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

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Cited by in corpus (7)

• Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets
• Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Lowest Landau level theory of the bosonic Jain states
• Is the composite fermion state of Graphene a doped Chern insulator?
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Very high-energy collective states of partons in fractional quantum Hall liquids