbitals. Suitable light polarization for observing either an electron or hole pocket are determined.

We rederive the semiconductor Bloch equations emphasizing the close link to the Berry connection. Our rigorous derivation reveals the existence of two further contributions to the current, in addition to the frequently considered intraband and polarization-related interband terms. The extra contributions become sizable in situations with strong dephasing or when the dipole-matrix elements are strongly wave-number dependent. We apply the formalism to high-harmonic generation for a Dirac metal. The extra terms add to the frequency-dependent emission intensity (high-harmonic spectrum) significantly at certain frequencies changing the total signal up to a factor of 10.

Recent experimental observation of an unexpectedly large current-induced spin-orbit torque in surface oxidized Cu on top of a ferromagnet pointed to a possibly prominent role of the orbital Rashba effect (ORE) in this system. Here, we use first principles methods to investigate the ORE in a system of oxygen monolayer deposited on top of a Cu(111) film. We show that surface oxidization of the Cu film leads to a gigantic enhancement of the ORE near the Fermi energy. The resulting chiral orbital texture in the momentum space is exceptionally strong, reaching as much as $\sim 0.5\hslash$ in magnitude. We find that resonant hybridization between O $p$ states and Cu $d$ states is responsible for the emergence of the ORE at the interface. We also present a minimal model that captures the emergence of the ORE through the $pd$ hybridization mechanism. We demonstrate that an application of an external electric field to the system generates colossal orbital Hall currents which are an order of magnitude larger than the spin Hall currents found in heavy metals. This implies that the “orbital torque” mechanism may be significant in surface oxidized Cu/ferromagnet structures. Our results encourage an experimental verification of the rich orbital physics in surface oxidized Cu films through optical measurements such as angle-resolved photoemission spectroscopy and momentum microscopy.

We investigate the cubic-to-tetragonal ferroelectric phase transition temperature $T_c$ of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ through a first-principles self-consistent phonon scheme. This method extends the harmonic approximation by incorporating anharmonic effects due to thermalized displacements, which are simultaneous excitations of phonons with a temperature-dependent random amplitude. The calculated forces are analyzed with an effective harmonic force constant model, which serves as the basis for a new set of thermalized displacements until self-consistency has been reached. The phonons with imaginary frequencies at $T=0$ K are stabilized due to anharmonic effects in the temperature range where the corresponding phase is stable and the dynamical instabilities disappear. Using the calculated free energies at various temperatures, volumes, and $c/a$ ratios, we obtain a thermal expansion in good agreement with the experimental values. Comparing the free energies of the tetragonal and cubic phases at different temperatures, we predict $T_c\approx 455\mathrm{K}$. This is in reasonable agreement with the experimental value of $\approx 393$ K in view of the strong influence of the particular density functional theory approximation on the unstable phonon modes.

Inspired by recent developments in the study of chaos in many-body systems, we construct a measure of local information spreading for a stochastic cellular automaton in the form of a spatiotemporally resolved Hamming distance. This decorrelator is a classical version of an out-of-time-order correlator studied in the context of quantum many-body systems. Focusing on the one-dimensional Kauffman cellular automaton, we extract the scaling form of our decorrelator with an associated butterfly velocity $v_b$ and a velocity-dependent Lyapunov exponent $\lambda \left(v\right)$. The existence of the latter is not a given in a discrete classical system. Second, we account for the behavior of the decorrelator in a framework based solely on the boundary of the information spreading, including an effective boundary random walk model yielding the full functional form of the decorrelator. In particular, we obtain analytic results for $v_b$ and the exponent $\beta$ in the scaling ansatz $\lambda \left(v\right)\sim \mu {(v-v_b)}^{\beta }$, which is usually only obtained numerically. Finally, a full scaling collapse establishes the decorrelator as a unifying diagnostic of information spreading.

We have investigated the multiferroicity and magnetoelectric (ME) coupling in $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$. With a noncentrosymmetric polar structure (space group Pna$2_1$) at room temperature, this compound shows an onset of electric polarization with an antiferromagnetic ordering at the Néel temperature ($T_N$) of 17.8 K. The magnetic properties of the polycrystalline samples were studied by DC and AC magnetization and heat capacity measurements. The metamagnetic behavior at low temperatures was found to be directly related to the dielectric properties of the compound. In particular, field-dependent measurements of capacitance show a magnetocapacitance (MC) effect with double-hysteresis loop behavior in direct correspondence with the magnetization. Our x-ray diffraction results show the Pna$2_1$ structure down to 8 K and suggest the absence of a structural phase transition across $T_N$. Soft x-ray absorption spectroscopy and soft x-ray magnetic circular dichroism (XMCD) measurements at the Fe $L{}_{2,3}$ and Ho $M{}_{4,5}$ edges revealed the oxidation state of Fe and Ho cations to be $3+$. Fe $L{}_{2,3}$ XMCD further shows that ${\mathrm{Fe}}^{3+}$ cations are antiferromagnetically ordered in a noncollinear fashion with spins arranged ${90}^{\circ }$ with respect to each other. Our findings show that $\mathrm{Ho}\mathrm{Fe}\mathrm{W}{\mathrm{O}}_6$ is a type-II multiferroic exhibiting a MC effect. The observed MC effect and the change in polarization by the magnetic field, as well as their direct correspondence with magnetization, further support the strong ME coupling in this compound.

In $\mathrm{RbCo}{\mathrm{Cl}}_3$, the magnetic ${\mathrm{Co}}^{2+}$ ions form weakly coupled Ising chains arranged on a triangular lattice. We have investigated the structure and magnetism in $\mathrm{RbCo}{\mathrm{Cl}}_3$ by high-resolution x-ray diffraction and neutron scattering measurements on powder and single-crystal samples between 1.5 and 300 K. Upon cooling, the ${\mathrm{Co}}^{2+}$ spins develop one-dimensional antiferromagnetic correlations along the chain axis ($c$ axis) below 90 K. Below the first Néel temperature, $T_{\mathrm{N}1}=28\mathrm{K}$, a partial three-dimensional magnetic order sets in, with propagation vector ${\mathbf{k}}_{\mathbf{1}}=\left(1/3,1/3,1\right)$, the moments aligned along the $c$ axis, and every third chain uncorrelated from its neighbors. Only below a second magnetic phase transition at $T_{\mathrm{N}2}=13\mathrm{K}$ does the system achieve a fully ordered state, with two additional propagation vectors: ${\mathbf{k}}_{\mathbf{2}}=\left(0,0,1\right)$ establishes a “honeycomb” $c$-axis order, in which one third of the chains are subject to a strong effective mean field due to their neighbors whereas two thirds experience no net field, while ${\mathbf{k}}_{\mathbf{3}}=\left(1/2,0,1\right)$ governs a small, staggered, in-plane ordered moment. We conclude that $\mathrm{RbCo}{\mathrm{Cl}}_3$ is an excellent material to study the physics of Ising chains in a wide variety of temperature-controlled environments, and our results build an important foundation for the accurate interpretation of the spin dynamics measured in each case.

${\mathrm{Co}}_2$-based Heusler alloys show diverse magnetic behavior, extending from the localized Heisenberg to the delocalized itinerant, and thus cannot be generalized with one specific model. Therefore, we bring together experiments and first-principles calculations to reveal the origin of long-range ferromagnetism in the ${\mathrm{Co}}_2$-based Heusler alloy ${\mathrm{Co}}_2\mathrm{HfSn}$. The precise value of the critical exponents $\beta =0.471\left(4\right), \gamma =1.02\left(4\right)$, and $\delta =3.273\left(5\right)$ with the Curie temperature ($T{}_c=430$ K) were determined experimentally by means of different analytical methods such as modified Arrott plot analysis, the Kouvel-Fisher method, and critical isotherm analysis. The deduced critical exponents belong to the theoretical prediction of the three-dimensional mean-field model. The magnetic exchange distance is found to decay as $J\left(r\right)\sim r^{-4.52}$, indicating the long-range magnetic interaction in ${\mathrm{Co}}_2\mathrm{HfSn}$. Moreover, the magnetic entropy change $-\mathrm{\Delta }{S}_M$ features a maximum at $T_c$, i.e., $-\mathrm{\Delta }{S}_M^{max}\sim$ 29.87(6) J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ at 5 T, whereas power law fitting of $-\mathrm{\Delta }{S}_M^{max}$ with $H$ gives $n^{\prime }=0.663\left(5\right)$, also confirming the mean-field-type magnetic interaction in ${\mathrm{Co}}_2\mathrm{HfSn}$. Meanwhile, in order to explore the origin of long-range ferromagnetic ordering in ${\mathrm{Co}}_2\mathrm{HfSn}$, spin-polarized density functional theory calculations were employed in this study. No stable antiferromagnetic solution with stable local magnetic moments at the Co or Hf site was observed in our fixed spin moment simulation, revealing that ${\mathrm{Co}}_2\mathrm{HfSn}$ is a highly itinerant magnet with a long-range ferromagnetic solution together with robust half-metallic conduction stable against thermal excitation higher than room temperature. Furthermore, our theoretical analysis shows that ${\mathrm{Co}}_2\mathrm{HfSn}$ belongs to an unconventional family of itinerant magnetism. Both the 100% spin-polarized metallicity and ferromagnetism arise from the Co $d$ orbitals, causing it to be unique compared to the conventional itinerant family of Ni, Co, or Fe, where magnetism and metallicity originate from different orbitals characters.

The search for an ideal Kitaev spin liquid candidate with anyonic excitations and long-range entanglement has motivated the synthesis of a new family of intercalated Kitaev magnets such as ${\mathrm{H}}_3\mathrm{Li}{\mathrm{Ir}}_2{\mathrm{O}}_6$, ${\mathrm{Cu}}_2\mathrm{Ir}{\mathrm{O}}_3$, and ${\mathrm{Ag}}_3\mathrm{Li}{\mathrm{Ir}}_2{\mathrm{O}}_6$. The absence of a susceptibility peak and a two-step release of the magnetic entropy in these materials have been proposed as evidence of proximity to the Kitaev spin liquid. Here we present a comparative study of the magnetic susceptibility, heat capacity, and muon spin relaxation ($\mu \mathrm{SR}$) between two samples of ${\mathrm{Ag}}_3\mathrm{Li}{\mathrm{Ir}}_2{\mathrm{O}}_6$ in the clean and disordered limits. In the disordered limit, the absence of a peak in either susceptibility or heat capacity and the lack of zero-field muon precession in the $\mu \mathrm{SR}$ signal give the impression of a proximate spin liquid state. However, in the clean limit, peaks are resolved in both susceptibility and heat capacity, and spontaneous oscillations appear in the $\mu \mathrm{SR}$ signal, confirming long-range antiferromagnetic order in the ground state. The $\mu \mathrm{SR}$ oscillations fit to a Bessel function, characteristic of incommensurate order, as reported in the parent compound $\alpha \text{−}{\mathrm{Li}}_2\mathrm{Ir}{\mathrm{O}}_3$. Our results clarify the role of structural disorder in the intercalated Kitaev magnets.

Using density functional theory, we study the lattice dynamical properties of magnetite (${\mathrm{Fe}}_3{\mathrm{O}}_4$) in the high-temperature cubic and low-temperature monoclinic phases. The calculated phonon dispersion curves and density of states are compared with the available experimental data obtained by inelastic neutron, inelastic x-ray, and nuclear inelastic scattering. We find a very good agreement between the theoretical and experimental results for the monoclinic $Cc$ structure revealing the strong coupling between the charge-orbital (trimeron) order and specific phonon modes. For the cubic phase, clear discrepancies arise due to fluctuation effects, which are not included in the calculation method. Despite this shortcoming, we argue that the main spectral features can be understood assuming that the strong trimeron-phonon coupling is extended above the Verwey transition, with lattice dynamics influenced by the short-range order instead of the average cubic structure. Our results indicate the validity of trimerons (and trimeron-phonon coupling) to explain the physics of magnetite much beyond their original formulation.

Magnetometry measurements of Fe/U and Ni/U bilayer systems reveal a nonmonotonic dependence of the magnetic anisotropy for U thicknesses in the range of 0–8 nm with the Fe/U bilayers showing a more prominent effect as compared to Ni/U. The stronger response for Fe/U is ascribed to the stronger $3d\text{−}5f$ hybridization of Fe and U. This nonmonotonic behavior is thought to arise from quantum well states in the uranium overlayers. Estimating an oscillation period from the nonmonotonic data, and comparing it to Density Functional Theory calculations, we find that wave vector matches to the experimental data can be made to regions of high spectral density in (010) and (100) cuts of the electronic structure of $\alpha$-U, consistent with the measured texture in the films. Unexpectedly, there are also indications of perpendicular magnetic anisotropy in a subset of Fe/U samples at relatively large U thickness.

The inverse Heusler alloy ${\mathrm{Mn}}_2\mathrm{CoAl}$ is known as a spin gapless semiconductor (SGS). It is believed that the positive linear magnetoresistance (PLMR) effect observed at low temperatures indicates the quantum linear MR effect in the gapless electronic band structures near the Fermi level, i.e., evidence of the realization of a SGS [Ouardi et al., Phys. Rev. Lett. 110, 100401 (2013)]. For this reason, one presumes that the observation of the PLMR effect is indirect proof of the demonstration of $XA$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$ consisting of the inverse Heusler structure. In this paper, we observe the PLMR effect at 10 K in homogeneous and single-phase ${\mathrm{Mn}}_2\mathrm{CoAl}$ epitaxial films grown by low-temperature molecular beam epitaxy at $100{}^{\circ }\mathrm{C}$. From anomalous x-ray diffraction measurements and analyses, we clarify that the $100{}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ epitaxial film is not composed of the $XA$-type structure but a disordered $L{2}_{1}B$-type structure including some amount of Mn(A site) $\iff \mathrm{Co}$(C site) swapping and Mn(B site) $\iff \mathrm{Al}$(D site) swapping. On the basis of first-principles density-functional theory calculations, we discuss the correlation between the PLMR effect observed at 10 K and the possible electronic band structure in the disordered $L{2}_{1}B$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$.

We critically reexamine the problem of interatomic exchange interactions, which describe the total energy change caused by infinitesimal rotations of spins near some equilibrium state in the framework of constrained spin-density functional theory (cSDFT). For small variations of the spin magnetization, such interactions can always be related to the response function (or transverse spin susceptibility). However, the form of this relation can depend on additional approximations supplementing the practical calculations. Particularly, the commonly used magnetic force theorem prescribes the linear relation between the exchange interactions and the response function, while the exact theory requires this dependence to be inverse, as it can be rigorously derived from cSDFT. We explore the origin and consequences of these differences in the definition for a wide class of materials, including ferromagnetic Ni, antiferromagnetic NiO, half-metallic ferromagnetic ${\mathrm{CrO}}_2$, multiferroic ${\mathrm{HoMnO}}_3$, and layered van der Waals magnets ${\mathrm{CrCl}}_3$ and ${\mathrm{CrI}}_3$. While in most of these cases, the magnetic force theorem produces quite reasonable results and can be rigorously justified in the long wavelength and strong-coupling limits, the exact formulation appears to be more consistent, especially in dealing with two important issues, which typically arise in the theory of exchange interactions: (i) the treatment of the ligand spins and (ii) the choice of the suitable variable for the description of infinitesimal rotations in the system of spins within cSDFT. Both issues can be efficiently resolved by employing the ideas of adiabatic spin dynamics supplemented with the exact expression for the exchange interactions. Particularly, the ligand spins can produce quite sizable contributions to the total energy change. For this case, we propose a simple downfolding procedure of elimination of the ligand spins from the model by transferring their effects to the interaction parameters between the localized $3d$ spins. Furthermore, the exchange interactions appear to be sensitive to the definition of the variable, which is used to describe the rotations of spins in cSDFT: Generally, the rotations of spin moments and spin magnetization matrix lead to different results. In this respect, we argue that the rotations of spin moments are more suitable for the description of low-energy excitations, while the rotations of the whole magnetization matrix cause much stronger perturbation in the system of spins.

We analyze the many-particle correlations that affect the optical properties of two-dimensional semiconductors. These correlations manifest themselves through the specific optical resonances such as excitons, trions, etc. Starting from the generic electron-hole Hamiltonian and employing the microscopic Heisenberg equation of motion the infinite hierarchy of differential equations can be obtained. In order to decouple the system we address the cluster expansion technique which provides a regular procedure of consistent accounting of many-particle correlation contributions into the interband polarization dynamics. In particular, the partially taken into account three-particle correlations modify the behavior of absorption spectra with the emergence of a trion-like peak additional to excitonic ones. In contrast to many other approaches, the proposed one allows us to model the optical response of 2d semiconductors in the regime when the Fermi energies are of the order of the exciton and trion binding energies, thus allowing us to rigorously model the onset of the excitonic Mott transition, the regime being recently studied in various 2d semiconductors, such as transition metal dichalcogenides.