# Connection between Fermi contours of zero-field electrons and $\nu=\frac12$ composite fermions in two-dimensional systems

## TL;DR

This paper explores the relationship between zero-field Fermi surfaces and composite fermion Fermi surfaces at half-filling in two-dimensional systems, revealing that their shapes and topologies are generally unrelated and unaffected by certain dispersion changes.

## Contribution

It demonstrates analytically that the composite Fermi liquid is insensitive to many zero-field dispersion modifications and discusses the implications of symmetry breaking on valley pseudospin transfer.

## Key findings

- CFL is insensitive to zero-field dispersion changes that preserve rotational symmetry.
- Breaking rotational symmetry affects valley pseudospin transfer to the CFL.
- Band structure modifications can lead to Landau level reordering, enabling higher-Landau-level physics.

## Abstract

We investigate the relation between the Fermi sea (FS) of zero-field carriers in two-dimensional systems and the FS of the corresponding composite fermions which emerge in a high magnetic field at filling $\nu = \frac{1}{2}$, as the kinetic energy dispersion is varied. We study cases both with and without rotational symmetry, and find that there is generally no straightforward relation between the geometric shapes and topologies of the two FSs. In particular, we show analytically that the composite Fermi liquid (CFL) is completely insensitive to a wide range of changes to the zero-field dispersion which preserve rotational symmetry, including ones that break the zero-field FS into multiple disconnected pieces. In the absence of rotational symmetry, we show that the notion of `valley pseudospin' in many-valley systems is generically not transferred to the CFL, in agreement with experimental observations. We also discuss how a rotationally symmetric band structure can induce a reordering of the Landau levels, opening interesting possibilities of observing higher-Landau-level physics in the high-field regime.