Multichannel topological Kondo models and their low-temperature conductances

TL;DR

This paper investigates the multichannel topological Kondo model, revealing its overscreened nature, deriving the fixed-point conductance for general N, and analyzing finite-temperature effects using conformal field theory techniques.

Contribution

The study verifies the existence of the intermediate fixed point, derives the strong-coupling Hamiltonian for M=4, and generalizes conductance calculations for arbitrary N using conformal field theory.

Findings

Confirmed overscreened nature of MCTK model.

Derived fixed-point conductance in terms of SO(M) S-matrix.

Identified different finite-temperature corrections for N=1 and N≥2.

Abstract

In the multichannel Kondo effect, overscreening of a magnetic impurity by conduction electrons leads to a frustrated exotic ground state. It has been proposed that multichannel topological Kondo (MCTK) model involving topological Cooper pair boxes with $M$ Majorana modes [SO($M$) "spin"] and $N$ spinless electron channels exhibits an exotic intermediate coupling fixed point. This intermediate fixed point has been analyzed through large-$N$ perturbative calculations, which gives a zero-temperature conductance decaying as $1/N^2$ in the large-$N$ limit. However, the conductance at this intermediate fixed point has not been calculated for generic $N$. Using representation theory, we verify the existence of this intermediate-coupling fixed point and find the strong-coupling effective Hamiltonian for the case $M=4$. Using conformal field theory techniques for SO($M$), we generalize the notion of overscreening and conclude that the MCTK model is an overscreened Kondo model. We find the fixed-point finite-size energy spectrum and the leading irrelevant operator (LIO). We express the fixed-point conductance in terms of the modular S-matrix of SO($M$) for general $N$, confirming the previous large-$N$ result. We describe the finite-temperature corrections to the conductance by the LIO and find that they are qualitatively different for the cases $N=1$ and $N\geq2$ due to the different fusion outcomes with the current operator. We also compare the multichannel topological Kondo model to the topological symplectic Kondo model.