Tunable even- and odd-denominator fractional quantum Hall states in trilayer graphene

TL;DR

This study demonstrates tunable fractional quantum Hall states in trilayer graphene, revealing control over Landau level mixing and phase transitions, and providing a promising platform for exploring non-Abelian anyons for quantum computing.

Contribution

We experimentally show tunable even- and odd-denominator FQH states in trilayer graphene, enabling control over Landau level mixing and phase transitions.

Findings

Observation of robust FQH states at specific filling factors

Control of Landau level mixing via external fields

Detection of quantum phase transitions in FQH states

Abstract

The fractional quantum Hall (FQH) states are exotic quantum many-body phases whose elementary charged excitations are neither bosons nor fermions but anyons, obeying fractional braiding statistics. While most FQH states are believed to have Abelian anyons, the Moore-Read type states with even denominators, appearing at half filling of a Landau level (LL), are predicted to possess non-Abelian excitations with appealing potentials in topological quantum computation. These states, however, depend sensitively on the orbital contents of the single-particle LL wavefunction and the mixing between different LLs. Although they have been observed in a few materials, their non-Abelian statistics still awaits experimental confirmation. Here we show magnetotransport measurements on Bernal-stacked trilayer graphene (TLG), whose unique multiband structure facilitates the interlaced LL mixing, which can be controlled by external magnetic and displacement fields. We observe a series of robust FQH states including even-denominator ones at filling factors $\nu=-9/2$, $-3/2$, $3/2$ and $9/2$. In addition, we are able to finetune the LL mixing and crossings to drive quantum phase transitions of these half-filling states and their neighboring odd-denominator ones, exhibiting a related emerging and waning behavior. Our results establish TLG as a controllable system for tuning the weights of LL orbitals and mixing strength, and a fresh platform to seek for non-Abelian quasi-particles.