Partial filled Landau Level at even denominator, a vortex metal with Berry phase

TL;DR

This paper develops a vortex metal theory for fractional filled Landau Levels at even denominators, revealing a Berry phase on the composite Fermi surface that affects scattering and potential phases.

Contribution

It introduces a novel vortex metal model with a fractional Berry phase resulting from Landau Level projection, and explores its implications in bilayer systems with particle-hole symmetry.

Findings

Berry phase of -π/n on the Fermi surface due to LL projection.

Suppression of 2k_f back-scattering in bilayer systems with this Berry phase.

Potential instabilities including a Z_{4n} topological order phase.

Abstract

We develop a vortex metal theory for partial filled Landau Level at $\nu=\frac{1}{2n}$, whose ground state contains a composite Fermi surface(FS) formed by the vortex of electrons. In the projected Landau Level limit, the composite Fermi surface contains $\frac{-\pi}{n}$ Berry phase. Such fractional Berry phase is a consequence of LL projection which produces the GMP guiding center algebra and embellishes an anomalous velocity to the equation of motion for the vortex metal. Further, we investigate a particle-hole symmetric bilayer system with $\nu_1=\frac{1}{2n}$ and $\nu_2=1-\frac{1}{2n}$ at each layer, and demonstrate that the $\frac{-\pi}{n}$ Berry phase on the composite Fermi surface leads to the suppression of $2k_f$ back-scattering between the PH partner bilayer, which could be a smoking gun to detect the fractional Berry phase. We also mention various instabilities and competing orders in such bilayer system including a $Z_{4n}$ topological order phase driven by quantum criticality.