Fermi surface topology and hot spot distribution in the Kondo lattice system ${\mathbf{CeB}}_{\mathbf{6}}$

Rare-earth hexaborides have attracted considerable attention recently in connection to a variety of correlated phenomena including heavy fermions, superconductivity, and low-temperature magnetic phases. Here, we present high-resolution angle-resolved photoemission spectroscopy studies of trivalent ${\mathrm{CeB}}_6$ and divalent ${\mathrm{BaB}}_6$ rare-earth hexaborides. We find that the Fermi surface electronic structure of ${\mathrm{CeB}}_6$ consists of large oval-shaped pockets around the $X$ points of the Brillouin zone, whereas the states around the zone center $\mathrm{\Gamma }$ point are strongly renormalized. Our first-principles calculations agree with our experimental results around the $X$ points but not around the $\mathrm{\Gamma }$ point, indicating areas of strong renormalization located near $\mathrm{\Gamma }$. The Ce quasiparticle states participate in the formation of hot spots at the Fermi surface, whereas the incoherent $f$ states hybridize and lead to the emergence of dispersive features absent in the non-$f$ counterpart ${\mathrm{BaB}}_6$. Our results provide an understanding of the electronic structure in rare-earth hexaborides, which will be useful in elucidating the nature of the exotic low-temperature phases in these materials.

Figure 1

Crystal structure and electronic band structure of ${\mathrm{CeB}}_6$. (a) Crystal structure of ${\mathrm{CeB}}_6$. Ce ions and ${\mathrm{B}}_6$ octahedra are located at the corners and the center of the cubic lattice structure. (b) The bulk Brillouin zone of ${\mathrm{CeB}}_6$. High-symmetry points are marked. (c) Band structure measured with ARPES along the $M-X-M$ momentum-space cut direction (left) and the corresponding integrated energy distribution curve (right). Dispersive Ce $5d$ band and nondispersive flat Ce $4f^1$ as well as a broad Ce $4f^0$ peak are observed. This spectrum is measured with a photon energy of 74 eV at a temperature of 17 K at the ALS beamline 4.0.3.

Figure 2

Distribution of hot spots in the electronic structure of ${\mathrm{CeB}}_6$. (a) ARPES measured Fermi surface of ${\mathrm{CeB}}_6$. Oval-shaped pockets are observed at the $X$ points. Horizontal blue dashed lines and numbers correspond to the dispersion maps presented in Fig. 3. (b) Band dispersion measured with ARPES along high-symmetry directions, which are marked on the plots. (c) ARPES measured constant energy contours. These data were collected at ALS BL 4.0.3 with a photon energy of 76 eV at a temperature of 17 K.

Figure 3

Evolution of hot spots in the electronic structure. (a) ARPES dispersion maps along cut 1, cut 2, and cut 3 as marked in Fig. 2. The vertical and horizontal parallel dashed lines represent the area of integration for momentum distribution curves (MDCs) and energy distribution curves (EDCs), respectively. The blue dashed rectangle denotes the area for stack EDCs. (b) MDCs along the cut directions marked in (a) by horizontal blue dashed parallel lines. (c) EDCs along the cut directions marked in (a) by vertical blue dashed parallel lines. The arrow in the vicinity of the Fermi level shows the shift in the spectral weight. (d) EDCs in the area marked by a blue dashed rectangle in (a) for cut 1.

Figure 4

Photon energy-dependent dispersion maps and first-principles electronic structure calculation of ${\mathrm{CeB}}_6$. (a) The photon energies used in experiments are noted on the plots. The $4f$ flat bands and dispersive $5d$ bands are observed in the vicinity of the Fermi level. These spectra are measured along the $M-X-M$ momentum space cut direction at a temperature of 17 K at the ALS beamline 4.0.3. (b) ARPES dispersion map of ${\mathrm{BaB}}_6$ along the high-symmetry direction, which is noted on the plot. The spectrum was measured at ALS beamline 10.0.1. (c) Theoretical bulk band structure along the high-symmetry direction $M-X-M$, the maximum weight of $f$ bands are above the Fermi level, in contrast to the experimental data. (d) Calculated bulk bands along the $X-\mathrm{\Gamma }-X$ high-symmetry direction.