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Fractionalized Fermi liquids
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In spatial dimensions d >= 2, Kondo lattice models of conduction and local moment electrons can exhibit a fractionalized, non-magnetic state (FL*) with a Fermi surface of sharp electron-like quasiparticles, enclosing a volume quantized by (\rho_a-1)(mod 2), with \rho_a the mean number of all electrons per unit cell of the ground state. Such states have fractionalized excitations linked to the deconfined phase of a gauge theory. Confinement leads to a conventional Fermi liquid state, with a Fermi volume quantized by \rho_a (mod 2), and an intermediate superconducting state for the Z_2 gauge case. The FL* state permits a second order metamagnetic transition in an applied magnetic field.
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Tractable model for a fractionalized Fermi liquid (FL$^*$) on a square lattice
The model has a hybridized phase where spin-liquid Majorana fermions and conduction electrons form a common small Fermi surface violating the Luttinger count, with momentum-dependent coherence factors that produce Fermi arcs.
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