Multichannel topological Kondo models and their low-temperature conductances
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| Format: | Preprint |
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2025
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| _version_ | 1866912484615520256 |
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| author | Li, Guangjie König, Elio J. Väyrynen, Jukka I. |
| author_facet | Li, Guangjie König, Elio J. Väyrynen, Jukka I. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_11682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multichannel topological Kondo models and their low-temperature conductances Li, Guangjie König, Elio J. Väyrynen, Jukka I. Strongly Correlated Electrons Mesoscale and Nanoscale Physics 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. |
| title | Multichannel topological Kondo models and their low-temperature conductances |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2507.11682 |