Linearity of the edge states energy spectrum in the 2D topological insulator

Linearity of the topological insulator edge state spectrum plays the crucial role for various transport phenomena. The previous studies found that this linearity exists near the spectrum crossing point, but did not determine how perfect the linearity is. The purpose of the present study is to answer this question in various edge states models. We examine Volkov and Pankratov (VP) model [1] for the Dirac Hamiltonian and the model of [2,3] (BHZ1) for the Bernevig, Hughes and Zhang (BHZ) Hamiltonian [4] with zero boundary conditions. It is found that both models yield ideally linear edge states. In the BHZ1 model the linearity is conserved up to the spectrum ending points corresponding to the tangency of the edge spectrum with the boundary of 2D states. In contrast, the model of[5] (BHZ2) with mixed boundary conditions for BHZ Hamiltonian and the 2D tight-binding (TB) model from [4] yield weak non-linearity.Comment: 5 pages, 4 figure

Friedel oscillations of the magnetic field penetration in systems with spatial quantization

The magnetic field, applied to a size-quantized system produces equilibrium persistent current non-uniformly distributed across the system. The distributions of dia- and paramagnetic currents and magnetic field in a quantum well is found. We discuss the possibility of observation of field distribution by means of NMR.Comment: 4 pages, 1 figure, uses nanosymp.sty. Accepted for 10th International Symposium "Nanostructures: Physics and Technology", St Petersburg, Russia, June 17-21(2002). The extended version, including the case of strip geometry submitted to "JETP Letters

High-frequency blockade in a tight-binding one-dimensional lattice with single vibrating atomic state

One-dimensional tight-binding lattice, single site of which possesses harmonically vibrating level is studied. The states of non-interacting electrons incident with fixed energy from infinity are considered. It is shown that at definite conditions the site reflects electrons {\it absolutely and elastically} (high-frequency blockade states). The problem is treated both numerically and (in the case of narrow band) analytically. The results are compared with the free-electron 1D problem with vibrating $\delta$-functional potential. Together with the blockade states the local and reflectionless states are examined. Possible realization of the system as a lattice of quantum dots is discussed.Comment: 4 pages, 8 figure