Transport in an inhomogeneous interacting one-dimensional system

Abstract

Transport through a one-dimensional wire of interacting electrons connected to semi-infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The dc conductance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions the central wire acts as a Fabry-Perot resonator. When one of the connected wires has a tendency towards superconducting order, partial Andreev reflection of an incident electron occurs. 73.40.Jn, 74.80.Fp Typeset using REVT E X 1

Junctions of multiple quantum wires with different Luttinger parameters

“…For two wires, it is known that the transport properties of the junction are fully controlled by one effective Luttinger parameter g e = 2/(g −1 1 + g −1 2 ) as found in Ref. 39. In the context of fractional Hall edge states 60 , the similar result have been found for tunneling between two chiral-TLL edge states.…”

“…Moreover, a single TLL can have inhomogeneities: e.g., a contact between an interacting TLL and a Fermi-liquid lead, a key ingredient of most transport measurements, is often studied as an inhomogeneous TLL wire smoothly interpolating between interacting (TLL) and noninteracting (Fermi-liquid) regions or as a two-wire junction with the Luttinger parameter abruptly changing at the junction. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] A junction of three quantum wires with different Luttinger parameters has been studied in the weak coupling regime. 21,[57][58][59] The experimental importance of junctions of TLL wires with generally unequal Luttinger parameters motivates an in-depth study of their properties, which is the main objective of the present paper.…”

Ground state structure and conductivity of quantum wires of infinite length and finite width

“…Interaction effects have been considered for some time, especially in the framework of the 1D Tomonaga-Luttinger model, where it is predicted that the conductance is renormalized to G = ␥͑2e 2 / h͒, with a parameter ␥ Ͼ 1 for attractive interactions, ␥ Ͻ 1 for repulsive interactions, and ␥ = 1 for a noninteracting electron gas. [4][5][6] However, it has been argued [7][8][9][10][11] that ␥ should be unity, since the measured conductance is determined by the noninteracting electrons which are injected in the wire.…”

A dynamic scattering approach for a gated interacting wire

“…1 Such a concept cannot be extended to interacting systems, as illustrated in Ref. [ 4]. 13,14 Rather, interactions give rise to collective excitations, or Laughlin quasiparticles in edge states, that are different from the electrons in the reservoirs.…”

“…[ 4,9,10] where reservoirs are simulated by the electrons they inject. The leads have served to define the incident and transmitted electrons, different from the proper modes of the wire.…”