Dielectric response of electron-doped ionic superconductor LixZrNCl

When electron doped, the layered transition metal nitrides TNCl (T=group IVB transition metal ion) become impressive superconductors with critical temperature Tc=15-26 K. Here we take the most studied member ZrNCl as a representative and calculate the dielectric response ε(ω) versus frequency and concentration of doped electronic carriers. The static dielectric constant ε=5 is reproduced extremely well. We establish that the differences between rigid band modeling and virtual crystal treatment are small, and compare also with actual lithium doping using supercells. We obtain the variations upon changing the doping level of the reflectivity and energy loss function as well, many of which are found not to be correlated with the observed (non)variation of Tc(x). The main plasmon peaks appear where the electron gas model suggests, in the range 1.2-2.0 eV for x varying from 0.16 to 0.50.