Large Fermi surface expansion through anisotropic mixing of conduction and $f$ electrons in the semimetallic Kondo lattice CeBi

Using angle-resolved photoemission spectroscopy (ARPES) and resonant ARPES, we report evidence of strong anisotropic conduction-$f$ electron mixing ($c\text{−}f$ mixing) in CeBi by observing a largely expanded Ce $5d$ pocket at low temperature, with no change in the Bi $6p$ bands. The anisotropic Fermi surface (FS) expansion is accompanied by a pronounced spectral weight transfer from the local $4f^0$ peak of Ce (corresponding to $\mathrm{C}{\mathrm{e}}^{3+}$) to the itinerant conduction bands near the Fermi level. Careful analysis suggests that the observed large FS change (with a volume expansion of the electron pocket up to 40%) can most naturally be explained by a small valence change $\left(\sim 1\%\right)$ of Ce, which coexists with a very weak Kondo screening. Our work therefore provides evidence for a FS change driven by real charge fluctuations deep in the Kondo limit, which is highly dependent on the orbital character and momentum and is made possible by the low carrier density.

Figure 1

Temperature-dependent FS of CeBi. (a) 3D and projected 2D BZs of CeBi (top), and the calculated 3D FS excluding Ce $4f$ electrons (bottom). (b,c) Experimental FS at 10 and $\sim 37\mathrm{K}$ (left and middle panels), in comparison with the DFT calculations (right panels, denoted by calc), for both the hole pocket near the $\overline{\mathrm{\Gamma }}$ point (b) and the electron pocket near the $\overline{M}$ point (c). The DFT calculations contain spectral contributions from all $k_z\text{'}s$ in the 3D BZ, as well as a small energy broadening (0.001 eV). (d,e) MDC cuts for the hole (d) and electron (e) pockets. The cut directions are indicated in (b,c). The rightmost panel in (e) shows the extracted contour of the electron pocket at low and high temperatures.

Figure 2

Temperature evolution of the hole and electron pocket for CeBi, in comparison with GdBi. (a,b) Temperature dependence of the energy-momentum cut for the electron (a) and hole (b) pocket. The data in (a) show the evolution during a warming and cooling cycle from the same sample. The rightmost panel in (b) shows the MDC cuts at $E_{\mathrm{F}}$; no change in $k_{\mathrm{F}}$ can be observed. (c) Temperature evolution of $k_{\mathrm{F}}$ for the electron pocket [indicated by a red arrow in (a)]. The top panel displays the raw data from a representative sample (#3), showing the onset of pocket expansion at $\sim 35\mathrm{K}$. The bottom panel summarizes the normalized Fermi vector $k_{\mathrm{norm}}=k_{\mathrm{F}}\left(T\right)/k_{\mathrm{F}}\left(T>35\mathrm{K}\right)$, for different samples. (d) Temperature evolution of the electron pocket for GdBi, showing no discernible change. (e) Resistivity vs temperature for CeBi and GdBi. The inset is the incremental part of the resistivity of CeBi, ${\rho }_{\mathrm{i}}={\rho }_{\mathrm{CeBi}}\text{–}{\rho }_{\mathrm{LaBi}}$, plotted as a function of $logT$.

Figure 3

Resonant ARPES results and temperature evolution. (a) Resonant ARPES results at Ce $N$ edge (122 eV) at two representative temperatures. The EDC cuts at the hole and electron pockets are shown on the right panels, respectively. (b) Left: X-ray absorption spectroscopy (XAS) data near Ce $M$ edge at 10 K. Right: Soft x-ray ARPES spectra taken at two representative photon energies (880.6 and 899.4 eV) at 10 K, indicated by black arrows in the XAS data. (c) Temperature dependence of EDCs at three representative photon energies (and momenta), indicated as white vertical lines in (b).

Figure 4

(a) Zoomed-in view of the ARPES spectra at the $\overline{\mathrm{\Gamma }}$ point near $E_F$ taken at two representative temperatures (the color bar is shown at the top). (b,c) Corresponding integrated EDC (b) and MDC at $E_F$ (c).