Universal Transport Theory for Paired Fractional Quantum Hall States in the Quantum Point Contact Geometry

TL;DR

This paper develops a unified, non-perturbative transport theory for paired fractional quantum Hall states with Majorana modes, providing experimental signatures to distinguish topological phases.

Contribution

It introduces a boundary effective action and instanton approximation for charge transport in paired FQH states, revealing dualities and stability conditions.

Findings

Derived boundary effective action for arbitrary Majorana modes

Established weak-strong duality in tunneling processes

Identified stable fixed points and experimental transport signatures

Abstract

Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and $|\mathcal{C}_{cf}|$ neutral Majorana modes set by the Chern number $\mathcal{C}_{cf}$. Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact (QPC) for general paired FQH states described by an $so(N)_1 \times u(1)$ conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions $N=|\mathcal{C}_{cf}|$ and develop a non-perturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.