Conductance of one-dimensional quantum wires

Abstract

We discuss the conductance of quantum wires (QW) in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of {\it bulk} contact the leading order corrections to the conductance for two different boundary conditions, which reproduce in the absence of {\it bulk} contact, respectively, the standard 2T source-drain (SD) conductance $G_{\mathrm{SD}}^{(2)}=e^2/h$ and $G_{\mathrm{SD}}^{(2)}=g{e}^2/h$, where $g$ is the TLL charge interaction parameter. We find that under these two boundary conditions for the {\it end} contacts the 3T SD conductance $G_{\mathrm{SD}}^{(3)}$ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the ohmic limit. Non-trivial scaling exponents are predicted as a result of electron fractionalization.

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References in corpus (1)

• Coulomb drag shot noise in coupled Luttinger liquids

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