In-plane electric fields and the $\nu=\frac{5}{2}$ fractional quantum Hall effect in a disk geometry

TL;DR

This study investigates how in-plane electric fields influence the $ u=5/2$ fractional quantum Hall state in a disk geometry, revealing that weak fields stabilize the state while strong fields destabilize it, with potential experimental implications.

Contribution

It provides the first analysis of electric field effects on the $ u=5/2$ state in a finite-thickness disk geometry, highlighting the impact of field polarity and strength.

Findings

Weak probe fields enhance the Moore-Read Pfaffian state.

Strong electric fields destroy the incompressible state.

Electric fields increase quasihole coherence length.

Abstract

The $\nu=\frac{5}{2}$ fractional quantum Hall effect is of experimental and theoretical interest due to the possible non-Abelian statistics of the excitations in the electron liquid. A small voltage difference across a sample applied in experiments to probe the system is often ignored in theoretical studies due to the Galilean invariance in the thermodynamic limit. No experimental sample, however, is Galilean invariant. In this work, we explore the effects of the probe electric fields in a disk geometry with finite thickness. We find that weak probe fields enhance the Moore-Read Pfaffian state but sufficiently strong electric fields destroy the incompressible state. In a disk geometry, the behavior of the system depends on the polarity of the applied radial field, which can potentially be observed in experiments using in a Corbino disk configuration. Our simulation also shows that the application of such a field enhances the coherence length of quasiholes propagating through the edge channels