Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)]. A standard approach for the calculation of topological invariants associated with defects is to deal with the spatial inhomogeneity raised by defects within a semiclassical approximation. In this paper, we propose a full quantum formulation for the topological invariants characterizing line defects in three-dimensional insulators with no symmetry by using the Green's function method. On the basis of the full quantum treatment, we demonstrate the existence of a nontrivial topological invariant in the topological insulator-ferromagnet tri-junction systems, for which a semiclassical approximation fails to describe the topological phase. Also, our approach enables us to study effects of electron-electron interactions and impurity scattering on topological insulators with spatial inhomogeneity which gives rise to the Axion electrodynamics responses.
A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasi-continuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multi-dimensional parametric space of these phases. Special points in this space correspond to setting some terminals to the phase 0 and the rest to the phase of $π$. For a generic nanostructure, three distinct spectra come together in the vicinity of a special point: two gapped phases of different topolo…
We show that the quasi-continuous gapless spectrum of Andreev bound states in multi-terminal semi-classical superconducting nanostructures exhibits a big number of topological singularities. We concentrate on Weyl points in a 4-terminal nanostructure, compute their density and correlations in 3D parameter space for a universal RMT model as well as for the concrete nanostructures described by the quantum circuit theory. We mention the opportunities for experimental observation of the effect in a quasi-continuous spectrum.
Topological insulators and superconductors are characterized by their gapless boundary modes. In this paper, we develop a recursive approach to the boundary Green function which encodes this nontrivial boundary physics. Our approach describes the various topologically trivial and nontrivial phases as fixed points of a recursion and provides direct access to the phase diagram, the localization properties of the edge modes, as well as topological indices. We illustrate our approach in the context of various familiar models such as the Su-Schrieffer-Heeger model, the Kitaev chain, and a model for…
We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, ill…
This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to the quantum energies of the circular and square potential pots of finite heights. The result justifies the proposed scattering phase correction which paves the way for correcting other semiclassical methods based on Green functions, like Gutzwiller trace formula, dynamical zeta functions, and Landauer-Büttiker formula.
Topological behavior can be masked when disorder is present. A topological insulator, either intrinsic or interaction induced, may turn gapless when sufficiently disordered. Nevertheless, the metallic phase that emerges once a topological gap closes retains several topological characteristics. By considering the self-consistent disorder-averaged Green function of a topological insulator, we derive the condition for gaplessness. We show that the edge states survive in the gapless phase as edge resonances and that, similar to a doped topological insulator, the disordered topological metal also h…
The Edelstein effect caused by the pristine surface states of three-dimensional topological insulators is investigated by means of a semiclassical approach. The combined effect of random impurity scattering and the spin-momentum locking of the gapless Dirac cone yields a current-induced surface spin accumulation independent from chemical potential and temperature. Through combing the semiclassical approach with the Bloch equation, the inverse Edelstein effect that converts the spin pumping spin current into a charge current is well explained. Consistency of these results with various experimen…
Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's functions. Here we show that the existence of the edge states directly follows from the existence of the topological invariant written in terms of the Green's functions, for all ten classes of topological insulators in all spatial dimensions. We also show that the resulting edge states are characterized by their own topological invariant, whose value is equal to t…
A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent state semiclassical wavepacket method which avoids singularity issues arising in the usual Green's function approach. We discuss the general conditions under which it is approximately correct to discuss quantum decoherence in terms of a ``dephasing'' picture and we derive semiclassical expressions for the phase and phase distribution. Remarkably, an effective system wavefunction emerges whose norm measures the decoherence and is equivalent to a …
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 e…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results and a variety of numerical methods have been developed to solve the time-dependent Schroedinger equation. The time-dependent methods work for nearly arbitrarily shaped potentials, including sources and sinks via complex-valued potentials. Many quantities are measured at fixed energy, which is seemingly not well suited for a time-dependent formulation. Very …
The angular momentum quantization of chiral gapless modes confined to a circularly shaped interface between two different topological phases is investigated. By examining several different setups, we show analytically that the angular momentum of the topological modes exhibits a highly chiral behavior, and can be coupled to spin and/or valley degrees of freedom, reflecting the nature of the interface states. The energies and the magnetic moments corresponding to these states can be understood from a semiclassical picture. These loops can be viewed as building blocks for artificial magnets with…
This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect non-interacting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional non-interacting topological insulators. By utilizing the eigenvector-eigenvalue ide…
Quantum transport properties of disordered graphene with structural defects (Stone-Wales and divacancies) are investigated using a realistic π-π* tight-binding model elaborated from ab initio calculations. Mean free paths and semiclassical conductivities are then computed as a function of the nature and density of defects (using an order-N real-space Kubo-Greenwood method). By increasing of the defect density, the decay of the semiclassical conductivities is predicted to saturate to a minimum value of 4e^2/πh over a large range (plateau) of carrier density (> 0.5 10^{14}cm^{-2}). Additionally,…
The Edelstein effect caused by the pristine surface states of three-dimensional topological insulators is investigated by means of a semiclassical approach. The combined effect of random impurity scattering and the spin-momentum locking of the gapless Dirac cone yields a current-induced surface spin accumulation independent from chemical potential and temperature. In a nearby ferromagnet that does not make direct contact with the topological insulator, the bound state nature of the pristine surface state causes a spin-transfer torque that is entirely field-like, whose magnitude is highly influ…
We study theoretically the electronic structure of topological nodal-line semimetals. We show that, in the presence of a gap-opening spatially dependent mass term that forms a domain wall, an in-gap charged localized mode emerges at the domain wall. It turns out that such a domain wall is realized by head-to-head (or tail-to-tail) bulk electric polarizations. The localized mode has a topological origin, i.e., a topological confinement is realized, which is understood by a semiclassical topological number defined in the semiclassical momentum-real space. In contrast to previous studies, our stu…
We propose an extensive report on the simulation of electronic transport in 2D graphene in presence of structural defects. Amongst the large variety of such defects in sp$^2$ carbon-based materials, we focus on the Stone-Wales defect and on two divacancy-type reconstructed defects. First, based on ab initio calculations, a tight-binding model is derived to describe the electronic structure of these defects. Then, semiclassical transport properties including the elastic mean free paths, mobilities and conductivities are computed using an order-N real-space Kubo-Greenwood method. A plateau of mi…
Quantum cascade lasers can be modeled within a hierarchy of different approaches: Standard rate equations for the electron densities in the levels, semiclassical Boltzmann equation for the microscopic distribution functions, and quantum kinetics including the coherent evolution between the states. Here we present a quantum transport approach based on nonequilibrium Green functions. This allows for quantitative simulations of the transport and optical gain of the device. The division of the current density in two terms shows that semiclassical transitions are likely to dominate the transport fo…
Magnetic tunnel junctions (MTJs) have attracted strong research interest within the last decades due to their potential use as nonvolatile memory such as MRAM as well as for magnetic logic applications. Half-metallic magnets (HMMs) have been suggested as ideal electrode materials for MTJs to achieve an extremely large tunnel-magnetoresistance (TMR) effect. Despite their high TMR ratios, MTJs based on HMMs do not exhibit current rectification, i.e., a diode effect, which was achieved in a magnetic tunnel junction concept based on HMMs and type-II spin-gapless semiconductors (SGSs). The proposed…
Electron transport properties in nanostructures can be modeled, for example, by using the semiclassical Wigner formalism or the quantum mechanical Green's functions formalism. We compare the performance and the results of these methods in the case of magnetic resonant-tunneling diodes. We have implemented the two methods within the self-consistent spin-density-functional theory. Our numerical implementation of the Wigner formalism is based on the finite-difference scheme whereas for the Green's function formalism the finite-element method is used. As a specific application, we consider the dev…
We present an extension of the Keldysh-Green's function method, which allows to calculate the full distribution of transmitted particles through a mesoscopic superconductor. The method is applied to the statistics of supercurrent in short contacts. If the current is carried by Andreev bound states the distribution corresponds to switching between long trains of electrons going in opposite directions. For weak (gapless) superconductors or tunnel junctions we find that at low temperatures the distribution has negative `probabilities'. Accounting for the quantum mechanical nature of the measuring…
Using a semiclassical Green's function formalism, we discover the emergence of chiral and topological orbital magnetism in two-dimensional chiral spin textures by explicitly finding the corrections to the orbital magnetization, proportional to the powers of the gradients of the texture. We show that in the absence of spin-orbit coupling, the resulting orbital moment can be understood as the electronic response to the emergent magnetic field associated with the real-space Berry curvature. By referring to the Rashba model, we demonstrate that by tuning the parameters of surface systems the engin…
