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 $\varphi =2\pi /N$ ($N$ is an integer) and the Zeeman splitting fixed, when increasing the Rashba SOC $\lambda$, 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 ${\lambda }_c$'s, and changes its sign at ${\lambda }_{c1}$ and ${\lambda }_{c3}$; while the CHC exhibits three quantum jumps by $-N{e}^2/h$, $+2N{e}^2/h$ and $-N{e}^2/h$. 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

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