Abstract
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 wavevector 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.
Highlights
Non Fermi liquids (NFLs) are among the most exotic quantum states in condensed matter
We propose one mechanism to reap yet another instability of composite Fermi liquid (CFL): the 2kF density wave instability, which is of equal importance to the previously discovered CFL instabilities and is likely to exhibit distinct physics from ordinary Fermi liquids [36,37,38]
Q where V (q) is the Fourier transform of the unprojected Coulomb interaction, F (q) denotes the density form factor introduced by projection, ρ(q) is the guiding center density operators, and A represents the area of the 2D plane
Summary
Non Fermi liquids (NFLs) are among the most exotic quantum states in condensed matter. Based on an exact diagonalization (ED) and renormalization group (RG) analysis, we propose one possible mechanism to trigger the density wave instability of CFL on half-filled LLs: tuning the interactions via the mixed LL form factors from an anisotropic CFL state. We demonstrate such an instability numerically and reveal the underlying mechanism by RG analysis. The mixed form factor is experimentally accessible in Dirac materials, e.g., in bilayer graphene, by tuning the interlayer electric bias and the magnetic field [39,40,41,42], rendering it possible to examine our findings
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