Dirac Kondo effect under magnetic catalysis

We develop a mean-field theory of a novel Kondo effect emerging in systems without a Fermi surface, which instead emerges under strong magnetic fields. We determine the magnitude of the Kondo condensate, which is a particle pairing composed of conducting Dirac fermions and localized impurities. We focus on the competition between the Kondo effect and the energy gap formation that stems from the pairing among the Dirac fermions leading to the dynamical chiral symmetry breaking. We find that this competition induces a quantum critical point. We also investigate finite-temperature effects. This system at vanishing fermion density can be studied with Monte Carlo lattice simulations, which do not suffer from the sign problem.

Figure 1

Magnetic-field dependencies of Kondo condensate $\mathrm{\Delta }$ (blue) and chiral condensate $M$ (red). The solid lines show the full results with fixed parameters, $m_l/\mathrm{\Lambda }=0.01$, $G_{ll}{\mathrm{\Lambda }}^2=1.0$, and $G_{hl}{\mathrm{\Lambda }}^2=3.0$. The dotted and dashed lines show $\mathrm{\Delta }$ with $m_l=G_{ll}=0$ and with $G_{ll}=0$, respectively.

Figure 2

Temperature dependencies of Kondo condensate $\mathrm{\Delta }$ and chiral condensate $M$ at a fixed magnetic-field strength $|q_{l}B|/{\mathrm{\Lambda }}^2=1.5$. The legends are the same as in Fig. 1. The red dashed line shows $M$ at $G_{hl}=0$.

Figure 3

Magnetic-field and temperature dependencies of chiral condensate $M$ (left) and Kondo condensate $\mathrm{\Delta }$ (right).

Figure 4

Schematic phase diagram extracted from Fig. 3.