Voltage profile and four-terminal resistance of an interacting quantum wire

Abstract

We investigate the behavior of the four-terminal resistance R 4pt in a quantum wire described by a Luttinger liquid in two relevant situations: ͑i͒ in the presence of a single impurity within the wire and ͑ii͒ under the effect of asymmetries introduced by disordered voltage probes. In the first case, interactions leave a signature in a power-law behavior of R 4pt as a function of the voltage V and the temperature T. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of R 4pt is explained in simple terms.

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“…within the high V > V c voltage regime, corresponding, respectively, to solid and dashed lines in the Figure. The 2k F modulation resembles the behavior found in the voltage profile of non-invasive probes in a system with an impurity, which is observed both in non-interacting 10,11,13 and interacting systems 20 . In those cases the origin is the occurrence of interference in the electronic wave packet generated by the back-scattering processes that take place at the impurity.…”

“…This is a natural assumption in the absence of magnetic fields and spin-orbit interactions (Recall that we are considering a spinless LL). Since our main interest is to discuss the effects originated in the strength of the couplings, later, in Sections III and IV, as a simplifying hypothesis, we will consider the same coupling for both probes (w 1 = w 2 ), although it is known that an asymmetrical coupling (w 1 = w 2 ) is sufficient to produce a negative resistance 14,20 .…”

“…Regarding the behavior of R 4t evaluated from a multiterminal setup in Luttinger liquids, the literature is restricted to Ref. 20. Previous estimates for this quantity were done on the basis of an interpretation of Landauer formula in a two terminal setup.…”

“…Besides Ref. 20, genuine multiterminal systems have been considered in Y-type geometries 22,23 , within linear response in the voltage and Hartree-Fock approximation of the interaction, respectively as well as in the study of the tunneling current of a quantum wire in the Fabry-Perot regime. 24 There are also some recent works on the effect of wires that are capacitively coupled to an additional reservoir.…”

“…25,26 In Ref. 20 we have considered the setup of Fig. 1, where an infinite Luttinger wire with a single impurity, through which a current I flows as a response to an applied voltage V , is connected at two points to voltage probes.…”