Fermi surface evolution of Na-doped PbTe studied through density   functional theory calculations and Shubnikov-de Haas measurements
  We present a combined experimental and theoretical study of the evolution of the low-temperature Fermi surface of lead telluride, PbTe, when holes are introduced through sodium substitution on the lead site. Our Shubnikov-de-Haas measurements for samples with carrier concentrations up to $9.4\times10^{19}$cm$^{-3}$ (0.62 Na atomic $\%$) show the qualitative features of the Fermi surface evolution (topology and effective mass) predicted by our density functional (DFT) calculations within the generalized gradient approximation (GGA): we obtain perfect ellipsoidal L-pockets at low and intermediate carrier concentrations, evolution away from ideal ellipsoidicity for the highest doping studied, and cyclotron effective masses increasing monotonically with doping level, implying deviations from perfect parabolicity throughout the whole band. Our measurements show, however, that standard DFT calculations underestimate the energy difference between the L-point and $\Sigma$-line valence band maxima, since our data are consistent with occupation of a single Fermi surface pocket over the entire doping range studied, whereas the calculations predict an occupation of the $\Sigma$-pockets at higher doping. Our results for low and intermediate compositions are consistent with a non-parabolic Kane-model dispersion, in which the L-pockets are ellipsoids of fixed anisotropy throughout the band, but the effective masses depend strongly on Fermi energy. 
P. Giraldo-Gallo, B. Sangiorgio, P. Walmsley, M. Fechner, S.C. Riggs,   T. H. Geballe, N. A. Spaldin, and I. R. Fisher
cond-mat.mtrl-sci