Helical edge magnetoplasmon in the quantum Hall effect regime

Abstract

We present the microscopic treatment of edge magnetoplasmons (EMPs) for the regime of not-too-low temperatures defined by the condition ℏωc⪢kBT⪢ℏvg/2ℓ0, where vg is the group velocity of the edge states, ℓ0=ℏ/m∗ωc is the magnetic length and ωc is the cyclotron frequency. We find a weakly damped symmetric mode, named helical EMP, which is localized at the edge states region for filling factors ν=1,2 and very strong dissipation ηT=ξ/kxℓT≳ln(1/kxℓT)⪢1, where the characteristic length ℓT=kBTℓ02/ℏvg⪢ℓ0/2 with ξ being the ratio of the local transverse conductivity to the local Hall conductivity at the edge states and kx is the wave vector along the edge; here other EMP modes are strongly damped. The spatial structure of the helical EMP, transverse to the edge, is strongly modified as the wave propagates along the edge. In the regime of weak dissipation, ηT⪡1, we obtain exactly the damping of the fundamental mode as a function of kx. For ν=4 and weak dissipation we find that the fundamental modes of n=0 and 1 Landau levels are strongly renormalized due to the Coulomb coupling. Renormalization of all these EMPs coming from a metal gate and air half-space is studied.