In Search of the Dirac Cone in the Half-filled-Landau-Level Composite-Fermion Liquid

The "web of duality" supports D. Son's Dirac picture of the composite fermion (CF) Fermi liquid state of a half-filled 2D Landau level, which implies that an analog of the "Dirac cone" state should describe a CFL state with a single empty "CF orbital" at the center of the "Fermi sea". WIth an inversion-symmetric Fermi surface, this implies that the "Dirac cone" k=0 quasihole state is an inversion-symmetric zero-momentum state with an even number of particles. With particle-hole symmetry, such states have an extra two-fold degeneracy. Model CFL states based on the Halperin-Lee-Read picture are remarkably close to having a generalized particle-hole (with inversion) symmetry but as a quasi-hole is moved inside the Fermi surface this breaks down: the two particle-hole conjugate states become orthogonal as the quasihole reaches the Fermi sea center k=0. By forming the two orthogonal linear combinations that diagonalize the overlap matrix, two branches of single-quasihole excitations strongly reminiscent of the (electron) hole and positron states of an electron-rich "Dirac sea" are obtained. As the quasihole k approaches k_F, the model states have large overlap with numerical exact eigenstates of the Coulomb interaction.