Carrier Density Dependence of Superconducting Transition Temperature in Electron-doped $\mathrm{SrTi}{\mathrm{O}}_3$ Based on the First-principles Calculations

Abstract

Electron-doped strontium titanate $\mathrm{SrTi}{\mathrm{O}}_3$, known to be one of the most dilute superconductors, is investigated on the basis of the first-principles calculations. When the carrier density n decreases, the frequencies of the ferroelectric optical phonons near the $\Gamma$-point monotonically decreases in the overdoped regime with $n<10^{20}/{\mathrm{cm}}^3$, while unphysical imaginary phonon frequencies due to ferroelectric instabilities appear in the underdoped regime with $n>10^{20}/{\mathrm{cm}}^3$. We estimate the superconducting transition temperature $T_{\mathrm{c}}$ by using the McMillan equation in the overdoped regime and find that $T_{\mathrm{c}}$ increases with decreasing n as consistent with experiments in the overdoped regime. Detailed analysis of the Eliashberg function reveals that the increases in $T_{\mathrm{c}}$ with decreasing n in the overdoped regime is mainly due to the contributions from the ferroelectric soft-mode optical phonons.

References in corpus (1)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials