Two relativistic Kondo effects: Classification with particle and antiparticle impurities

We investigate two different types of relativistic Kondo effects, distinguished by heavy-impurity degrees of freedom, by focusing on the energy-momentum dispersion relations of the ground state with condensates composed of a light Dirac fermion and a nonrelativistic impurity fermion. Heavy-fermion degrees of freedom are introduced in terms of two types of heavy-fermion effective theories, in other words, two heavy-fermion limits for the heavy Dirac fermion, which are known as the heavy-quark effective theories (HQETs) in high-energy physics. While the first one includes only the heavy-particle component, the second one contains both the heavy-particle and heavy-antiparticle components, which are opposite in their parity. From these theories, we obtain two types of Kondo effects, in which the dispersions near the Fermi surface are very similar, but they differ in the structure at low momentum. We also classify the possible forms of condensates in the two limits. The two Kondo effects will be examined by experiments with Dirac/Weyl semimetals or quark matter, lattice simulations, and cold-atom simulations.

Figure 1

Examples of dispersion relations of quasiparticles with $S+V$ condensate at $\lambda =0$. The colored region means the Fermi sea. Left: Dispersion relations of light Dirac fermions ($E=\pm p-\mu$) and heavy fermions ($E=0$) without condensates. Middle: Eqs. (13) and (14) in the conventional HQET. Right: Eqs. (29) and (30) in the FW-HQET.

Figure 2

Schematic picture of dispersion relations in nonrelativistic topological Kondo insulators. The $d$-electron band ${\epsilon }_c\left(\vec{k}\right)$ and $f$-electron band ${\epsilon }_f\left(\vec{k}\right)$ are hybridized, and the quasiparticle bands $E_{\pm }\left(\vec{k}\right)$ with a gap $\mathrm{\Delta }$ appear. The shaded region means the Fermi sea.