Phase diagram of compressible and paired states in the quarter-filled Landau level

TL;DR

This paper investigates the phase diagram of quarter-filled Landau levels, revealing how tuning pseudopotentials can stabilize various quantum Hall states, with implications for understanding experimental observations in graphene and quantum wells.

Contribution

It introduces a Monte Carlo method to compute trial energies for pseudopotentials and demonstrates how tuning these can stabilize different quantum Hall states at quarter filling.

Findings

Anti-Pfaffian state stabilization requires minimal deviation from Coulomb interactions.

Presence of anti-Pfaffian state is supported by recent experimental daughter states.

Tuning pseudopotentials can stabilize Moore-Read and f-wave states.

Abstract

Quantum Hall plateaus at quarter fillings occur in GaAs wide quantum wells, hole-doped GaAs, and bilayer graphene. However, the interactions favoring incompressible states over compressible composite-Fermi liquids at such fillings are not well understood. We devise a method of computing the trial energies for Haldane pseudopotentials via Monte Carlo sampling. Applying it to the quarter-filled lowest Landau level, we find that tuning the third and fifth pseudopotential can stabilize anti-Pfaffian, Moore-Read, and f-wave states. The smallest deviations from pure Coulomb interactions are required by anti-Pfaffian, whose presence is indicated by daughter states in recent experiments of bilayer graphene at $\nu=\frac{3}{4}$.