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arXiv:0801.3824 · Physical Review B

Junctions of three quantum wires for spin- 12 electrons

Chang-Yu Hou, Claudio Chamon

Published Apr 15, 2008• 56 citations
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Abstract

We study the effects of electron-electron interactions on the transport properties of a junction of three quantum wires enclosing a magnetic flux. The wires are modeled as single channel spin-$\frac{1}{2}$ Tomonaga--Luttinger liquids. The system exhibits a rich phase diagram as a function of the electronic interaction strength, which includes a chiral fixed point with an asymmetric current flow highly sensitive to the sign of the flux and another fixed point where pair tunneling dominates, which is similar to the case of spinless electrons. While in the case of spinless electrons the perturbations that correspond to unequal couplings between the three wires are always irrelevant, we find that, when the electron spin is included, there are small regions in the phase diagram where a current flows only between two of the wires and the third wire is decoupled.

DOI
10.1103/physrevb.77.155422

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We study a system consisting of a junction of NNN wires, where the junction is characterized by a scalar SSS-matrix, and an impurity spin is coupled to the electrons near the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group (RG) equations for the Kondo couplings of the spin to the electrons on different wires. We analyze the RG flows and fixed points for different values of the initial Kondo couplings and of the junction SSS-matrix, such as the decoupled SSS-matrix and the Griffiths (connected) SSS-matrix. We find that the Kondo couplings flow either towards a ferromagnetic (FM) fixed point or towards large and antiferromagnetic (AFM) values in one of two ways. For the Griffiths SSS-matrix, one of the strong coupling flows is towards a FM fixed point with decoupled wires; this is seen by a perturbative analysis. Thus if we start with a system of connected wires with an AFM coupling to the spin impurity, the flow at large distances is towards a system of disconnected wires at the FM fixed point. For the decoupled SSS-matrix, the flow is either to a FM fixed point or to one of two strong coupling fixed points in which all the channels are strongly coupled to each other through the impurity spin. Strong interactions between the electrons with ${K}_{\ensuremath{\rho}}<N∕(N+2)$ can stabilize a multichannel fixed point in which the coupling between different channels goes to zero. We also study the temperature dependence of the conductance at the decoupled and Griffiths SSS-matrices.
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