Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

The finite-bandwidth conductance of a Luttinger liquid (LL) with a cluster of impurities is studied and its variation with respect to temperature is shown. The calculations are done using the correlation functions obtained using the powerful non-chiral bosonization technique (NCBT). The results are compared with those obtained by Matveev, Yue and Glazman [K. Matveev et al., Phys. Rev. Lett. 71, 3351 (1993)] who deal with a weakly interacting LL. By contrast, NCBT correctly provides the conductance for all values of the interaction strength (as well as the sign). In addition to finding perfect agreement with the results of Matveev et al. for both weakly repulsive and weakly attractive mutual interactions, we are also able to probe novel physics seen when the repulsion is strong - in the form of a weakly temperature dependent conductance when there is a definite relationship between the transmission amplitude of the non-interacting system and the holon velocity. Secondly, an unusual high conductance for strongly repulsive mutual interactions is observed for a weak barrier at low temperatures. Lastly, inclusion of backward scattering leads to the non-monotonic temperature dependence of conductance when dealing with fermions with spin. This work is also important as a validation of the NCBT itself.