Multichannel topological Kondo models and their low-temperature conductances

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 M Majorana modes SO (M M) “spin” and N N spinless electron channels exhibits an exotic intermediate coupling fixed point. This intermediate fixed point has been analyzed through large- N N perturbative calculations, which gives a zero-temperature conductance decaying as 1/N² 1 / N 2 in the large- N N limit. However, the conductance at this intermediate fixed point has not been calculated for generic N 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 M = 4. Using conformal field theory techniques for SO (M 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 M) for general N N, confirming the previous large- N 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 N = 1 and N≥2 N ≥ 2 due to the different fusion outcomes with the current operator. We also compare the multichannel topological Kondo model to the topological symplectic Kondo model.