Observation of a kink during the formation of the Kondo resonance band in a heavy-fermion system

We have shown that the kink behavior in the spectral function of a heavy fermion can appear during the formation of the Kondo resonance (KR) band and the hybridization gap. We have investigated the heavy fermion compound CeCoGe${}_2$, using a combined approach of the density functional theory and the dynamical mean field theory. Low temperature $T$ spectral functions show dispersive KR states, similarly to the recent experimental observation. During the evolution from the $\text{non-}f$ conduction band state at high $T$ to the dispersive KR band state at low $T$, which have topologically different band shapes, we have found the existence of kinks in the $\text{non-}f$ spectral function near the Fermi level $E_F$. The observation of kink is clearly in correspondence with the multiple temperature scales of the formation of the KR band.

Figure 1

Crystal structure and its Brillouin zone (a) The crystal structure of CeCoGe${}_2$ (Ref. 33). (b) The conventional Brillouin zone. Red line represents the path used in Fig. 3.

Figure 2

Theoretical demonstration of the HG feature from $T$-dependent $A^{\text{non-}f}(\mathbf{k},\omega )$. $A^{\text{non-}f}(\mathbf{k},\omega )$'s are provided along $S$-$R$-$T$-$Y$ (a) at $T=1200$ and (b) at $T=10$ K. $S$, $R$, $T$, and $Y$ are $\mathbf{k}=(\pi /2,\pi /2,0)$, $(\pi /2,\pi /2,\pi /2)$, $(0,\pi /2,\pi /2)$, and $(0,\pi /2,0)$, respectively. The green circle in (b) is for the emphasis of the $T$-dependent change. Blue dotted lines marked by $A$, $B$, $C$, and $D$ represent $\mathbf{k}$ points, where the $T$-dependent $A^{\text{non-}f}(\mathbf{k},\omega )$ calculations in (c) to (f) are done. Theoretically predicted ${\Delta }_{HG}$ is given at each $\mathbf{k}$ point.

Figure 3

(a),(d),(g) $T$-dependent $A^{\text{non-}f}(\mathbf{k},\omega )$ and (b),(e),(h) $A^f(\mathbf{k},\omega )$ between $R$ $(\pi /2,\pi /2,\pi /2)$ and $T$ $(0,\pi /2,\pi /2)$. The corresponding DOS's are also given in (c), (f), and (i). The insets show the detail of the spin-orbit multiplet at $-300$ meV. The purple rectangle in (h) indicates the weak spectrum of the spin-orbit multiplet, which can be seen clearly at $-0.3$ eV below $E_F$ in (i). Yellow points in (g) represent the off-resonant ARPES spectra in the measurement (Ref. 3), which are shifted along the $\mathbf{k}$ path for better alignment of $\text{non-}f$ bands.

Figure 4

The formation of the HG can be divided into four processes in (a) to (d), using $T_f$ and $T_m$ that are obtained by the scaling analysis in (g) and (h). (a) The high $T$ quasiparticle band is displayed. The blue color represents $A^{\text{non-}f}(\mathbf{k},\omega )$. (b) For $T$ $\sim$ $T_f$, the quasiparticle band is interrupted by the incoherent $4f$ electrons. The red dotted line is provided as a guide for the high $T$ band. (c) For $T_f$ $>$ $T$ $>$ $T_m$, the hybridization between $\text{non-}f$ and $4f$ electrons is strengthened. (d) For $T$ $<$ $T_m$, the HG and $k$-dependent (dispersive) KR state can be well defined. The orange color represents $A^f(\mathbf{k},\omega )$. With lowering $T$, $E_F$ increases gradually due to the participation of the new carrier from the incoherent $4f$ electrons. The FS on the $\mathbf{k}=Y$ plane at high and low $T$ are provided in (e) and (f), respectively. Color represents the different band indices. The scaling behaviors of the $T$-dependent renormalized de Haas van Alphen frequency $F$ and cyclotron effective mass $m^{*}$ for the FS branch $\alpha$ shown in (e) and (f) are analyzed in (g) and (h), respectively.