Dynamical mean-field theory for the anisotropic Kondo semiconductor: Temperature and magnetic field dependence

We investigate the periodic Anderson model with $\bm{k}$-dependent $c$-$f$ mixing reproducing the point nodes of the hybridization gap by using the dynamical mean-field theory combined with the exact diagonalization method. At low temperature below a coherence temperature $T_0$, the imaginary part of the self-energy is found to be proportional to $T^2$ and the pseudogap with two characteristic energies $\tilde{\it \Delta}_1$ and $\tilde{\it \Delta}_2$ is clearly observed for $T\ll T_0$, while the pseudogap is smeared with increasing $T$ and then disappears at high temperature $T \simg T_0$ due to the evolution of the imaginary self-energy. When the Coulomb interaction between $f$ electrons $U$ increases, $\tilde{\it \Delta}_1$, $\tilde{\it \Delta}_2$, and $T_0$ together with $T_{\rm max}$ at which the magnetic susceptibility is maximum decrease in proportion to the renormalization factor $Z$ resulting in a heavy-fermion semiconductor with a large mass enhancement $m^*/m=Z^{-1}$ for large $U$. We also examine the effect of the external magnetic field $H$ and find that the magnetization $M$ shows two metamagnetic anomalies $H_1$ and $H_2$ corresponding to $\tilde{\it \Delta}_1$ and $\tilde{\it \Delta}_2$ which are reduced due to the effect of $H$ together with $Z$. Remarkably, $Z^{-1}$ is found to be largely enhanced due to $H$ especially for $H_1 \siml H \siml H_2$, where the field induced heavy-fermion state is realized. The obtained results seem to be consistent with the experimental results observed in the anisotropic Kondo semiconductors such as CeNiSn.