Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further requirements arise fr
om the symmetric handling of particles and holes (excitations above and below the Fermi level). Naive replacements of the exponential function or cut and paste solutions fail to satisfy this symmetry and to be smooth at the Fermi level at the same time. We solve this problem by a general ansatz dividing the deformed exponential to odd and even terms and demonstrate that how earlier suggestions, like the kappa- and q-exponential behave in this respect.
Angle resolved photoelectron spectroscopic measurements have been performed on an insulating cuprate Ca_2CuO_2Cl_2. High resolution data taken along the Gamma to (pi,pi) cut show an additional dispersive feature that merges with the known dispersion
of the lowest binding energy feature, which follows the usual strongly renormalized dispersion of ~0.35 eV. This higher energy part reveals a dispersion that is very close to the unrenormalized band predicted by band theory. A transfer of spectral weight from the low energy feature to the high energy feature is observed as the Gamma point is approached. By comparing with theoretical calculations the high energy feature observed here demonstrates that the incoherent portion of the spectral function has significant structure in momentum space due to the presence of various energy scales.
The low-energy excitations of the lightly doped cuprates were studied by angle-resolved photoemission spectroscopy. A finite gap was measured over the entire Brillouin zone, including along the d_{x^2 - y^2} nodal line. This effect was observed to be
generic to the normal states of numerous cuprates, including hole-doped La_{2-x}Sr_{x}CuO_{4} and Ca_{2-x}Na_{x}CuO_{2}Cl_{2} and electron-doped Nd_{2-x}Ce_{x}CuO_{4}. In all compounds, the gap appears to close with increasing carrier doping. We consider various scenarios to explain our results, including the possible effects of chemical disorder, electronic inhomogeneity, and a competing phase.
