# Transference of Fermi Contour Anisotropy to Composite Fermions

## TL;DR

This study investigates how anisotropy in the energy-band structure of 2D holes influences the properties of composite fermions and fractional quantum Hall states, revealing a specific relationship between low-field and high-field anisotropies.

## Contribution

It demonstrates tunable anisotropy in holes and CFs via in situ strain and establishes a quantitative relation between their Fermi contour anisotropies.

## Key findings

- CF Fermi contour anisotropy is less than hole anisotropy.
- CF anisotropy follows the relation: a_ = a_^{1/2}.
- Energy gap of  = 2/3 FQHS is unaffected by anisotropy up to   3.3.

## Abstract

There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying \textit{in situ} in-plane strain and measuring their Fermi wavevector anisotropy through commensurability oscillations. For strains on the order of $10^{-4}$ we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field ($\alpha_\mathrm{CF}$) is less than the anisotropy of their low-field hole (fermion) counterparts ($\alpha_\mathrm{F}$), and closely follows the relation: $\alpha_\mathrm{CF} = \sqrt{\alpha_\mathrm{F}}$. The energy gap measured for the $\nu = 2/3$ FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to $\alpha_\mathrm{F} \sim 3.3$, the highest anisotropy achieved in our experiments.