Finite lattices with spin-orbit interactions

Author: Merab ELIASHVILI
Co-authors: George Tsitsishvili
Keywords: “bulk” and “edge” phases
Annotation:

During the recent years we studied 2D electron systems in constrained geometry. During last year two papers [1,2] have been published in that direction. In the first paper the spinless particles have been studied on a honeycomb lattice; the eigenvalue problem has been solved exactly in terms of Chebyshev polynomials and the peculiarities of bulk and edge phases have been analyzed. The other paper concernes spinning particles in continuum where the occurrence of pure spin currents have been detected. The problem under the present studies is a kind of a merger of the aforementioned two. In particular, the spin degrees of freedom are incorporated in finite lattice models. The project is still in progress. In addition to “bulk” and “edge” phases the possibility of third “intermediate” phase has been observed at the given stage. [1] M. Eliashvili, G.I. Japaridze, G. Tsitsishvili. G. Tukhashvili, “Edge States in 2D Lattices with Hopping Anisotropy and Chebyshev Polynomials”, J. Phys. Soc. Jpn. 83 (2014) 044706. [2] M. Eliashvili, G. Tsitsishvili, “Boundary conditions and formation of pure spin currents in magnetic field”, Physica E 93 (2017) 196