Interlayer coherent composite Fermi liquid in Half-filled Landau Level bilayers, a window toward the hidden $\pi$ Berry phase

TL;DR

This paper investigates the interlayer coherent composite Fermi liquid phase in bilayer half-filled Landau levels, revealing its Dirac nature, Berry phase structure, nematic order, and topological responses, thus providing insights into the hidden $ ext{pi}$ Berry phase.

Contribution

It introduces the interlayer coherent composite Fermi liquid phase in bilayer systems as a platform to verify the Dirac composite fermion theory and uncover the Berry phase structure.

Findings

Identification of nematic Fermi surface structure due to Berry phase

Support for Dirac composite fermion theory over HLR theory

Presence of topological Wen-Zee term linking EM response and geometry

Abstract

For interacting 2D electrons in the presence of magnetic field at half filling, the system forms a `composite Fermi liquid(CFL)' with emergent Fermi surface and exhibits metallic behavior, based on the standard Halperin, Lee, and Read(HLR) field theory. Recently, Son introduces a composite Dirac theory as the low energy effective description of Half-filled Landau Level. Such theory exhibits particle-hole symmetry and the underlying composite Fermi surface displays a robust $\pi$ Berry phase. In this paper, we start from the bilayer Half-filled Landau Level system where the two composite Fermi surface acquires interlayer coherence and forms bonding/anti-bonding composite fermi sea. The corresponding interlayer coherent composite Fermi liquid(ICCFL) phase provides a straightforward landscape to verify the Dirac nature in Son's theory and extract the hidden Berry phase structure of the composite Fermi surface. The ICCFL phase contains two Fermi surfaces which are detached in most regions but adhesive at two hot spots. Such nematic structure is a consequence of the Berry phase encoded in the Dirac Fermi surface which is absent in HLR theory. Due to the nematicity in ICCFL, the system supports half-quantum vortex with deconfined $\frac{\pi}{2}$ gauge flux and the phase transition toward ICCFL contains a Lifshitz criticality with $z=3$ dynamical exponent. In addition, the exciton order parameter carries topological spin number so the ICCFL contains a unique Wen-Zee term which connects EM response with the background geometry curvature.