Contacts, equilibration, and interactions in fractional quantum Hall edge transport

Abstract

We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter-playing the role of an effective interaction strength within an idealized model of thermal reservoirs-is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

“…This value was indeed measured, but only on engineered edges at interfaces between two FQH states 10 . In experiments on a conventional edge (the boundary of a ν = 2/3 FQH state), G = 2/3 e 2 h is found to be robust and essentially equal to the filling factor ν = 2/3, implying that charge propagates only downstream direction; one cannot tell anything about the presence or absence of upstream modes 9,11,12 . The second question is whether the upstream mode can be detected by measuring the thermal conductance.…”