We report the structural and physical properties of two Y-Au-Si (YAS) compounds, ${\mathrm{Y}}_{14.1}{\mathrm{Au}}_{69.2}{\mathrm{Si}}_{16.7}$ and ${\mathrm{Y}}_{15.4}{\mathrm{Au}}_{68.6}{\mathrm{Si}}_{16.1}$, which are 1/1 approximant crystals of a Tsai-type quasicrystal without intrinsic magnetic moments. The compounds differ by the presence of either a tetrahedron (Au,Si)${}_4$ or a single Y atom at the center of their characteristic structural building unit consisting of concentric polyhedral shells. Both compounds exhibit bulk superconductivity, which seems to be of a conventional type-II BCS type. The compound with Y atoms at the cluster center has a slightly higher transition temperature with a sharper step in the specific heat than the compound with tetrahedral units. We discuss the occurrence of this superconducting state in the light of the specific structural and physical properties of these quasicrystal approximants.

We discuss physical constructions and the boundary properties of various symmetry-protected topological phases that involve 1-form symmetries from one spatial dimension to four spatial dimensions ($4d$). For example, the prototype three-dimensional ($3d$) boundary state of $4d$ SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries; that is, the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomalies of $3d$ states of matter. Connection between SPT states with 1-form symmetries and condensed-matter systems such as quantum dimer models at one lower dimension will also be discussed. Whether a quantum dimer model can have a trivial gapped phase depends on the nature of its corresponding bulk state in one higher dimension.

We study the tunnel magnetoresistance (TMR) effect and magnetocrystalline anisotropy in a series of magnetic tunnel junctions (MTJs) with $L{1}_1$-ordered fcc ferromagnetic alloys and MgO barrier along the [111] direction. Considering the (111)-oriented MTJs with different $L{1}_1$ alloys, we calculate their TMR ratios and magnetocrystalline anisotropies on the basis of the first-principles calculations. The analysis shows that the MTJs with Co-based alloys (CoNi, CoPt, and CoPd) have high TMR ratios over 2000%. These MTJs have energetically favored Co-O interfaces where interfacial antibonding between Co $d$ and O $p$ states is formed around the Fermi level. We find that the resonant tunneling of the antibonding states, called the interface resonant tunneling, is the origin of the obtained high TMR ratios. Such a mechanism is similar to that found in our recent work on the simple Co/MgO/Co(111) MTJ [K. Masuda et al., Phys. Rev. B 101, 144404 (2020)]. In contrast, different systems have different spin channels where the interface resonant tunneling occurs; for example, the tunneling mainly occurs in the majority-spin channel in the CoNi-based MTJ while it occurs in the minority-spin channel in the CoPt-based MTJ. This means that even though the mechanism is similar, different spin channels contribute dominantly to the high TMR ratio in different systems. Such a difference is attributed to the different exchange splittings in the particular Co $d$ states contributing to the tunneling though the antibonding with O $p$ states. Our calculation of the magnetocrystalline anisotropy shows that many $L{1}_1$ alloys have large perpendicular magnetic anisotropy (PMA). In particular, CoPt has the largest value of anisotropy energy $K_{\mathrm{u}}\approx 10\mathrm{MJ}/{\mathrm{m}}^3$. We further conduct a perturbation analysis of the PMA with respect to the spin-orbit interaction and reveal that the large PMA in CoPt and CoNi mainly originates from spin-conserving perturbation processes around the Fermi level.

Magnetic transition element doping in topological insulators, which breaks the time-reversal symmetry, gives rise to the diverse range of exotic consequences, though proper understanding of the magnetic order has rarely been attempted by using any microscopic experiments. We report the occurrence of the magnetic order in (${\mathrm{Sb}}_{0.95}{\mathrm{Cr}}_{0.05}{)}_2{\mathrm{Te}}_3$ using the muon spin relaxation studies. The asymmetry curve at low temperature ($T$) shows an evidence of a damped oscillation, providing a clue about the internal magnetic field ($H_{\mathrm{int}}$), which follows $H_{\mathrm{int}}\left(T\right)=H_{\mathrm{int}}\left(0\right){[1-T/T_C]}^{\beta }$ with ordering temperature $T_C\approx 6.1$ K and critical exponent $\beta \approx 0.22$. The critical exponent is close to the two-dimensional XY-type interaction. The magnetization curves at low $T$ exhibit a ferromagnetic behavior at low field ($H$) and the de Haas–van Alphen (dHvA) effect at high $H$. The analysis of the dHvA oscillation proposes the charge carrier that acts like a massive Dirac fermion. The Berry phase, as obtained from the Landau-level fan diagram, suggests a surface state gap at the Dirac point. The complex electronic structure is discussed by correlating the magnetic order attributed to the Cr doping in ${\mathrm{Sb}}_2{\mathrm{Te}}_3$.

We propose a general theory of ferromagnetic resonance (FMR) spectroscopy for symmetry-breaking synthetic antiferromagnets (SAFs). Generally, both inhomogeneity and different thickness of the two ferromagnetic sublayers of a SAF result in the intrinsic symmetry breaking, thus excludes the crossing between pure in-phase and out-of-phase resonance modes with opposite parity. Alternatively, new frequency branches become hybridization of original bare modes in terms of symmetry breaking induced magnon-magnon coupling, hence generate an indirect gap in FMR frequencies. The gap widths for several typical cases are presented and compared with existing data. In particular, for the inhomogeneity case, the indirect gap width is linearly proportional to the asymmetry degree and takes a square (rather than linear) dependence on the magnon-magnon coupling strength, indicating a case-by-case recalibration of the measuring method of the latter. Our theory provides a simple but physical understanding of the rich structure of FMR spectra for asymmetric SAFs.

The theoretical description and experimental study of a reversible vibrational vortex motion induced in a type-II superconductor by a weak low-frequency ac magnetic field are discussed. The case where the external magnetic field and vortex lines are parallel to the surface of the superconductor is considered. The equilibrium positions of vortices near a surface, the amplitude of their vibrations, and the contribution of this process to the dynamic permeability ${\mu }_v$ are calculated. In these calculations, the interactions of vortices with each other, with the surface, and with pinning centers are considered within the discrete vortex lattice model. The calculations in the London approximation are compared with the results obtained within a more accurate model, including the spatial variation of the order parameter in the vortex core by means of a variational function. It is shown that the structural parameters of the vortex lattice near the surface depend on the accuracy of the description of the intervortex interactions, but the contribution ${\mu }_v$ appears to be model independent. It is important that this conclusion is valid in the case of the exponential approximation for the interaction between vortex rows. In this approximation, the problem under consideration is analytically examined, and formulas describing the dependences of the parameters of the vortex lattice and the contribution ${\mu }_v$ on the external dc magnetic field and the characteristics of a superconductor are derived. The theoretical results are compared with experimental data for a $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ high-$T_c$ superconducting single-crystal plate. The magnetic field is parallel to the plate, i.e., to the crystallographic $ab$ plane. A strong anisotropy of the properties and shape of the crystal is considered when analyzing the experimental data. A procedure for the determination of the experimental dependence ${\mu }_v\left(H\right)$ is described. It is shown that the reversible vibrations of vortices occur near the planes of the single-crystal plate in the direction of the crystallographic $c$ axis, whereas vortices enter its lateral ends and leave them (along the structural layers) even at a small magnetic field amplitude of about 1 Oe. It is found that the developed theoretical description reproduces the experimental data ${\mu }_v\left(H\right)$ in the entire studied range of temperatures and magnetic fields under the assumptions that pinning is isotropic and the length of interaction of vortices with pinning centers is close to the coherence length.

We perform a systematic study of static and dynamical magnetic properties of the $t\text{−}{t}^{\prime }$ Hubbard model in a parameter regime relevant for high-temperature superconducting cuprates. We adopt as solution method the dynamical mean-field theory approximation and its real-space cluster extension. Our results show that large $t^{\prime }/t$ suppresses incommensurate features and eventually leads to ferromagnetic instabilities for sufficiently large hole doping $x$. We identify isosbestic points which separate parts of the Brillouin zone with different scaling behaviors. Calculations are compared to available nuclear magnetic resonance, nuclear quadrupole resonance, inelastic neutron scattering, and resonant inelastic x-ray scattering experiments. We show that while many trends are correctly described, e.g., the evolution with $x$, some aspects of the spin-lattice relaxation rates can apparently only be explained invoking accidental cancellations. In order to capture the material dependence of magnetic properties in full, it may be necessary to add further degrees of freedom.

An unprecedented graphyne allotrope with square symmetry and nodal line semimetallic behavior has been proposed in the two-dimensional (2D) realm. The emergence of the Dirac loop around the high-symmetry points in the presence of both the inversion and time-reversal symmetries is a predominant feature of the electronic band structure of this system. Besides, the structural stability in terms of the dynamic, thermal, and mechanical properties has been critically established for the system. Following the exact analytical model based on the real-space renormalization group scheme and tight-binding approach, we have inferred that the family of 2D nodal line semimetals with square symmetry can be reduced to a universal four-level system in the low-energy limit. This renormalized lattice indeed explains the underlying mechanism responsible for the fascinating emergence of 2D square nodal line semimetals. Besides, the analytical form of the generic dispersion relation of these systems is well supported by our density-functional theory results. Finally, the nontrivial topological properties have been explored for the predicted system without breaking the inversion and time-reversal symmetry of the lattice. We have obtained that the edge states are protected by the nonvanishing topological index, i.e., Zak phase.

We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities, and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we obtained can also be used to help construct improved density functionals.

Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the topological invariants—giving a symmetry classification table. Here we consider various topological phases protected by different symmetries and examine how the corresponding topological invariants evolve once the protecting symmetry is spontaneously lost. To our surprise, we find that the topological invariants and edge states can sometimes be robust to symmetry-breaking quantum orders. This topological robustness persists as long as the mean-field Hamiltonian in a symmetry-breaking ordered phase maintains its adiabatic continuity to the noninteracting Hamiltonian. For example, for a time-reversal symmetric topological phase in $2+1$ dimensions, we show that the ${\mathbb{Z}}_2$ time-reversal polarization continues to be a good topological invariant even after including distinct time-reversal breaking order parameters. Similar conclusions are drawn for various other symmetry-breaking cases. Finally, we discuss that the change in the internal symmetry associated with the spontaneous symmetry breaking has to be accounted for to reinstate the topological invariants into the expected classification table.

We present a theoretical study of the effect of an external dc magnetic field in the near-field radiative heat transfer between two one-dimensional magnetophotonic crystals with unit cells comprising a magneto-optical layer made of $n$-doped InSb and a dielectric layer. We find that in the absence of an external field, and depending on the gap size, the radiative heat transfer between these multilayer structures can be larger or smaller than that of the case of two InSb infinite plates. On the other hand, when an external magnetic field is applied, the near-field radiative heat transfer is reduced as a consequence of the suppression of hybridized surface polariton waves that are supported for transverse magnetic polarized light. We show that such reduction is exclusively due to the appearance of magnetic-field induced hyperbolic modes and not to the polarization conversion in this magneto-optical system.

Two-dimensional magnetic materials have great potential applications in designing spintronics devices. Here, electronic structures and magnetic properties of monolayer molybdenum trihalides $\mathrm{Mo}{X}_3$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are systematically investigated by using first-principles calculations with hybrid functional HSE06. Our calculations show that the magnetic ground state of the monolayer ${\mathrm{MoI}}_3$ is ferromagnetic (FM) with a Curie temperature of 24 K, while the monolayer $\mathrm{Mo}{\mathrm{Cl}}_3$ and $\mathrm{Mo}{\mathrm{Br}}_3$ are $\mathrm{N}\acute{\mathrm{e}}\mathrm{el}$ antiferromagnetic. The monolayer $\mathrm{Mo}{\mathrm{Cl}}_3$ and $\mathrm{Mo}{\mathrm{Br}}_3$ can be tuned into FM phase with a tensile strain. The monolayer ${\mathrm{MoI}}_3$ has a large magnetic anisotropy energy (MAE) of 1.051 meV/Mo with an out-of-plane easy axis. The Curie temperature and MAE of the monolayer ${\mathrm{MoI}}_3$ can be increased by about $50\%$ with a tensile strain of $3\%$. Remarkably, the monolayer ${\mathrm{MoI}}_3$ and the tensile strained $\mathrm{Mo}{\mathrm{Cl}}_3$ and $\mathrm{Mo}{\mathrm{Br}}_3$ are found to be bipolar ferromagnetic semiconductors. The Curie temperature of the monolayer ${\mathrm{MoI}}_3$ can be increased up to room temperature by carrier doping. For the monolayer $\mathrm{Mo}{\mathrm{Br}}_3$, a magnetic phase transition from the antiferromagnetic to FM can be triggered by an electron doping. In addition, the room-temperature half-metallic states can be achieved in the carrier-doped monolayer ${\mathrm{MoI}}_3$ and tensile strained $\mathrm{Mo}{\mathrm{Br}}_3$. The topological properties for the valence bands of the monolayer $\mathrm{Mo}{X}_3$ are also studied. Chern insulating states are obtained in the tensile strained monolayer $\mathrm{Mo}{\mathrm{Cl}}_3$ and $\mathrm{Mo}{\mathrm{Br}}_3$. Our paper shows that the monolayer $\mathrm{Mo}{X}_3$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are promising candidates for exploring two-dimensional magnetism and spintronics in experiments.

In this paper, we study an Anderson-localization-induced quantized transport in disordered Chern insulators (CIs). By investigating the disordered CIs with a step potential, we find that the chiral interface states emerge along the interfaces of the step potential, and the energy range for such quantized transport can be manipulated through the potential strength. Furthermore, numerical simulations on the case with a multistep potential demonstrate that such a chiral state can be spatially shifted by varying the Fermi energy, and the energy window for quantized transport is greatly enlarged. Experimentally, such a chiral interface states can be realized by imposing transverse electric field, in which the energy window for quantized transport is much broader than the intrinsic band gap of the corresponding CI. These phenomena are quite universal for disordered CIs due to the direct phase transition between the CI and the normal insulator.

We show that annihilating a pair of Dirac fermions implies a topological transition from the critical semimetallic phase to an obstructed atomic limit insulator phase instead of a trivial insulator. This is shown to happen because of branch cuts in the phase of the wave functions, leading to nontrivial Zak phase along certain directions. To this end, we study their ${\mathbb{Z}}_2$ invariant and also study the phase transition using entanglement entropy. We use low-energy Hamiltonians and numerical result from model systems to show this effect. These transitions are observed in realistic materials, including strained graphene and buckled honeycomb group V (Sb/As).

The observation of chiral-induced spin selectivity (CISS) in biological molecules still awaits a full theoretical explanation. In a recent Rapid Communication, Varela et al. [Phys. Rev. B 101, 241410(R) (2020)] presented a model for electron transport in biological molecules by tunneling in the presence of spin-orbit interactions. They then claimed that their model produces a strong spin asymmetry due to the intrinsic atomic spin-orbit strength. As their Hamiltonian is time-reversal symmetric, this result contradicts a theorem by Bardarson [J. Phys. A: Math. Theor. 41, 405203 (2008)], which states that such a Hamiltonian cannot generate a spin asymmetry for tunneling between two terminals (in which there are only a spin-up and a spin-down channel). Here we solve the model proposed by Varela et al. and show that it does not yield any spin asymmetry, and therefore cannot explain the observed CISS effect.

Topological pumping has numerous applications in quantum information processing, e.g., the spatial entanglement distribution of the two correlated particles via the disordered bulk channel in the modulated Rice-Mele model [Phys. Rev. A 101, 052323 (2020)]. This spatial entanglement distribution actually indicates that, via the bulk Thouless pumping channel assisted by the disorder, the particle initially prepared at the middle site can be pumped towards the two-end sites with the approximately equal probability, which exhibits the latent possibility to implement the topological split-flow device, such as the topological beam splitter. However, the introduction of the disorder inevitably destroys the correlation of the phase at two-end sites, which is crucial for the applications of the topological beam splitters. To handle it, here we induce a topological interface via introducing the defect into the nearest-neighbor (NN) hopping of the Rice-Mele model, which can be further treated as a topological edge channel to implement the topological edge pumping. We show that, based on this topological edge channel, the particle initially prepared at the middle site can also be transferred into two-end sites with the approximately equal probability, implying the fact of implementing the topological beam splitter by the defect-induced topological edge channel. Significantly, compared with the topological beam splitter assisted via the disordered bulk channel, the topological beam splitter assisted by the defect-induced topological interface cannot destroy the correlation of the phase at two-end sites, even when the very slight on-site disorder or relatively large NN disorder is added into the system. Our scheme provides a perspective to implement the quantum information processing and prepare the quantum optical devices based on the topological edge pumping.

We show how $1+1$-dimensional fermionic symmetry-protected topological states (SPTs, i.e., nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity ${(-1)}^F$, while the antiunitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., “parity” anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multilayers of $1+1\mathrm{d}$ Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher space-time dimensions via a cobordism theory.

Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The ‘energy-weighted’ density matrix embedding theory (EwDMET) was established recently as a way to systematically control the resolution of the fragment-environment coupling and allow for true quantum fluctuations over this boundary to be self-consistently optimized within a fully static framework. In this work, we reformulate the algorithm to ensure that EwDMET can be considered equivalent to an optimal and rigorous truncation of the self-consistent dynamics of dynamical mean-field theory (DMFT). A practical limitation of these quantum embedding approaches is often a numerical fitting of a self-consistent object defining the quantum effects. However, we show here that in this formulation, all numerical fitting steps can be entirely circumvented, via an effective Dyson equation in the space of truncated dynamics. This provides a robust and analytic self-consistency for the method, and an ability to systematically and rigorously converge to DMFT from a static, wave function perspective. We demonstrate that this improved approach can solve the correlated dynamics and phase transitions of the Bethe lattice Hubbard model in infinite dimensions, as well as one- and two-dimensional Hubbard models where we clearly show the benefits of this rapidly convergent basis for correlation-driven fluctuations. This systematically truncated description of the effective dynamics of the problem also allows access to quantities such as Fermi liquid parameters and renormalized dynamics, and demonstrates a numerically efficient, systematic convergence to the zero-temperature dynamical mean-field theory limit.

In experimentally measured temperature-composition ferroelectric phase diagrams of ${\mathrm{BaTiO}}_3$-based binary systems, a quadruple point where cubic (C), tetragonal (T), orthorhombic (O), and rhombohedral (R) phases converge has been frequently reported in previous work. More interestingly, the quadruple points are experimentally found to behave as a critical point with large enhancement in properties. However, it has remained a fundamental question as to whether a quadruple point in a binary ferroelectric system defies the thermodynamic phase rule and whether such a point necessarily goes critical. In this study, it is demonstrated by Landau theory that a C-T-O-R quadruple point in a binary ferroelectric system can only exist in the form of a unique type of critical point at which two first-order transition lines and two second-order ones meet, and such critical quadruple points do not defy the thermodynamic phase rule. It is further shown that at such a critical C-T-O-R quadruple point, the system exhibits infinitely large piezoelectric coefficients, which agrees with the high piezoelectricity observed at the C-T-O-R quadruple point in a number of ${\mathrm{BaTiO}}_3$-based binary ferroelectric systems and also helps to explain the large piezoelectricity obtained at the morphotropic phase boundaries of these quadruple point based systems.