Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

Quantum transport for Bloch electrons in homogeneous time dependent electric fields

Quantum Transport Equations for Bloch electrons interacting with randomly distributed impurities in the presence of a homogeneous electric field of arbitrary strength and time dependence are derived. The equations account for all possible quantum effects to lowest nonzero order in the scattering strength, including intra and interband scattering, interband Zener tunneling and non-linear transient transport, and contain effects previously not anticipated, such as coherent impurity scattering, and field and time dependent scattering matrix elements.     

磁场中拓扑物态的量子输运

拓扑物态包括拓扑绝缘体、拓扑半金属以及拓扑超导体.拓扑物态奇异的能带结构以及受拓扑保护的新奇表面态,使其具有了独特的输运性质.拓扑半金属作为物质的一种三维拓扑态具有无能隙的准粒子激发,根据导带和价带的接触类型分为外尔半金属、狄拉克半金属和节线半金属.本文以拓扑半金属为主回顾了在磁场下拓扑物态中量子输运的最新工作,在不同...     

Quantum transport in diffusive microstructures in high magnetic fields

We have studied magnetotransport in diffusive submicron wires (n⁺-GaAs) at high magnetic fields where ω_cτ>1. The system allowed us to follow a transition from orthodox mesoscopic behaviour to the regime of edge state transport.We found that for ω_cτ>1 the universal conductance fluctuations (UCF) can no longer be scaled in terms of only one parameter, the phase coherence length. This breakdown of universal scaling is seen as a large increase of the Lee-Stone correlation field while the magnitude of UCF is unchanged in strong disagreement with the theoretical prediction.A qualitatively new magnetoresistance oscillatory effect has been observed at intermediate temperatures (10K<T<50K) when the quantum transport along the edges coexists with classical (diffusive and dissipative) conduction in the bulk. The effect arises due to Landau quantization but entirely disappears at low temperatures. The latter distinguishes it from the other quantum transport phenomena and indicates the importance of dissipation in resistance measurement.     

Quantum transport in an anisotropic two-dimensional system under strong magnetic fields

Characteristics of the conductivity tensor are obtained in an anisotropic two-dimensional system where the Fermi surface is given by elliptic form. The anisotropy of the transverse conductivity _xx and _yy depends strongly on the range of scattering potentials: It becomes maximum in case of short-ranged scatterers, and decreases with the increase of the range. The conductivity becomes isotropic in the limit of slowly-varying scatterers if the scattering potential is isotropic. The Hall conductivity is, on the other hand, not affected by the anisotropy strongly.     

Quantum transport in topological semimetals under magnetic fields (II)

Research about two-dimensional (2D) materials is growing exponentially across various scientific and engineering disciplines due to the wealth of unusual physical phenomena that occur when charge transport is confined to a plane. The applications of 2D materials are highly affected by the electrical properties of these materials, including current distribution, surface potential, dielectric response, conductivity, permittivity, and piezoelectric response. Hence, it is very crucial to characterize these properties at the nanoscale. The Atomic Force Microscopy (AFM)-based techniques are powerful tools that can simultaneously characterize morphology and electrical properties of 2D materials with high spatial resolution, thus being more and more extensively used in this research field. Here, the principles of these AFM techniques are reviewed in detail. After that, their representative applications are further demonstrated in the local characterization of various 2D materials’ electrical properties.

     

Quantum Langevin equation and input-output fields for arbitrary linear response

A retarded quantum Langevin equation is derived for a small subsystem coupled to an arbitrary number of large reservoirs by treating the small back-action on the reservoir within linear response theory. Interpreting the coupling to the reservoirs as input to the small subsyste, and using the advanced quantum Langevin equation to define the corresponding output emitted into the reservoirs, causally connected input and output variables are constructed which are used to set up anS-matrix formalism relating input and output variables in a unitary and causal way. An application to squeezing by subharmonic generation with arbitrary linear response is given.     

Quantum rings in tilted magnetic fields

The electronic states of semiconductor quantum rings (QRs) under tilted magnetic fields are studied in the framework of the effective mass and envelope function approximations. For an axial field, the orbital Zeeman contribution prevails leading to the well-known Aharanov–Bohm spectrum, but it slowly decreases as the magnetic field direction declines. For an in-plane field, only the diamagnetic shift survives and it leads to the formation of double quantum well solutions, this result being relevant for experimental techniques which use in-plane magnetic fields to determine the spin of QR ground states. We also investigate the magnetic response of partially overlapped QRs, which are characteristic of high-density samples of self-assembled rings, and find that the spectrum is quite sensitive to ring coupling.     

Effects of electric and magnetic fields on electronic states and transport of a Hall bar

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.     

Hofstadter spectrum in electric and magnetic fields

The problem of Bloch electrons in two dimensions subjected to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution, and energy translation operators are used to specify the solutions of the Schrödinger equation. For rational values of the magnetic flux quanta per unit cell and commensurate orientations of the electric field relative to the original lattice, an extended superlattice can be defined and a complete set of mutually commuting space-time symmetry operators is obtained. Dynamics of the system is governed by a finite difference equation that exactly includes the effects of: an arbitrary periodic potential, an electric field orientated in a commensurable direction of the lattice, and coupling between Landau levels. A weak periodic potential broadens each Landau level in a series of minibands, separated by the corresponding minigaps. The addition of the electric field induces a series of avoided and exact crossing of the quasienergies, for sufficiently strong electric field the spectrum evolves into equally spaced discreet levels, in this “magnetic Stark ladder” the energy separation is an integer multiple of hE/aB, with a the lattice parameter.     

Semiconductor electrons in electric and magnetic fields

Optical properties of semiconductors in the simultaneous presence of electric and magnetic fields are reviewed, with particular emphasis on the possibilities of modulation techniques. First, the problem of an electron in crossed and parallel fields is solved in the one-level effective mass approximation (EMA), and the results are used to interpret the experimental interband transitions in Ge, with due account of the degenerate character of the valence band in this material. The limitations of the one-level EMA are discussed, and the two-level model is introduced, which correctly describes the experimentally observed transition from a magnetic type to an electric type of motion in increasing transverse electric field. Possibilities to observe electric field effects in cyclotron resonance transitions are discussed in this approximation. Finally, the three-level model is used to describe properly both orbital and spin properties of conduction electrons. It is demonstrated that in a small-gap semiconductor with large spin-orbit interaction a sufficiently strong transverse electric field destroys the Landau orbital quantization but not the Pauli spin quantization. Possible experimental consequences of this situation are discussed. Influence of finite dimensions of the sample on the character of the electron motion in crossed and parallel fields is examined. A possibility to achieve the semiconductor-semimetal transition in a symmetryinduced zero-gap semiconductor in crossed field configuration is predicted and described, taking into account the Luttinger effects in the magnetic level structure.     

Exact solution to the classical equation of motion for a charged particle in external electric and magnetic fields

An exact solution to the equation of classical motion of a charged particle in external uniform time-dependent electric and magnetic fields is obtained in two forms by two methods. An exact solution of a more general initial-value problem is found as well.     

Quantum transport in parallel magnetic fields: a realization of the Berry-Robnik symmetry phenomenon

We analyze the magnetoconductance of two-dimensional electron and hole gases subject to a parallel magnetic field. It is shown that, for confining potential wells which are symmetric with respect to spatial inversion, a temperature-dependent weak localization signal exists even in the presence of a magnetic field. Deviations from this symmetry lead to magnetoconductance profiles that contain information on both the geometry of the confining potential and characteristics of the disorder.