Metallic States with Charge Fractionalization

We construct examples of two-dimensional metallic states with exotic behaviors at low and intermediate temperatures. The simplest example we construct involves fermionic partons of electrons at finite density coupled to a Z_N gauge field, whose properties can be studied through rudimentary methods. This simple state already has the following exotic features: (1) at low temperature this state is a "bad metal" whose resistivity can be much larger than the Mott-Ioffe-Regel limit; (2) while increasing temperature T the resistivity ρ(T) is a nonmonotonic function, and it crosses over from a bad metal at low T to a good metal at intermediate T; (3) the AC conductivity σ(ω) has a small Drude weight at low T, and a larger Drude weight at intermediate T; (4) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law; (5) the state also has a large thermopower (Seebeck coefficient). A more complex example with fermionic partons at finite density coupled to a SU(N) gauge field will also be discussed. Within a finite energy window, the physics is dominated by the non-fermi liquid fixed point of partons. The potential instability towards "color superconductivity" will also be discussed. In addition, we will illustrate how the SU(N) state reduces to the Z_N state using an N=3 example on the triangular lattice.