Interface superconductivity in ${\mathrm{LaAlO}}_3-{\mathrm{SrTiO}}_3$ heterostructures

The interface superconductivity in ${\mathrm{LaAlO}}_3-{\mathrm{SrTiO}}_3$ heterostructures reveals a nonmonotonic behavior of the critical temperature as a function of the two-dimensional density of charge carriers. We develop a theoretical description of interface superconductivity in strongly polar heterostructures, based on the dielectric function formalism. The density dependence of the critical temperature is calculated, accounting for all phonon branches including different types of optical (interface and half-space) and acoustic phonons. The longitudinal-optic- and acoustic-phonon mediated electron-electron interaction is shown to be the dominating mechanism governing the superconducting phase transition in the heterostructure.

Figure 1

Kernel function $K(\omega ,{\omega }^{\prime })$ for the ${\mathrm{LaAlO}}_3-{\mathrm{SrTiO}}_3$ structure using the set of parameters described in the text.

Figure 2

(a) Critical temperature for the ${\mathrm{LaAlO}}_3-{\mathrm{SrTiO}}_3$ heterostructure as a function of the 2D electron density, compared to the experimental data extracted from Refs. [2, 3, 4]. (b) The calculated critical temperatures divided by the Fermi energy ${\epsilon }_F$, plotted as a function of $n^{1/2}$.