Superconductivity from the Slater mode: Application to KTaO3 heterostructures

TL;DR

This paper investigates superconductivity in the 2DEG at KTaO3 interfaces via pairing mediated by the soft TO1 Slater mode. Using ab initio‑based parameters in a bilayer tight‑binding framework with dynamic Rashba couplings, the authors solve the linearized gap equation and reproduce the orientation dependence of $T_c$ and an anisotropic gap structure, but find that the resulting $\lambda$ falls short of the value needed to explain the observed $T_c$; they identify forward scattering enhanced by the TO1 dispersion as a key feature of the pairing kernel and argue that additional phonon channels are required. The results provide a coherent microscopic picture linking orbital degeneracy, spin–orbit coupling, and interface physics to superconductivity in KTaO3 heterostructures and propose measurable signatures in the gap's angular and band‑index dependence. The work lays groundwork for more complete strong‑coupling treatments and Poisson–Schrödinger‑level modeling of realistic oxide interfaces.

Abstract

Superconductivity has been observed for the 2D electron gas (2DEG) at the interface of KTaO3 with other oxides, with a transition temperature about an order of magnitude higher than its 3d cousin SrTiO3. The superconducting transition temperature is strongly dependent on the orientation of the interface. Motivated by this observation, we study pairing due to exchange of the soft transverse optic phonon mode characteristic of quantum paraelectrics and use the resulting theory to comment on the nature of superconductivity of this 2DEG. We find (1) an orientation dependence consistent with experiment along with an anisotropic gap function, but (2) a BCS coupling constant that is smaller than needed and so must be augmented by contributions from other phonons to be consistent with the observed values of Tc.

Figures (11)

• Figure 1: Fermi surface for the bilayer 111 tight binding model (TB model 1) with $\mu$ set to give $n_{2D}=10^{14}cm^{-2}$. (a) the static Rashba case ($t_0=2$ meV) and (b) the dynamic Rashba case ($t_0=48.8/\sqrt{3}$ meV). $k$ is in units of $\pi/c$ where $c=\sqrt{2/3}a$ with $a$ the bulk lattice constant. $k_x$ ($\Gamma-K$) is along the (1,-1,0) direction and $k_y$ ($\Gamma-M$) along the (-1,-1,2) direction. Note the profound impact of the dynamic Rashba coupling on the Fermi surface.
• Figure 2: Plots of Eq. \ref{['vr']} using the Fermi surface from Fig. 1a versus $\phi'-\phi$ (where $\phi$ is the Fermi surface angle for $k$ and $\phi'$ for $k'$) for various $\phi$. $\phi'-\phi=0$ corresponds to forward scattering ($k'=k$). Plots are for one of the outer Fermi surfaces (band 1) and one of the inner Fermi surfaces (band 3). The top plots do not include the term in brackets in Eq. \ref{['vr']} (the phonon dispersion), the bottom plots do. Note the tendency for the interaction to peak near forward scattering and to be completely suppressed for back scattering. This tendency is even more pronounced when the phonon dispersion is included.
• Figure 3: Phonon dispersion $\omega(q=k'-k)$ as a function of $\phi'-\phi$ for the outer Fermi surface (band 1) from Fig. 1a for two different values of $\phi$ assuming $\omega(0)$=5.6 meV. $\phi'-\phi=0$ corresponds to $q=0$ and 180 corresponds to $q=2k_F$. The larger value for $\omega(q)$ at $\phi'-\phi=180$ for $\phi=30$ is due to being at the tip of the star in Fig. 1a.
• Figure 4: Plots of Eq. \ref{['gto']} versus $\phi$ (the Fermi surface angle for $k$) using the Fermi surface from Fig. 1a for various $n,n'$. (a) are the intraband terms ($n=n'$) and (b) and (c) the interband terms. The largest interband terms connect bands with the same helicity ($nn'=13, 31, 24, 42$).
• Figure 5: The superconducting order parameter $\Delta_{nk}$ versus $\phi$ (the Fermi surface angle for $k$) using the Fermi surface from Fig. 1a for the different bands. (a) includes the phonon dispersion, (b) does not, i.e., $\omega(q)=\omega(0)$. The plot headers list the value of the BCS coupling constant, $\lambda$.