Fig. 2
From: Lifshitz transition from valence fluctuations in YbAl3
Correspondence between r-space and k-space electronic structure in YbAl3. a Evolution of the low-energy electronic structure with temperature. E vs. k dispersions are divided by the corresponding resolution-broadened Fermi-Dirac distribution to emphasize thermally occupied states above E F. White lines are guides to the eye showing evolution of the electron-like pocket centered at (0, 0, 0). b XPS spectra showing the temperature-dependent intensity variation of the 4f 13 and 4f 12 final states in YbAl3, after Shirley background subtraction37 and normalized by the 4f 12 final state intensity. c Temperature dependence of the change in Luttinger volume, estimated from the size of the electron pocket at (0, 0, 0) and of the change in Yb valence, measured by core-level spectroscopy, revealing a precise one-to-one correspondence. Error bars reflect uncertainty in the Luttinger volume estimation due to a statistical error of one standard deviation in the extracted k F values from the fits to the Momentum distribution curves (MDCs) taken at E F. d Schematic illustrating the temperature-dependent relationship between r-space and k-space electronic structure in YbAl3
