Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State

TL;DR

This paper investigates edge tunneling in the anti-Pfaffian quantum Hall state at filling factor 5/2, using RG analysis and instanton methods to predict conductance behavior and distinguish it from the Pfaffian state.

Contribution

It provides a theoretical framework for understanding nonlinear tunneling conductance and introduces a method to differentiate anti-Pfaffian from Pfaffian states experimentally.

Findings

Calculated intermediate conductance plateau value.

Showed non-perturbative quasi-particle tunneling as perturbative electron tunneling.

Derived conductance as a function of gate voltage.

Abstract

We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor $\nu=5/2$. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-terminals conductance is written as a function of the gate voltage. The obtained results enable us to distinguish the anti-Pfaffian state from the Pfaffian state experimentally.