Phase transitions and symmetry breaking in disordered quantum Hall edge states

Abstract

Tunneling into the edge of a quantum Hall droplet is a sensitive probe of the topological orders believed to exist in fractional quantum Hall states. The tunneling behavior of a general hierarchy state is studied within the chiral-Luttinger-liquid model of low-energy edge dynamics. Adding random hopping of quasiparticles between edge modes results in "symmetry restoration by disorder" and universal weak tunneling behavior in edges with modes traveling in both directions. We develop a boost coordinate technique and apply it to find the edge phases and tunneling exponents of all topologically stable principal hierarchy states. States with neutral modes in both directions along the edge have multiple stable fixed points which can be classified by their symmetries. When the tunneling current into an edge is large, the system can cross over from the weak-tunneling fixed point to a different strongly coupled fixed point with different conductance and effective charge. Edges with multiple modes can have multiple strongly coupled fixed points. We develop a general formalism to analyze weakly and strongly coupled fixed points of point tunneling. Adding interactions to tunneling between two Laughlin edges is shown to lead to a continuous variation of effective quasiparticle charge and conductance with interaction strength.