Four-Step Evolution of Spin-Hall Conductance: Tight-Binding Electrons with Rashba Coupling in a Magnetic Field

Abstract

An intriguing magneto-transport property is demonstrated by tight-binding lattice electrons with Rashba spin-orbit coupling (SOC) in a magnetic field. With the flux strength $ϕ={2π/N}$ ($N$ is an integer) and the Zeeman splitting fixed, when increasing the Rashba SOC $λ$, the spin-Hall and charge-Hall conductances (SHC and CHC) undergo four-step evolutions: the SHC shows size-dependent resonances and jumps at three critical $λ_{c}$'s, and changes its sign at $λ_{c1}$ and $λ_{c3}$; while the CHC exhibits three quantum jumps by $-Ne^2/h$, $+2Ne^2/h$ and $-Ne^2/h$. Such four-step evolutions are also reflected in topological characters and spin polarizations of edge states of a cylindrical system, and are robust against weak disorder.

4 pages, 5 figures