Super-diffusive 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, $E_c$. To study transport, we place the wire in contact with electron reservoirs biased around a Fermi level, $E$. We show that the conductance scales super-diffusively for $|E|<E_c$ and decays exponentially for $|E|>E_c$. At $|E|=E_c$, we show that the conductance scales diffusively or with different sub-diffusive power-laws depending on the sign of the expectation value of the disorder and the parameters of the wire.