Electron-doped strontium titanate SrTiO3 is one of the most dilute superconductors studied extensively for more than half a century [1]. The superconductivity is observed for extremely low carrier concentrations n = 1018~1021/cm3 corresponding to about 10-4~10-1 electrons per Ti atom. The superconducting transition temperature Tc shows a characteristic dome shape as a function of n with a peak of Tc=0.45K at n~1020/cm3 [2]. In the non-doped case, SrTiO3 shows a huge dielectric constant of about 2×104 at low temperatures and is considered to be close to a ferroelectric transition [3]. In fact, the ferroelectric transition is induced by replacing 16O with 18O [4] and by replacing Sr with Ca [5]. Furthermore, Tc is found to be enhanced towards the quantum critical point (QCP) of the ferroelectric transition [5]. Theoretically, Edge et al. has proposed a model of superconductivity due to quantum ferroelectric fluctuations by taking into account of doping dependence of the ferroelectric soft-mode optical phonons based on the first-principles calculations [6]. Explicit estimates of Tc based on the first-principles calculations, however, were not done there as unphysical imaginary phonon frequencies due to ferroelectric instabilities are obtained at low doping n<1020/cm3.
In this study, we explicitly estimate Tc of electron-doped SrTiO3 on the basis of the first-principles calculations (Quantum ESPRESSO) in the over-doped regime with n=1020~1021/cm3, where the imaginary frequencies were not obtained. When n decreases from 1021/cm3 to 1020/cm3, the frequencies of the ferroelectric optical phonons near the Γ-point monotonically decreases while the electron–phonon coupling constant λ monotonically increases, and then estimated Tc monotonically increase as consistent with experiments in the over-doped regime.
[1] M. N. Gastiasoro, J. Ruhman, R. M. Fernandes, Ann. Phys. 417, 168107 (2020)
[2] J. F. Schooley et al., Phys. Rev. Lett. 14, 305 (1965)
[3] E. Sawaguchi, A. Kikchi, Y. Kodera, J. Phys. Soc. Jpn. 17, 1666 (1962)
[4] M. Itoh et al., Phys. Rev. Lett. 82, 3540 (1999)
[5] C. W. Rischau et al., Nat. Phys. 13, 643 (2017)
[6] J. M. Edge et al., Phys. Rev. Lett. 115, 247002 (2015)
This work was partially supported by JSPS KAKENHI Grant Number 21K03399 and the Niigata University Fellowship System. Numerical calculations were performed in part using the facilities of the Center for Computational Sciences, University of Tsukuba and Center for Computational Materials Science, Institute for Materials Research, Tohoku University.
Keywords: SrTiO3, Superconductivity, First-principles calculation, Density functional theory