Tunneling of Interacting Fermions in 1D Systems

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single δ barrier in a finite one-dimensional wire connected to contacts. Our results exhibit features known from correlated many-body models. In particular, the conductance decays with the wire length as ∝ L$\text{}^{-2α}$, where the powerα is universal. We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through theδ barrier in a one-dimensional ring, where it is known that I∝ L$\text{}^{-1-α}$.