Magneto-optical and optical probes of gapped ground states of bilayer graphene

TL;DR

This paper investigates how different energy gaps in bilayer graphene influence its optical conductivities, deriving exact formulas and proposing experimental methods to distinguish symmetry-breaking states via optical polarization effects.

Contribution

It provides exact analytical expressions for magneto-optical conductivity in bilayer graphene with various gaps and explores experimental detection of time-reversal symmetry breaking states.

Findings

Exact magneto-optical conductivity formulas derived.

Distinction of symmetry-breaking states via optical Hall conductivity.

Feasibility of experimental detection through optical polarization rotation.

Abstract

We study the influence of different kinds of gaps in a quasiparticle spectrum on longitudinal and transverse optical conductivities of bilayer graphene. An exact analytical expression for magneto-optical conductivity is derived using a low-energy two-band Hamiltonian. We consider how the layer asymmetry gap caused by a bias electric field and a time-reversal symmetry breaking gap affect the absorption lines. The limit of zero magnetic field is then analyzed for an arbitrary carrier density in the two-band model. For a neutral bilayer graphene, the optical Hall and longitudinal conductivities are calculated exactly in the four-band model with four different gaps and zero magnetic field. It is shown that two different time-reversal symmetry breaking states can be distinguished by analyzing the dependence of the optical Hall conductivity on the energy of photon. These time-reversal symmetry breaking states are expected to be observed experimentally via optical polarization rotation either in the Faraday or Kerr effects. We analyze a possibility of such an experiment for a free-standing graphene, graphene on a thick substrate, and graphene on a double-layer substrate.