Superdiffusive transport in two-dimensional fermionic wires

We present a two-dimensional model of a fermionic wire which shows a power-law conductance behavior despite the presence of uncorrelated disorder along the direction of the transport. The power-law behavior is attributed to the presence of energy eigenstates of diverging localization length below some energy cutoff, Ec. To study transport, we place the wire in contact with electron reservoirs biased around a Fermi level, E. We show that the conductance scales superdiffusively for |E|<Ec and decays exponentially for |E|>Ec. At |E|=Ec, we show that the conductance scales diffusively or with different subdiffusive power laws, depending on the sign of the expectation value of the disorder and the parameters of the wire.