Generalized Rashba Electron-Phonon Coupling and Superconductivity in Strontium Titanate

Abstract

SrTiO3 is known for its proximity to a ferroelectric phase and for showing an "optimal" doping for superconductivity with a characteristic dome-like behaviour resembling systems close to a quantum critical point. Several mechanisms have been proposed to link these phenomena, but the abundance of undetermined parameters prevents a definite assessment. Here, we use ab initio computations supplemented with a microscopic model to study the linear coupling between conduction electrons and the ferroelectric soft transverse modes allowed in the presence of spin-orbit coupling. We find a robust Rashba-like coupling, which can become surprisingly strong for particular forms of the polar eigenvector. We characterize this sensitivity for general eigenvectors and, for the particular form deduced by hyper-Raman scattering experiments, we find a BCS pairing coupling constant of the right order of magnitude to support superconductivity. The ab initio computations enable us to go beyond the linear-in-momentum conventional Rashba-like interaction and naturally explain the dome behaviour including a characteristic asymmetry. The dome is attributed to a momentum dependent quenching of the angular momentum due to a competition between spin-orbit and hopping energies. The optimum density for having maximum Tc results in rather good agreement with experiments without free parameters. These results make the generalized Rashba dynamic coupling to the ferroelectric soft mode a compelling pairing mechanism to understand bulk superconductivity in doped SrTiO3.

Anisotropic Rashba coupling to polar modes in KTaO3

“…In fact, like the related material STO, the dielectric constant of KTO grows to extremely large values at low T [9], staying on the verge of a FE transition, with a concomitant softening of a TO mode [10]. In STO, the Rashba pairing mechanism has been found to have a BCS coupling constant of the right order of magnitude to support bulk superconductivity, and develop a dome of T c vs carrier density with remarkable experimental agreement [11].…”

“…In this work, we will explore distortions of the cubic structure with polar axis û along the [001] direction for the Si modes. While the soft TO mode in bulk KTO is in general a linear combination of all three Si modes ( 9)- (11), according to neutron scattering and hyper-Raman experiments the S1 mode has the dominant contribution [10,15]. Moreover, since we are interested in the coupling of the electronic bands to the polar modes to linear order, we consider only displacements small enough to stay in the linear regime near the Γ point (for details see appendix B).…”

“…Following [8,11] we will now use the electronic band split computed from frozen-phonon ab initio to extract the Rashba-like couplings τ n of the three electronic bands of KTO (figure 1(b)). For a mode with the polar axis along np ∥ [001] the electronic split in equation ( 14) allowed by symmetry becomes:…”

“…We now illustrate how the anisotropy of the Rashba split in the lower j = 3/2 multiplet naturally emerges when considering microscopic processes induced by a polar displacement [8,11,[22][23][24][25][26] and applying degenerate perturbation theory for the hopping term equation (2).…”

“…Motivated by these promising results and encouraging implications for the Rashba pairing mechanism, in this work we present a careful study of the linear coupling between polar modes and the three SOC bands of KTO, going beyond the approximate estimates given in [5]. Following the approach we developed in [8,11] we perform relevant frozen-phonon ab initio computations in bulk KTO and extract the odd-in-momentum Rashba-like couplings from the reconstructed electronic band structure. We find that besides substantial Rashba couplings to relevant polar modes, a minimal phenomenological form of the interaction goes beyond the isotropic Rashba model for the two lowest electronic bands of the j = 3/2 manifold, and quantify the anisotropy of the coupling.…”