Junction of several weakly interacting quantum wires:  A renormalization group study

Abstract

We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range densitydensity interaction, and they encounter a general scattering matrix at the junction. We derive the renormalization group equations satisfied by the S-matrix, and we identify its fixed points and their stabilities. The conductance between any pair of wires is then studied as a function of physical parameters such as temperature. We discuss the possibility of observing the effects of junctions in present day experiments, such as the four-terminal conductance of a quantum wire and crossed quantum wires.

Junctions of multiple quantum wires with different Luttinger parameters

“…Such asymmetric fixed points have been identified using perturbative renormalization-group analysis in the weak coupling regime. 21,57,58 Another important result of this paper is a direct numerical verification, through DMRG computations, 65 of the analytical predictions for the conductance of a junction of two nonidentical wires. Using a recently developed method, 66,67 which allows us to extract the conductance from a ground-state calculation in a finite system, we compute, in a microscopic lattice model, the conductance of a junction of two chains of interacting spinless electrons with different interaction strengths.…”

“…[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.…”

“…Junctions of three quantum wires, known as Y junctions, also have highly nontrivial transport properties. 21,22 Due to their rich transport behavior, junctions of quantum wires and their networks have thus attracted much attention. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] Most of the previous works on the transport properties of junctions of TLL wires focus on wires with the same Luttinger parameter.…”

“…For instance, at low temperature and low bias voltage, a TLL with repulsive interactions (g < 1) is totally disconnected in the presence of an impurity, while one with attractive interactions (g > 1) conducts as in the absence of the impurity. [14][15][16][17][18][19] From a practical viewpoint, junctions of TLL wires serve as important building blocks of quantum circuits, 20,21 and are thus of technological significance. Junctions of three quantum wires, known as Y junctions, also have highly nontrivial transport properties.…”

Electron-spin motion: a new tool to study ferromagnetic films and surfaces

“…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.…”