Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

Abstract

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. arXiv:1809.05484v3 [cond-mat.str-el]

Density-density correlation function of strongly inhomogeneous Luttinger liquids

“…Also it is unlikely that such numerical methods are able to capture the most singular parts of the Greenʼs functions that NCBT provides. The NCBT results have already been validated analytically using the Schwinger-Dyson equation [22] and a host of other ways as shown in our group's published works [21,23,[42][43][44][45].…”

Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

“…Once the Green function of a given system is obtained, it may be used to predict different physical phenomena occurring in the system. Typical physical phenomena studied in Luttinger liquids with impurities includes Friedel oscillations [15], conductance [16][17][18][19][20][21], Kondo effect [22,23] and so on. In the famous work by Kane and Fisher [24], it has been shown how impurities can cause extreme effects in the transport properties of constituent particles based on the nature of mutual interaction between them, viz., attractive or repulsive.…”