Emergent Z_2 topological invariant and robust helical edge states in two-dimensional topological metals

In this work, we study the effects of disorder on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall(QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent Z_2 topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in various transport experiments on QSH materials that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

Density of states of a two-dimensional electron in a strong magnetic field and a random potential

The density of states of a two-dimensional electron in a strong magnetic field moving in a periodic and a random potential is calculated. The results are compared with the density of states of the Landau model with disorder as obtained in the single band approximation. The limitations of the single band model are discussed.     

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.     

Time evolution of initially localized states in two-dimensional quantum dot arrays in a magnetic field

The evolution of non-stationary localized states |Ψ(t=0) is investigated in two-dimensional tight binding systems of N potential wells with and without a homogeneous field perpendicular to the plane. Most results are presented in analytical form, what is almost imperative if the patterns are as complex as for rings in a magnetic field, where the qualitatively different features arise depending on rational or irrational numbers. The systems considered comprise finite linear chains (N=2,3), finite rings (N=3–6), infinite chains, finite rings (N=3–6) in a magnetic field, and rings with leads attached to each ring site. The position of the particle at time t is described by the projection of the wave function P_m(t)=|m|Ψ(t)|² onto the localized basis function at site m. For finite chains and rings with N=3,4,6 the time evolution is periodic, whereas it is non-periodic for N=5 and N greater then 6. Rings in a magnetic field show a rich spectrum of different features depending on N and the number of flux quanta through the ring, including periodic oscillation and rotation of the charge as well as non-periodic charge fluctuations.     

Spin edge helices in a perpendicular magnetic field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.     

二维声学系统中的拓扑相变及边界传输

拓扑声学的发现产生了一种可以有效抑制反射的声学边界传输态,不仅让人们重新认识了声传输现象,也扩展了声学新原理功能器件的研究领域。文章将介绍二维系统中拓扑声学的基本概念以及一些拓扑非平庸体系。主要关注利用背景流体构造的声类量子霍尔效应,利用共振耦合环形波导构造Floquet拓扑绝缘体,声类量子自旋霍尔效应以及声谷霍尔效应等。     

Excited states of two-dimensional hydrogen atom in tilted magnetic field: Quantum chaos

The aim of the current work is the research of the influence of a tilted magnetic field direction on the spectrum and the energy level spacing distribution of a two-dimensional (2D) hydrogen atom and of an exciton in GaAs/Al_0.33Ga_0.67As quantum well. It was discovered that the quantum chaos (QC) is initiated with an increasing angle α between the magnetic field direction and the normal to the atomic plane. It is characterized by the repulsion of levels leading to the eliminating of the shell structure and by changing the spectrum statistical properties. The statement about the initiation of chaos and its dominance over regular motion with increasing angle α is confirmed by the results of our calculations of the classical dynamics presented in this paper. The evolution of the spatial distribution of the square of the absolute value of the wave function at an increasing angle α was observed. The differences of calculated dependencies of energies for various excited states on the tilt angle at a wide range of the magnetic field strength were described.     

On the thermodynamics of a degenerate two-dimensional electron gas in a strong magnetic field: density of states

Systematic expansions, in powers ofB ^–1, for the free energy and the density of states, are derived for a two-dimensional degenerate electron gas in the presence of a strong magnetic field and an arbitrary potential. They are then applied to a system involving random impurities. Landau levels are shown to be broadened, with level widths related to the impurity concentration and potential. We show that level broadenings, induced by long range electron-impurity ineractions, do not depend on the magnetic field in the strong field limit, confirming the existing theories. But broadened Landau levels can have a large variety of shapes as one changes the impurity potential, distribution and concentration. Our theory, with a Gaussian potential, leads to a good agreement with the recent experiment on the de Haas-van Alphen effect in Br₂-graphite intercalation compounds