Study of integer quantum hall edge states in monolayer and bilayer graphene

Abstract

Quantum Hall states in 2D materials are characterised by robust edge states which reflect some bulk topological order through Bulk-Edge correspondence. It is of interest to realize complex states that emerge by coupling of Quantum Hall systems. Disorder plays a critical role in the stabilization of Quantum Hall states. Presence of impurities and scattering due to impurities are very important for the studies of transport properties and Quantum Hall effect experiments as they influence the conductivity, magnetic properties etc. In addition, the structure of the quantum states (more precisely, the nature of the correlations) around the disorder reveals details of the topological order contained in the system.

A Quantum Hall edge state, with it's chiral edge mode is a 1D system. In case of bilayer graphene, there is a possibility of creating edge modes that are helical, robust and with suppressed back scattering with integer and fractional statistics.

Due to the fact that density of states vanish at the dirac points for graphene, resulting in an absence of screening, the disorders become quite important in determining transport properties. We add a single local impurity that can couple two edge modes and provide strong short range scattering. We also change chemical potential(in case of Bilayer),tune the interlayer coupling, and study it's effects on the energy spectrum in the Hofstadter regime. By threading a magnetic flux adiabatically, spectral flow of edge states and band structures are studied. Through this work, we have identified the numerical quantities and tools that are tractable through which the physics of coupled edge theory can be studied.