Spin-orbit gauge and quantum spin Hall effect

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.     

Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.     

Spin-orbit hybrid entanglement quantum key distribution scheme

We propose a novel quantum key distribution scheme by using the SAM-OAM hybrid entangled state as the physical resource.To obtain this state,the polarization entangled photon pairs are created by the spontaneous parametric down conversion process,and then,the q-plate acts as a SAM-to-OAM transverter to transform the polarization entangled pairs into the hybrid entangled pattern,which opens the possibility to exploit the features of the higher-dimensional space of OAM state to encode information.In the manipulation and encoding process,Alice performs the SAM measurement by modulating the polarization stateπ lθx on one photon,whereas Bob modulates the OAM sector state lx' on the other photon to encode his key elements using the designed holograms which is implemented by the computer-controlled SLM.With coincidence measurement,Alice could extract the key information.It is showed that N-based keys can be encoded with each pair of entangled photon,and this scheme is robust against Eve’s individual attack.Also,the MUBs are not used.Alice and Bob do not need the classical communication for the key recovery.     

On the quantum Hall effect

We consider a particle in a 2 dimensional plane in a periodic potential and a homogeneous magnetic field perpendicular to the plane. Kubo's expression for conductivity of the Hall current is an integer.

This result of Thouless, Kohomoto, Nightingale and den Nijs is interpreted geometrically.     

Concise analytic solutions to the quantum Rabi model with two arbitrary qubits

Using extended coherent states, an analytical exact study has been carried out for the quantum Rabi model (QRM) with two arbitrary qubits in a very concise way. The G$G$-functions with 2×2$2\times 2$ determinants are generally derived. For the same coupling constants, the simplest G$G$-function, resembling that in the one-qubit QRM, can be obtained. Zeros of the G$G$-function yield the whole regular spectrum. The exceptional eigenvalues, which do not belong to the zeros of the G$G$ function, are obtained in the closed form. The Dark states in the case of the same coupling can be detected clearly in a continued-fraction technique. The present concise solution is conceptually clear and practically feasible to the general two-qubit QRM and therefore has many applications.     

Umklapp scattering at reconstructed quantum Hall edges

We study the low-lying excitations of a quantum Hall sample that has undergone edge reconstruction such that there exist three branches of chiral edge excitations. Among the interaction processes that involve electrons close to the three Fermi points is a new type of Umklapp-scattering process which has not been discussed before. Using bosonization and a refermionization technique, we obtain exact results for electronic correlation functions and discuss the effect Umklapp scattering has on the Luttinger-liquid properties of quantum Hall edges.     

Three-dimensional quantum Hall effect in Weyl and double-Weyl semimetals

The well-known quantum Hall effect (QHE) was usually studied in 2D systems. In this work, we investigate the integer QHE in 3D Weyl and double-Weyl semimetals. Based on the lattice models of Weyl and double-Weyl semimetals subjected to a uniform magnetic field, we derive the generalized 3D spinfull Hofstadter Hamiltonians and Harper equations for the two systems, and obtain their corresponding energy spectra. Furthermore, we show that for proper hopping parameters and rational magnetic fluxes, both systems exhibit the 3D QHE when the Fermi level lies in some band gaps. The 3D QHE is topologically characterized by three Chern numbers with one or two nonzero Chern values which are respectively defined for three crystal planes. The possible experimental realization and detection of the 3D QHE are also discussed.     

Ohm's law in the quantum Hall effect

The linearity of the Hall currents as functions of the voltage is investigated. We consider interacting electrons on a torusT ₂. They are subjected to a strong perpendicular magnetic field and a smooth but disordered substrate potential. In a moving frame of reference the Hamiltonian is time-dependent due to the constantly shifted substrate. Assuming a small energy gap separating the lowlying subspace, adiabatic expansion is used to construct a solution. Its general properties allow to calculate the Hall currents. Any power-law corrections to linearity are absent. The reliability of the result is assessed by estimates of the parameter controlling the expansion which is asymptotic.     

Vortex drag in the quantum Hall effect

A new model of momentum and electric field transfer between two adjacent 2D electron systems in the quantum Hall effect is proposed. The drag effect is due to momentum transfer from the vortex system of one layer to the vortex system of another layer. The remarkable result of this approach is a periodic change of sign of the dragged electric field as a function of the difference between the layer filling factors. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 4, 276–279 (25 February 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.