Quantum Hall Effects in Silicene

TL;DR

This paper explores how electric fields influence quantum Hall effects in silicene, revealing controllable valley degeneracy and unique zero-energy state behaviors due to silicene's buckled structure and massive Dirac fermions.

Contribution

It demonstrates electric field control over valley degeneracy and zero-energy states in silicene, highlighting differences from graphene and enriching understanding of 2D topological materials.

Findings

Zero-energy states are absent except at critical electric field.

Valley degeneracy can be externally controlled via electric field.

Hall plateaux appear at multiple filling factors, with level crossings affecting them.

Abstract

We investigate quantum Hall effects in silicene by applying electric field $E_z$ parallel to magnetic field. Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, and shares almost every remarkable property with graphene. A new feature is its buckled structure, due to which the band structure can be controlled externally by changing $E_z$. The low energy physics of silicene is described by massive Dirac fermions, where the mass is a function of $E_z$ and becomes zero at the critical field $E_{\text{cr}}$. We show that there are no zero energy states due to the Dirac mass term except at the critical electric field $E_{\text{cr}}$. Furthermore it is shown that the 4-fold degenerate zero-energy states are completely resolved even without considering Coulomb interactions. These features are highly contrasted with those in graphene, demonstrating that silicene has a richer structure. The prominent feature is that, by applying the electric field, we can control the valley degeneracy. As a function of $E_z$, Hall plateaux appear at the filling factors $\nu =0,\pm 1,\pm 2,\pm 3,...$ except for the points where level crossings occur.