Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect (QAHE), but it is difficult to realize. Here, we predict the two-dimensional (2D) single-atomic-layer ${\mathrm{V}}_2{\mathrm{O}}_3$ with a honeycomb-Kagome structure is a QAH insulator with a large band gap (larger than 0.1 eV) and a high ferromagnetic Curie temperature (about 900 K). Combining the first principles calculations with the effective Hamiltonian analysis, we find that the spin-majority $d_{xy}$ and $d_{yz}$ orbitals of V atoms on the honeycomb lattice form a massless Dirac cone near the Fermi level which becomes massive when the on-site spin-orbit coupling (SOC) is included. Interestingly, we find that the large band gap is caused by a cooperative effect of electron correlation and SOC. Both first principles calculations and the effective Hamiltonian analysis confirm that 2D ${\mathrm{V}}_2{\mathrm{O}}_3$ has a nonzero Chern number (i.e., one). This paper paves a direction toward realizing the QAHE at room temperature.

Introducing a powerful method, we obtain the exact solutions for a Coulomb impurity in two-dimensional infinite and finite topological insulators. The level order and zero-energy degeneracy of the spectra are found to be quite different between topological trivial and nontrivial phases. For quantum dots of topological insulator, the variation of the edge and Coulomb states with dot size, Coulomb potential, and magnetic field are clearly shown. It is found that for small dots the edge states can be strongly coupled with the Coulomb states and for large dots the edge states are insensitive to the Coulomb fields but sensitive to the magnetic fields.

We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalization-localization transition with increasing disorder. We find an interesting regime in this noninteracting disordered chain where the long-time entanglement entropy scales as $S\left(t\right)\sim lnt$ and the saturated entanglement entropy scales with system size $L$ as $S(L,t\to \infty )\sim lnL$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.

The influence of recently discovered topological transition between type-I and type-II Weyl semimetals on superconductivity is considered. A set of Gorkov equations for weak superconductivity in Weyl semimetal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spikes in the transition point as functions of the tilt parameter of the Dirac cone determined, in turn, by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: The sharp cone pinnacle is characteristic for type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition to demonstrate the different weights of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.

Recently it has been found that models with at least two lifetimes have to be considered when analyzing the angle-resolved photoemission data in the nodal region of the cuprates [Kondo et al., Nat. Commun. 6, 7699 (2015)]. In this paper we compare two such models. First we show that the phenomenological model used by Kondo et al. violates the sum rule for the occupation number. Next we consider the recently proposed model of the so-called Dynes superconductors, wherein the two lifetimes measure the strengths of pair-conserving and pair-breaking processes. We demonstrate that the model of the Dynes superconductors is fully consistent with known exact results, and we study in detail the resulting spectral functions. Finally, we show that the spectral functions in the nodal region of the cuprates can be fitted well by the model of the Dynes superconductors.

Phonon lifetime in materials is an important observable that conveys basic information about structure, dynamics, and anharmonicity. Recent vibrational transient-grating measurements, using picosecond infrared pulses from free-electron lasers, have demonstrated that the vibrational-population decay rates of localized high-frequency stretching modes (HSMs) in hydrogenated and deuterated amorphous silicon $(a$-Si:H/D) increase with temperature and the vibrational energy redistributes among the bending modes of Si in $a$-Si:H/D. Motivated by this observation, we address the problem from first-principles density-functional calculations and study the time evolution of the vibrational-population decay in $a$-Si:H/D, the average decay times, and the possible decay channels for the redistribution of vibrational energy. The average lifetimes of the localized HSMs in $a$-Si:H and $a$-Si:D are found to be approximately 51–92 ps and 50–78 ps, respectively, in the temperature range of 25–200 K, which are consistent with experimental data. A weak temperature dependence of the vibrational-population decay rates has been observed via a slight increase of the decay rates with temperature, which can be attributed to stimulated emission and increased anharmonic coupling between the normal modes at high temperature.

The ordered hexagonal perovskite ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$ hosts weakly coupled $S=\frac{1}{2}$ spin ladders produced by an orbital ordering of ${\mathrm{Cu}}^{2+}$. The magnetic susceptibility $\chi \left(T\right)$ of ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$ is well described by that expected for isolated spin ladders with exchange coupling of $J\approx 86\mathrm{K}$ but shows a deviation from the expected thermally activated behavior at low temperatures below $T^{*}\approx 25\mathrm{K}$. An anomaly in $\chi \left(T\right)$, indicative of magnetic ordering, is observed at $T_{\mathrm{mag}}=16\mathrm{K}$. No clear signature of long-range ordering, however, is captured so far in NMR $1/T_1$, specific heat or neutron diffraction measurements at and below $T_{\mathrm{mag}}$. The marginal magnetic transition, indicative of strong quantum fluctuations, is evidence that ${\mathrm{Ba}}_2{\mathrm{CuTeO}}_6$ is in very close proximity to a quantum critical point between magnetically ordered and spin-gapped phases controlled by interladder couplings.

We propose quantum devices having spin-orbit coupling (but no magnetic fields or magnetic materials) that, when attached to leads, yield a high degree of transmitted electron polarization. An example of such a simple device is treated within a tight binding model composed of two one-dimensional chains coupled by several consecutive rungs (i.e., a ladder) and subject to a gate voltage. The ensuing scattering problem (with Rashba spin-orbit coupling) is solved, and a sizable polarization is predicted. When the ladder is twisted into a helix (as in DNA), the curvature energy augments the polarization. For a system with random spin-orbit coupling, the distribution of polarization is broad; hence a high degree of polarization can be obtained in a measurement of a given disorder realization. When disorder occurs in a double helix structure then, depending on scattering energy, the variance of the polarization distribution can increase even further due to helix curvature.

The rotational dynamics of magnetic nanoparticles in rotating magnetic fields in the presence of thermal noise is studied both theoretically and by performing numerical calculations. Equations for the dynamics of particles with uniaxial magnetic anisotropy are studied and the phase lag between the rotating magnetic moment and the driving field is obtained. It is shown that for large enough anisotropy energy the magnetic moment is locked to the anisotropy axis so that the particle behaves like a rotating magnetic dipole. The corresponding rigid dipole model is analyzed both numerically by solving the appropriate Fokker-Planck equation and analytically by applying an effective field method. In the special case of a rotating magnetic field applied analytic results are obtained in perfect agreement with numerical results based on the Fokker-Planck equation. The analytic formulas derived are not restricted to small magnetic fields or low frequencies and are therefore important for applications. The illustrative numerical calculations presented are performed for magnetic parameters typical for iron oxide.

We report the effects of heavy-ion irradiation on FeSe single crystals by irradiating uranium up to a dose-equivalent matching field of $B_{\varphi }=16$ T. Almost continuous columnar defects along the $c$ axis with a diameter of $\sim 10$ nm are confirmed by high-resolution transmission electron microscopy. $T_c$ is found to be suppressed by introducing columnar defects at a rate of $d{T}_c/d{B}_{\varphi }\sim -0.29$ K/T, which is much larger than those observed in iron pnictides. This unexpected large suppression of $T_c$ in FeSe is discussed in relation to the large diameter of the columnar defects as well as its unique band structure with a remarkably small Fermi energy. The critical current density is first dramatically enhanced with irradiation reaching a value over $\sim 2\times {10}^5\mathrm{A}/{\mathrm{cm}}^2$ $(\sim 5$ times larger than that of the pristine sample) at 2 K (self-field) with $B_{\varphi }=2$ T, then gradually suppressed with increasing $B_{\varphi }$. The $\delta l$ pinning associated with charge-carrier mean-free-path fluctuations and the $\delta T_c$ pinning associated with spatial fluctuations of the transition temperature are found to coexist in the pristine FeSe, while the irradiation increases the contribution from $\delta l$ pinning and makes it dominant over $B_{\varphi }=4$ T.

We investigate proximity-induced superconductivity in monolayers of transition-metal dichalcogenides (TMDs) in the presence of an externally generated exchange field. A variety of superconducting order parameters is found to emerge from the interplay of magnetism and superconductivity, covering the entire spectrum of possibilities to be symmetric or antisymmetric with respect to the valley and spin degrees of freedom, as well as even or odd in frequency. More specifically, when a conventional $s$-wave superconductor with singlet Cooper pairs is tunnel-coupled to the TMD layer, both spin-singlet and triplet pairings between electrons from the same and opposite valleys arise due to the combined effects of intrinsic spin-orbit coupling and a magnetic-substrate-induced exchange field. As a key finding, we reveal the existence of an exotic even-frequency triplet pairing between equal-spin electrons from different valleys, which arises whenever the spin orientations in the two valleys are noncollinear. All types of superconducting order turn out to be highly tunable via straightforward manipulation of the external exchange field.

Most theoretical studies of nanoscale transport in molecular junctions rely on the combination of the Landauer formalism with Kohn-Sham density functional theory (DFT) using standard local and semilocal functionals to approximate exchange and correlation effects. In many cases, the resulting conductance is overestimated with respect to experiments. Recent works have demonstrated that this discrepancy may be reduced when including many-body corrections on top of DFT. Here we study benzene-dithiol (BDT) gold junctions and analyze the effect of many-body perturbation theory (MBPT) on the calculation of the conductance with respect to different bonding geometries. We find that the many-body corrections to the conductance strongly depend on the metal-molecule coupling strength. In the BDT junction with the lowest coupling, many-body corrections reduce the overestimation on the conductance to a factor 2, improving the agreement with experiments. In contrast, in the strongest coupling cases, many-body corrections on the conductance are found to be sensibly smaller and standard DFT reveals a valid approach.

The search for symmetry-protected two-dimensional (2D) Dirac semimetals analogous to graphene is important both for fundamental and practical interest. The 2D Dirac cones are protected by crystalline symmetries and magnetic ordering may destroy their robustness. Here we propose a general framework to classify stable 2D Dirac semimetals in spin-orbit coupled systems having the combined time-reversal and inversion symmetries, and show the existence of the stable Dirac points in 2D antiferromagnetic semimetals. Compared to 3D Dirac semimetals which fall into two distinct classes, Dirac semimetals in 2D with combined time-reversal and inversion symmetries belong to a single class which is closely related to the nonsymmorphic space-group symmetries. We further provide a concrete model in antiferromagnetic semimetals which supports symmetry-protected 2D Dirac points. The symmetry breaking in such systems leads to 2D chiral topological states such as quantum anomalous Hall insulator and chiral topological superconductor phases.

We study Veselago lensing of massless Dirac fermions by n-p junctions for electron sources with a certain polarization. This polarization corresponds to pseudospin for graphene and to real spin for topological insulators. Both for a point source and for injection into a sample through a narrow lead, we find that polarization leads to spatial symmetry breaking. For the Green's function, this results in a vertical displacement, or even complete vanishing of the main focus, depending on the exact polarization. For injection through a lead, it leads to a difference between the amounts of current emitted with positive and negative transversal momenta. We study both systems in detail using the semiclassical approximation. By comparing the results to the exact solutions, we establish that semiclassical methods provide a very effective way to study these systems. For the Green's function, we derive an easy-to-use analytical formula for the vertical displacement of the main focus. For current injection through a lead, we use semiclassical methods to identify two different scattering regimes.

We investigate scattering of the topological surface state of a three-dimensional time-reversal invariant topological insulator when graphene is deposited on the topological-insulator surface. Specifically, we consider the (111) surface of a ${\mathrm{Bi}}_2{\mathrm{Se}}_3$-like topological insulator. We present a low-energy model for the graphene–topological insulator heterostructure and we calculate the transmission probability at zigzag and armchair edges of the deposited graphene, and the conductance through graphene nanoribbon barriers, and show that its features can be understood from antiresonances in the transmission probability.

The Stokes paradox is the statement that in a viscous two-dimensional fluid, the “linear response” problem of fluid flow around an obstacle is ill posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any realistic electron liquid, resolves the classical paradox. Nonetheless, this paradox imprints itself in the resistance, which can be parametrically larger than predicted by Ohmic transport theory. We find a remarkably rich set of behaviors, depending on whether or not the quasiparticle dynamics in the Fermi liquid should be treated as diffusive, hydrodynamic, or ballistic on the length scale of the obstacle. We argue that all three types of behavior are observable in present day experiments.

Zigzag edges of the honeycomb structure of graphene exhibit magnetic polarization, making them attractive as building blocks for spintronic devices. Here, we show that devices with zigzag-edged triangular antidots perform essential spintronic functionalities, such as spatial spin splitting or spin filtering of unpolarized incoming currents. Near-perfect performance can be obtained with optimized structures. The device performance is robust against substantial disorder. The gate-voltage dependence of transverse resistance is qualitatively different for spin-polarized and spin-unpolarized devices, and can be used as a diagnostic tool. Importantly, the suggested devices are feasible within current technologies.

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville–von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid–real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at $n=0.875$ filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both $U/t=4.0$ and $8.0$. We find that the strength of the charge ordering depends on $U/t$ and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.