Abstract
We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter region realizing the Aoki phase. Our findings will be useful for understanding the roles of heavy impurities in Dirac semimetals, topological insulators, and lattice simulations.
Highlights
The Kondo effect has a long history in solid-state physics [1,2,3,4,5]
First we focus on the Kondo effect for the massless Wilson fermion
Fermi level, which is caused by a mechanism similar to the chiral symmetry restoration as in the χGN model. μc2 is the effect from the lattice cutoff for the Wilson fermion, as interpreted in terms of its dispersion relations
Summary
The Kondo effect has a long history in solid-state physics [1,2,3,4,5]. It was observed as an enhancement of electric resistance of a metal, and it is induced by a strong correlation between nonrelativistic itinerant electrons and localized spin impurities. For QCD in continuum space, the Aoki phase is regarded as an artifact due to the discretization of the spacetime, but in solid-state physics, similar phase structures were pointed out by an interacting Su-Schrieffer-Heeger model [66], an interacting Kane-Mele model [67], and a Fu-Kane-Mele-Hubbard model [68]. Such parity-broken materials are closely related to axion insulators
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