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, ${E}_{c}$. To study transport, we place the wire in contact with electron reservoirs biased around a Fermi level, $E$. We show that the conductance scales superdiffusively 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 subdiffusive power laws, depending on the sign of the expectation value of the disorder and the parameters of the wire.