Conductance of a Mott Quantum Wire

We consider transport through a one-dimensional conductor subjected to an external periodic potential and connected to noninteracting leads (a “Mott quantum wire”). In the case of a strong periodic potential, the conductance is shown to jump from zero, for the chemical potential lying within the Mott-Hubbard gap, to the noninteracting value of ${2e}^2/h$, as soon as the chemical potential crosses the gap edge. This behavior is strikingly different from that of optical conductivity, which varies continuously with the carrier concentration. In the case of a weak potential, the perturbative correction to the conductance due to umklapp scattering is absent away from half filling.