Dielectric Response of Electron-doped Ionic Superconductor Li$_x$ZrNCl

摘要

When electron doped, the layered transition metal nitrides ${\cal T}$NCl(${\cal T}$ = group IVB transition metal ion) become impressive superconductorswith critical temperature T$_c$= 15-26K. Here we take the most studied member,ZrNCl, as a representative and calculate the dielectric response$\epsilon(\omega)$ versus frequency and concentration of doped electroniccarriers. The static dielectric constant $\epsilon_{\infty}$=5 is reproducedextremely well. We establish that the differences between rigid band modelingand virtual crystal treatment are small, and compare also with actual lithiumdoping using supercells. We obtain the variations upon changing the dopinglevel of the reflectivity and energy loss function as well, many of which arefound not to be correlated with the observed (non)variation of T$_c(x)$. Themain plasmon peaks appear where the electron gas model suggests, in the range1.2-2.0 eV for $x$ varying from 0.16 to 0.50.