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

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