We theoretically investigate defect formation energies in $\mathrm{La}\mathrm{O}X{\mathrm{S}}_2$ $(X=\mathrm{Sb},\mathrm{Bi})$ using first-principles calculation. We find that the oxygen vacancy is relatively stable, where its formation energy is higher in $X=\text{Sb}$ than in $X=\text{Bi}$. An interesting feature of $X=\text{Sb}$ is that the vacancy of the in-plane sulfur atom becomes more stable than in $X=\text{Bi}$, caused by the formation of an ${\mathrm{Sb}}_2$ dimer and the electron occupation of the impurity energy levels. The formation energies of cation defects and anion-cation antisite defects are positive for the chemical equilibrium condition used in this study. Fluorine likely replaces oxygen, and its defect formation energy is negative for both $X=\text{Sb}$ and Bi, while that for $X=\text{Sb}$ is much higher than $X=\text{Bi}$. Our study clarifies the stability of several point defects and suggests that the in-plane structural instability is enhanced in $X=\text{Sb}$, which seems to affect a structural change caused by some in-plane point defects.

We consider a spin-$j$ particle coupled to a structured bath of bosonic modes that decay into thermal baths. We obtain an analytic expression for the reduced spin state and use it to investigate non-Markovian spin dynamics. In the heavily overdamped regime, spin coherences are preserved due to a quantum Zeno affect. We extend the solution to two spins and include coupling between the modes, which can be leveraged for preservation of the symmetric spin subspace. For many spins, we find that intermode coupling gives rise to a privileged symmetric mode gapped from the other modes. This provides a handle to selectively address that privileged mode for quantum control of the collective spin. Finally, we show that our solution applies to defects in solid-state systems, such as negatively charged nitrogen vacancy centers in diamond.

The compensated ferrimagnet orthoferrite $\mathrm{ErFe}{\mathrm{O}}_3$ exhibits the exchange bias (EB) effect, which was previously detected as the traditional shift of the magnetization hysteresis loops $M$ vs $H$ near the compensation temperature $T_{\mathrm{comp}}=45\mathrm{K}$. This paper shows that another specific phenomenon, temperature-driven spin switching and exchange bias, occurs in this ferrimagnet. Namely, the EB manifests itself as the temperature shift of the hysteresis loops $M$ vs $T$, which occurs upon successive cooling and heating in a weak magnetic field. The $M$ vs $T$ loops limiting the region of coexistence of negative and positive magnetization are shifted towards lower or higher temperatures, depending on the sign of the applied magnetic field, which causes the unidirectional EB anisotropy. The EB anisotropy energy, which contributes to the energy barrier for switching spins to an equilibrium state, determines the shift in the switching temperature $T_{\mathrm{sw}}$. Exchange-biased spin switching in $\mathrm{ErFe}{\mathrm{O}}_3$ is discussed within a model, which explains the magnetic compensation of the canted ferromagnetic moment of the ${\mathrm{Fe}}^{3+}$ spins and the opposite moment of paramagnetic ${\mathrm{Er}}^{3+}$ spins induced by the antiferromagnetic exchange interaction between the Er and Fe ions.

The functional characteristics of double perovskites with a unique ferromagnetic-insulator ground state have been controversial due to the unavoidable presence of antisite disorders (ASDs). Here, we aim to investigate the origin of magnetic ordering on local and global scales in the ${\mathrm{Sm}}_2{\mathrm{NiMnO}}_6$ (SNMO) double perovskite system. Different calcination routes are exploited to generate different cation arrangements in SNMO and the corresponding magnetic configurations are examined using the high-energy $(E\sim 0.3\mathrm{eV})$ “hot neutrons”, which has helped to overcome Sm absorption as well as to record total (Bragg $+$ diffuse) scattering profiles with high momentum transfer ($Q_{\max }\sim 24{\AA }^{-1}$). We have observed that the Ni-Mn sublattice adopts long-range collinear ferromagnetic $F_x{F}_z$ structure with a commensurate $\mathbf{k}=(0,0,0)$ propagation vector, below ordering temperature $T\lesssim 160\mathrm{K}$, irrespective of variable ASD concentrations. In addition, the signatures indicating the antiparallel polarization of Sm paramagnetic moments with respect to the Ni-Mn network are noticed in the vicinity of anomalous magnetic transitions at $T\lesssim 35\mathrm{K}$. The real-space pair distribution function calculations have provided a direct visualization of ASDs by means of broadening in Ni/Mn-Mn/Ni linkage. Employing the reverse Monte Carlo approach on diffuse magnetic scattering profiles, we have observed the negative spin-spin correlation function which suggests the Ni-Ni antiferromagnetic exchange interactions ranging up to first-nearest-neighbor distance. These results confirm that the existence of ASDs in a cation ordered host matrix leads to competing ferromagnetic-antiferromagnetic phases in a broad temperature range, which quantitatively governs the temperature-dependent bulk magnetic observables of the SNMO system.

The Dirac point in Pt-doped ${\mathrm{IrTe}}_2$ is known to be tuned by controlling the doping concentration. For 10% Pt, it is seen that the Dirac point exists close to the Fermi energy of the system. This leads to the expectation that, for such doping, the system might host unconventional (topological) superconductivity. Here, we present a detailed microscopic and spectroscopic investigation of $\mathrm{Pt}\text{−}{\mathrm{IrTe}}_2$ under an ultrahigh vacuum, low-temperature scanning tunneling microscope. We find that, for the crystals of ${\mathrm{Ir}}_0{.}_9{\mathrm{Pt}}_0{.}_1{\mathrm{Te}}_2$, the surface shows patches of atomic scale over which defects are seen to be randomly distributed. Tunneling spectroscopy reveals that ${\mathrm{Ir}}_0{.}_9{\mathrm{Pt}}_0{.}_1{\mathrm{Te}}_2$ condenses into a fully gapped Bardeen-Cooper-Schrieffer-like (BCS) $s$-wave superconducting state. The superconducting gap was measured to be $460\mu \mathrm{eV}$ at 310 mK. The value of $2{\mathrm{\Delta }}_0/k_B{T}_c\sim 6$ is consistent with a conventional BCS superconductor in the strong-coupling limit. The conventional behavior is surprising, given the topological band structure of the material.

Hydrogen (H) and silicon (Si) are considered as important light elements for the planetary cores. A large amount of H is able to alloy with pure Fe metal at high pressures. Si can also alloy well with Fe. However, it remains uncertain how much H can alloy with iron silicides and if it alloys how H can alter the crystal structures of Fe-Si alloys at high pressures-temperatures ($P\text{−}T$). We performed experiments on Fe-9Si and Fe-16Si alloys (9 and 16 wt % Si, respectively) in a H medium up to 42.2 GPa and 3000 K in diamond-anvil cells coupled with pulsed laser heating and gated synchrotron x-ray diffraction techniques. We found conversion of the Fe-Si alloys into Fe-rich (fcc and dhcp $\mathrm{Fe}{\mathrm{H}}_x$), Si-rich (B20 and B2 FeSi), and intermediate (${\mathrm{Fe}}_5{\mathrm{Si}}_3{\mathrm{H}}_x$) phases. The new ${\mathrm{Fe}}_5{\mathrm{Si}}_3{\mathrm{H}}_x$ phase has a structure similar to the hexagonal ${\mathrm{Fe}}_5{\mathrm{Si}}_3$ phase but with expanded volumes, and thus, possible H incorporation. Both the observed volume expansion and the H content estimated by density-functional theory calculations support a significant amount of H with H/Fe ≈ 0.6 in the crystal structure. Because ${\mathrm{Fe}}_5{\mathrm{Si}}_3$ is known to break down above ∼1300 K at ∼18 GPa, our results suggest that hydrogen stabilizes the hexagonal structure at high $P\text{−}T$. These results have implications for the crystallization of Fe-rich liquid at the solid-to-liquid boundary of planetary cores and possible existence of chemical heterogeneities in the solid cores.

In amorphous solids, soft vibrational modes derived from normal mode analysis can be utilized to identify the soft particles that are prone to irreversible rearrangements. However, the normal mode analysis approach cannot explain why the spatial distributions of clustered soft particles do not change over time. We define a softness parameter based on the vibrational density of states calculated directly from molecular dynamics simulations with both the harmonic vibrations and anharmonic relaxations being properly captured at finite temperatures. This parameter spontaneously correlates with the real space atomic motions and the dynamics heterogeneity. Using the softness parameter, we show that the softest particles are confined within rigid cages. These particles keep rearranging reversibly without long-range diffusion. The moderately soft particles rearrange irreversibly, and the hard particles mainly participate in vibrations without rearrangement. We also show that the soft particles form locally disordered structures, while the hard particles present strong ordering. These findings confirm the defective nature of soft particles, and provide insights on the nature of softness as the ability to rearrange, but not necessarily irreversibly.

Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical points (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J\text{−}{Q}_3$ model. In this paper, we study the nonequilibrium imaginary-time relaxation dynamics in the $J\text{−}{Q}_2$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss possible experimental realizations in devices of quantum computers.

We consider trilayer ${\mathrm{F}}_1{\mathrm{F}}_2{\mathrm{F}}_3$ Josephson junctions that are finite in two dimensions and have arbitrary magnetizations in each ferromagnet ${\mathrm{F}}_i(i=1,2,3)$. The trilayers are sandwiched between two $s$-wave superconductors with a macroscopic phase difference $\mathrm{\Delta }\phi$. Our results reveal that when the magnetizations have three orthogonal components, a supercurrent can flow at $\mathrm{\Delta }\phi =0$. With our generalized theoretical and numerical techniques, we study the planar spatial profiles and $\mathrm{\Delta }\phi$ dependencies of the charge supercurrents, spin supercurrents, spin torques, and density of states. Remarkably, upon increasing the magnetization strength in the central ferromagnet layer up to the half-metallic limit, the self-biased current and induced second harmonic component become dramatically enhanced while the critical supercurrent reaches its maximum value. Additionally, for a broad range of exchange-field strengths and orientations, the ground state of the system can be tuned to an arbitrary phase difference ${\phi }_0$. For intermediate exchange-field strengths in the middle layer ${\mathrm{F}}_2$, a ${\phi }_0$ state can arise that creates a superconducting diode effect, whereby $\mathrm{\Delta }\phi$ can be tuned to create a one-way dissipationless current flow. The spin currents and effective magnetic moments reveal a long-ranged spin torque in the half-metallic phase. Moreover, the density of states unveils the emergence of zero-energy peaks for the mutually orthogonal magnetization configurations. Our results suggest that this simple trilayer Josephson junction can be an excellent candidate for producing experimentally accessible signatures for long-ranged self-biased supercurrents and supercurrent diode effects.

We investigate the proximity spin-orbit and exchange couplings in ABA and ABC trilayer graphene encapsulated within monolayers of semiconducting transition-metal dichalcogenides and the ferromagnetic semiconductor ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. Employing first-principles calculations, we obtain the electronic structures of the multilayer stacks and extract the relevant proximity-induced orbital and spin interaction parameters by fitting the low-energy bands to model Hamiltonians. We also demonstrate the tunability of the proximity effects by a transverse electric field. Using the model Hamiltonians, we also study mixed spin-orbit/exchange coupling encapsulation, which allows us to tailor the spin interactions very efficiently by the applied field. We also summarize the spin-orbit physics of bare ABA, ABC, and ABB trilayers, and we provide—along with the first-principles results of the electronic band structures, density of states, spin splittings, and electric-field tunabilities of the bands—a qualitative understanding of the observed behavior and realistic model parameters as a resource for model simulations of transport and correlation physics in trilayer graphene.

The energy and wave function of a harmonically confined $N$-electron system coupled to light is calculated by separating the wave functions of the relative and center-of-mass (CM) motions. The light only couples to the CM variable, and the coupled equation can be solved analytically. The relative motion wave function has to be numerically approximated, but the relative Hamiltonian is independent of the coupling strength and it only gives a shift in the energy. The approach works for any coupling strength and the effective coupling strength can be increased by increasing the number of electrons. This gives an extra degree of freedom to fine tune the resonances and other properties of the light-matter coupled systems. Examples of wave functions of light-matter hybrid states are presented.

Restricted Boltzmann machines (RBMs) have proven to be a powerful tool for learning quantum wave-function representations from qubit projective measurement data. Since the number of classical parameters needed to encode a quantum wave function scales rapidly with the number of qubits, the ability to learn efficient representations is of critical importance. In this paper, we study magnitude-based pruning as a way to compress the wave-function representation in an RBM, focusing on RBMs trained on data from the transverse-field Ising model in one dimension. We find that pruning can reduce the total number of RBM weights, but the threshold at which the reconstruction accuracy starts to degrade varies significantly depending on the phase of the model. In a gapped region of the phase diagram, the RBM admits pruning over half of the weights while still accurately reproducing relevant physical observables. At the quantum critical point, however, even a small amount of pruning can lead to significant loss of accuracy in the physical properties of the reconstructed quantum state. Our results highlight the importance of tracking all relevant observables as their sensitivity varies strongly with pruning. Finally, we find that sparse RBMs are trainable, and we discuss how a successful sparsity pattern can be created without pruning.

We propose a multiboundary generalization of thermofield double states (TFD) of a two-dimensional conformal field theory (CFT) and show, through a conformal map to the complex plane, that they are closely related to multipoint correlation functions. We then also describe how to approximately realize these multiboundary TFD states numerically on the lattice, starting from a critical quantum spin-chain Hamiltonian. In addition, finite-size corrections on the lattice are seen to be significantly reduced by the use of smoothers, numerically optimized unitary transformations that locally rearrange the quantum spin degrees of freedom. One merit of the spin-chain realization is that it allows us to probe the properties of the proposed multiboundary TFD states through numerical experiments, including the characterization of their entanglement structure. As an illustration, we explicitly construct generalized TFD states with three and four boundaries for the Ising CFT and compute entanglement quantities using free-fermion techniques. We find ranges of parameters where their multipartite entanglement is significant or negligible.

Applying electric or magnetic fields is widely used to not only create and manipulate topological states but also facilitate their observations in experiments. In this paper, we show by first-principles calculations and topological analysis that the time-reversal (TR) symmetry-broken quantum spin Hall (QSH) phase emerges in a two-dimensional (2D) ferromagnetic ${\mathrm{Bi}}_2{\mathrm{Te}}_3/{\mathrm{MnBi}}_2{\mathrm{Te}}_4$ bilayer. This TR-symmetry broken QSH phase possesses a highly tunable nontrivial band gap under external electric fields (or tuning interlayer distance). Furthermore, based on the Wannier-function-based tight-binding approach, we reveal that a topological phase transition from the TR-symmetry broken QSH phase to the quantum anomalous Hall (QAH) phase occurs with the increase of magnetic fields. Besides, we also find that a reverse electric fields can facilitate the realization of QAH phase. Our paper not only uncovers the ferromagnetic topological properties of ${\mathrm{Bi}}_2{\mathrm{Te}}_3/{\mathrm{MnBi}}_2{\mathrm{Te}}_4$ bilayer tuned by electric and magnetic fields, but also can stimulate further applications to spintronics and topological devices.

We present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for the ground state is performed with the $O\left(N\right)$ Krylov subspace method implemented in openmx. Second, the crystal momentum-dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of the Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures down to the first magic angle ($\theta =1.{08}^{\circ }$) with high enough accuracy at affordable costs. The band structures are in good agreement with those from tight-binding models, continuum models, plane-wave pseudopotential based ab initio calculations, and experimental observations. This method is also shown to be efficient in twisted double-bilayer graphene and bilayer ${\mathrm{WSe}}_2$. We think this two-step method can play a crucial role in other twisted two-dimensional materials, especially those with much more complex band structure and where the effective model is hard to construct.

While the internal structure of Abelian topological order is well understood, how to characterize the non-Abelian topological order is an outstanding issue. We propose a distinctive scheme based on the many-body Chern number matrix to characterize non-Abelian multicomponent fractional quantum Hall states. As a concrete example, we study the many-body ground state of two-component bosons at the filling faction $\nu =4/3$ in topological flat band models. Utilizing density-matrix renormalization group and exact diagonalization calculations, we demonstrate the emergence of non-Abelian spin-singlet fractional quantum Hall effect under three-body interaction, whose topological nature is classified by sixfold degenerate ground states and a fractionally quantized Chern-number matrix.

Ligand field density functional theory calculations of the dioxides of thorium, uranium, and plutonium have been combined with high-energy-resolution fluorescence detection (HERFD) in x-ray absorption spectroscopy and inverse photoelectron spectroscopy (IPES) measurements to provide powerful insight into the underlying composition of the unoccupied $5f$ electronic structure in these $5f$ localized systems. Fine structure in the $5f_{5/2}$ transitions in HERFD can be directly correlated with the fine structure in the leading edge of the IPES. The shapes, intensities, and systematics in HERFD and IPES are explained in a consistent and rigorous fashion in terms of the j-specific $5f$ electronic structure.

We studied the linear electro-optic effect of chiral topological semimetals which are characterized by high-fold chiral fermions separated in energy space. We identify that the general second-order conductivity ${\sigma }_{xyz}^{\left(2\right)}\left(\omega \right)$ includes three sources from the shift current, injection current, and nonlinear anomalous current with frequency $\omega$, respectively. The ${\sigma }_{xyz}^{\left(2\right)}\left(\omega \right)$ contributed by the nonlinear anomalous current is antisymmetric under the exchange of indices $x$ and $y$, and it is proportional to relaxation time and Chern number. We demonstrate that the electro-optic coefficient below 0.65 eV in chiral crystal RhSi is dominated by the nonlinear anomalous current and injection current, and it renders a relatively low half-wave voltage in the order of hundreds of volts. This work classifies how the Berry curvature modifies the linear electro-optic effect in chiral topological semimetals and opens an avenue to design the electro-optic modulator with half-wave voltage compatible with the complementary metal-oxide semiconductor circuit.

Under high-pressure conditions, the changes of atomic arrangement and stacking of the lattice structures lead to enhanced electronic correlation effect and even superconductivity. Motivated by a recent experimental demonstration of pressure-induced superconductivity in a C-S-H system, in this work, we construct a ${\mathrm{CSH}}_3$ system via simple combining of ${\mathrm{H}}_3\mathrm{S}$ and C to study the crystal structural evolution and possible superconductivity at high pressure using first-principles calculations. We predicted the trigonal and orthorhombic crystal structures of ${\mathrm{CSH}}_3$ under pressure, with the space groups $R\text{−}3m, Pbcm$, and $Pmmn$, respectively. We find that the trigonal $R\text{−}3m$ phase transform to the orthorhombic $Pbcm$ phase at 210 GPa, at which the volume of ${\mathrm{CSH}}_3$ phases drops by $\sim 7\%$. Due to large the electronic density of states of the H component near the Fermi level, the $T_c$ is higher in the $Pbcm$ and the $Pmmn$ phases than in the $R\text{−}3m$ phase. A $T_c$ as high as 98 K is found for the $Pbcm$ phase at 250 GPa.