We investigate the $2k_F$ density wave instability of non-Fermi-liquid states by combining exact diagonalization with renormalization group analysis. At the half-filled zeroth Landau level, we study the fate of the composite Fermi liquid in the presence of the mass anisotropy and mixed Landau level form factors. These two experimentally accessible knobs trigger a phase transition towards a unidirectional charge density wave state with a wave vector equal to $2k_F$ of the composite Fermi liquid. Based on exact diagonalization, we identify such a transition by examining both the energy spectra and the static structure factor of charge density-density correlations. Moreover, the renormalization group analysis reveals that gauge fluctuations render the non-Fermi-liquid state unstable against density wave orders, consistent with numerical observations. Possible experimental probes of the density wave instability are also discussed.

• Received 15 January 2020
• Revised 25 August 2020
• Accepted 26 August 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033414

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society