In this work, we present some new understanding of topological order, including three main aspects. (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of gapped quantum liquid as a special kind of gapped quantum states that can “dissolve” any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant—topological entanglement entropy—to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by stochastic local (SL) transformations (i.e., local invertible transformations): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.

On the basis of the multiorbital dynamical mean-field theory, a three-orbital Hubbard model with relativistic spin-orbit coupling (SOC) is studied at five electrons per site. The numerical calculations are performed by employing the continuous-time quantum Monte Carlo (CTQMC) method based on the strong-coupling expansion. We find that appropriately choosing bases, i.e., the maximally spin-orbit-entangled bases, drastically improves the sign problem in the CTQMC calculations, which enables us to treat exactly the full Hund's coupling and pair-hopping terms. This improvement is also essential to reach at low temperatures for a large SOC region where the SOC most significantly affects the electronic structure. We show that a metal-insulator transition is induced by the SOC for fixed Coulomb interactions. The insulating state for smaller Coulomb interactions is antiferromagnetically ordered with the local effective total angular momentum $j=1/2$, in which the ($j=1/2$)-based band is essentially half filled, while the ($j=3/2$)-based bands are completely occupied. More interestingly, for larger Coulomb interactions, we find that an excitonic insulating state emerges, where the condensation of an electron-hole pair in the ($j=1/2$)- and ($j=3/2$)-based bands occurs. The origin of the excitonic insulator as well as the experimental implication is discussed.

We implement the universal wave-function overlap (UWFO) method to extract modular $S$ and $T$ matrices for topological orders in Gutzwiller-projected parton wave functions (GPWFs). The modular $S$ and $T$ matrices generate a projective representation of $SL(2,\mathbb{Z})$ on the degenerate-ground-state Hilbert space on a torus and may fully characterize the 2+1D topological orders, i.e., the quasiparticle statistics and chiral central charge (up to $E_8$ bosonic quantum Hall states). We use the variational Monte Carlo method to computed the $S$ and $T$ matrices of the chiral spin liquid (CSL) constructed by the GPWF on the square lattice, and we confirm that the CSL carries the same topological order as the $\nu =\frac{1}{2}$ bosonic Laughlin state. We find that the nonuniversal exponents in the UWFO can be small, and direct numerical computation can be applied on relatively large systems. The UWFO may be a powerful method to calculate the topological order in GPWFs.

We present an extensive first-principles study of a large set of native defects in ${\mathrm{MoS}}_2$ in order to find out the types and concentrations of the most important defects in this system. The calculations are carried out for both bulk and monolayer forms of ${\mathrm{MoS}}_2$, which allows us to study how defect properties change between these two limiting cases. We consider single- and few-atom vacancies, antisites, adatoms on monolayer, and interstitials between layers in the bulk material. We calculate the formation energies of neutral and charged defects, determine the charge transition levels, and from these self-consistently assess the concentration of defects at thermal equilibrium as well as the resulting positions of the Fermi level. The chemical potential values corresponding to different growth conditions are carefully accounted for, and for all values of chemical potentials relevant to the growth of ${\mathrm{MoS}}_2$, the S vacancies are found to be the most abundant defects. However, they are acceptors and cannot be the cause of the often observed $n$-type doping. At the same time, Re impurities, which are often present in natural ${\mathrm{MoS}}_2$ samples, naturally provide good $n$-type doping behavior. We also calculate migration barriers for adatoms and interstitials and discuss how they can affect the growth process.

We utilize magnetic field dependencies to identify two hitherto unobserved quantum interference processes in a triple quantum dot circuit. The first observation involves the interplay of Landau-Zener-Stückelberg behavior from two separate anticrossings between two energy levels that anticross twice as a function of a detuning parameter. The second process involves quantum interference between all-exchange and hyperfine qubits activated in a three-spin system.

A two-dimensional disordered system of noninteracting fermions in a homogeneous magnetic field is investigated numerically. By using a modified Landau gauge, we explore the renormalization group flow of the longitudinal and Hall conductances and find that the flow is consistent with the predictions of Pruisken and Khmelnitskii. The extracted critical exponents agree with the results obtained by using transfer matrix methods. The necessity of a second scaling parameter is also demonstrated in the level curvature distribution. Near the critical point the distribution slightly differs from the prediction of random matrix theory, in agreement with previous works. Close to the quantum Hall fixed points the distribution is lognormal since here states are strongly localized.

Our study highlights spin-polarization mechanisms in metals by focusing on the mobilities of conducting electrons with different spins instead of their quantities. Here, we engineer electron mobility by applying chemical disorder induced by nonstoichiometric variations. As a practical example, we discuss the scheme that establishes such variations in tetragonal ${\mathrm{Mn}}_3\mathrm{Ga}$ Heusler material. We justify this approach using first-principles calculations of the spin-projected conductivity components based on the Kubo-Greenwood formalism. It follows that, in the majority of cases, even a small substitution of some other transition element instead of Mn may lead to a substantial increase in spin polarization along the tetragonal axis.

Based on model calculations we predict electric-field control of the spin-transfer torque (STT) in magnetic tunnel junctions with ferroelectric barriers. We demonstrate that the bias dependence of the in-plane $T_{\parallel }$ and out-of-plane $T_{\perp }$ components of the STT can be dramatically modified by the ferroelectric polarization. In particular, the magnitude of the STT can be enhanced or suppressed by switching the polarization direction and in some cases the sign of STT can be toggled. The underlying mechanism is the combination of polarization-induced symmetry breaking and the interplay of the bias-induced and polarization-induced spin-dependent screening giving rise to a rich behavior of the electrostatic potential energy profile. These properties could lead to enhanced switching efficiency in STT-based devices and open a new avenue for applications of multiferroic devices.

Discovering new antiferromagnetic (AF) compounds is at the forefront of developing future spintronic devices without fringing magnetic fields. The AF gapless semiconducting $\mathrm{D}{0}_3$ phase of ${\mathrm{V}}_3\mathrm{Al}$ was successfully synthesized via arc-melting and annealing. The AF properties were established through synchrotron measurements of the atom-specific magnetic moments, where the magnetic dichroism reveals large and oppositely oriented moments on individual V atoms. Density functional theory calculations confirmed the stability of a type G antiferromagnetism involving only two-thirds of the V atoms, while the remaining V atoms are nonmagnetic. Magnetization, x-ray diffraction, and transport measurements also support the antiferromagnetism. This archetypal gapless semiconductor may be considered as a cornerstone for future spintronic devices containing AF elements.

Spin-torque oscillators (STOs) are devices that allow for the excitation of a variety of magnetodynamical modes at the nanoscale. Depending on both external conditions and intrinsic magnetic properties, STOs can exhibit regimes of mode hopping and even mode coexistence. Whereas mode hopping has been extensively studied in STOs patterned as nanopillars, coexistence has been only recently observed for localized modes in nanocontact STOs (NC-STOs), where the current is confined to flow through a NC fabricated on an extended pseudo spin valve. By means of electrical characterization and a multimode STO theory, we investigate the physical origin of the mode-coupling mechanisms favoring coexistence. Two coupling mechanisms are identified: (i) magnon-mediated scattering and (ii) intermode interactions. These mechanisms can be physically disentangled by fabricating devices where the NCs have an elliptical cross section. The generation power and linewidth from such devices are found to be in good qualitative agreement with the theoretical predictions, as well as provide evidence of the dominant mode-coupling mechanisms.

${\mathrm{Ta}}_4{\mathrm{Pd}}_3{\mathrm{Te}}_{16}$ is a newly discovered layered superconductor with quasi-one-dimensional (1D) structure. Recent thermal transport measurements show the possible existence of nodes in the superconducting gap. Here we report low-temperature scanning tunneling microscopy/spectroscopy study on ${\mathrm{Ta}}_4{\mathrm{Pd}}_3{\mathrm{Te}}_{16}$ single crystals. We observed stripelike structure composed of atom chains on the cleaved ($\overline{1}03)$ surface. There exists charge-density-wave (CDW)-like modulations along stripes with commensurate periods. Meanwhile, the tunneling conductance shows an s-wave-like superconducting gap. The magnetic vortex mapped at low field is highly anisotropic with a bound state in the core. At increased field, strong vortex overlapping is directly observed and the bound state is suppressed, indicating the delocalization of the superconducting quasiparticles. Our observations suggest that ${\mathrm{Ta}}_4{\mathrm{Pd}}_3{\mathrm{Te}}_{16}$ is of multiband superconductivity with strong 1D characters, which possibly coexist with CDW transition.

We study the thermally fluctuating state of a bilayer cuprate superconductor under the periodic action of a staggered field oscillating at optical frequencies. This analysis distills essential elements of the recently discovered phenomenon of light-enhanced coherence in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$, which was achieved by periodically driving infrared active apical oxygen distortions. The effect of a staggered periodic perturbation is studied using a Langevin and Fokker-Planck description of driven, coupled Josephson junctions, which represent two neighboring pairs of layers and their two plasmons. In a toy model including only two junctions, we demonstrate that the external driving leads to a suppression of phase fluctuations of the low-energy plasmon, an effect which is amplified via the resonance of the high-energy plasmon. When extending the modeling to the full layers, we find that this reduction becomes far more pronounced, with a striking suppression of the low-energy fluctuations, as visible in the power spectrum. We also find that this effect acts on the in-plane fluctuations, which are reduced on long length scales. All these findings provide a physical framework to describe light control in cuprates.

Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin $S^z$ conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the ${\mathbb{Z}}_{16}$ classification of the topological superconductor ${}^3\mathrm{He}\text{−}B$ phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic $O\left(4\right)$ nonlinear sigma model field theory with a $\Theta$ term.

We study itinerant ferromagnetism in a $t_{2g}$ multiorbital Hubbard system in the cubic lattice, which consists of three planar oriented orbital bands of $d_{xy},d_{yz}$, and $d_{zx}$. Electrons in each orbital band can only move within a two-dimensional plane in the three-dimensional lattice parallel to the corresponding orbital orientation. Electrons of different orbitals interact through the on-site multiorbital interactions including Hund's coupling. The strong-coupling limit is considered in which there are no doubly occupied orbitals but multiple on-site occupations are allowed. We show that in the case in which there is one and only one hole for each orbital band in each layer parallel to the orbital orientation, the ground state is a fully spin-polarized itinerant ferromagnetic state, which is unique apart from the trivial spin degeneracy. When the lattice is reduced into a single two-dimensional layer, the $d_{zx}$ and $d_{yz}$ bands become quasi-one-dimensional while the $d_{xy}$ band remains two-dimensional. The ground-state ferromagnetism also appears in the strong-coupling limit as a generalization of the double-exchange mechanism. Possible applications to the systems of ${\mathrm{SrRuO}}_3$ and ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface are discussed.

We analyze a candidate theory for the strange metal near optimal hole doping in the cuprate superconductors. The theory contains a quantum phase transition between metals with large and small Fermi surfaces of spinless fermions carrying the electromagnetic charge of the electron, but the transition does not directly involve any broken global symmetries. The two metals have emergent SU(2) and U(1) gauge fields respectively, and the transition is driven by the condensation of a real Higgs field, carrying a finite lattice momentum and an adjoint SU(2) gauge charge. This Higgs field measures the local antiferromagnetic correlations in a “rotating reference frame.” We propose a global phase diagram around this Higgs transition, and describe its relationship to a variety of recent experiments on the cuprate superconductors.

Known experimental artificial magnetic conductors for terahertz and optical frequencies are formed by arrays of nanoparticles of various shapes. In this paper, we show that artificial magnetic conductors for the visible spectrum can be realized as simple, effectively quasistatic resonating structures, where the effective inductance is due to the magnetic flux inside a uniform metal substrate, and the effective capacitance is due to electric polarization of a thin uniform dielectric cover. To illustrate the main potential application of artificial magnetic conductors, we concentrate on the perfect-absorption regime, achieved by adjusting the loss factor of the artificial magnetic conductor to match its real input impedance to free space. We provide approximate analytical design formulas and introduce a simple equivalent circuit to explain the physical mechanism of emulation of magnetic response and perfect absorption of light. A prototype of a nearly perfect absorber for optical (from green to ultraviolet) frequencies is designed and experimentally tested. The results confirm the theoretical predictions and show polarization insensitivity and angular independence of response in a wide range of incidence angles.

We report the results of time-domain thermoreflectance (TDTR) measurements of two strongly bonded metal-oxide systems with unusually large thermal conductances. We find that TDTR data for the epitaxial $\mathrm{SrRu}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ interface is consistent with an interface conductance $G>0.8\mathrm{GW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$. For an $\mathrm{Al}\text{/}\mathrm{MgO}$ interface at a pressure of 60 GPa, we find $G\approx 1.1\mathrm{GW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$. Both are within 40% of the maximum possible conductance for these systems, as predicted by simple theory.

In this paper, we show that for a range of configurations of inhomogeneous magnetic fields, it is possible to create flat bands of Majorana states localized on the edges of two-dimensional lattices. Majorana bound states have been predicted to exist in both one-dimensional and two-dimensional systems with Rashba spin-orbit coupling, magnetic fields, and placed in proximity to a superconductor. For the proposed systems, we present the topological phase diagrams, and we study the conditions for weak topology which predict the formation of bands of Majorana states. The Majorana bands are demonstrated to be relatively stable with respect to a variety of different perturbations on both square and hexagonal lattices.

Topological insulators (TIs) are a recently discovered quantum state of matter which is characterized by unconventional bulk topological invariants. Proposals for practical applications of the TIs are mostly based on their metallic surface or edge states. Here, we report the theoretical discovery of a bulk quantum pumping effect in a two-dimensional TI electrically modulated in adiabatic cycles. In each cycle, an amount of spin proportional to the sample width can be pumped into a nonmagnetic electrode, which is attributed to nonzero spin Chern numbers $C_{\pm }$. Moreover, by using a half-metallic electrode, universal quantized charge pumping conductivities $-C_{\pm }{e}^2/h$ can be measured. This discovery paves the way for direct investigation of the robust topological properties of the TIs.

${\mathrm{Mn}}_5\mathrm{Ge}{}_3$(001) thin films grown on Ge(111) were studied by angle- and spin-resolved photoemission using synchrotron radiation in the 17–40 eV photon energy range. The photoelectron spectra were simulated starting from a first-principles band-structure calculation for the ground state, using the free-electron approximation for the final states, taking into account photohole lifetime effects and $k_{\perp }$ broadening plus correlation effects, but ignoring transition matrix elements. The measured spin polarizations for the various k points investigated in the $\Gamma \mathrm{MLA}$ plane of the Brillouin zone are found to be in fair enough agreement with the simulated ones, providing a strong support to the ground-state band-structure calculations. Possible origins for the departures between either simulations and experiments or previous and present experiments are discussed.