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arXiv · 2210.04937

$\mathbb{Z}_3$ parafermion in the double charge-Kondo model

D. B. Karki·Edouard Boulat·Winston Pouse·David Goldhaber-Gordon·Andrew K. Mitchell·Christophe Mora
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Abstract

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a $\mathbb{Z}_3$ parafermion emerges at the critical point, characterized by a fractional $\tfrac{1}{2}\ln(3)$ residual entropy, and scattering fractional charges $e/3$. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.

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D. B. Karki, Edouard Boulat, Winston Pouse, David Goldhaber-Gordon, Andrew K. Mitchell, Christophe Mora. 2022-10-10. $\mathbb{Z}_3$ parafermion in the double charge-Kondo model. https://doi.org/10.1103/physrevlett.130.146201

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