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Inhomogeneous superconductivity in (001), (110) and (111) KTaO$_3$ two-dimensional electronic gas: $T_c$ driven from electronic confinement

Matta Trama, Roberta Citro, Carmine Antonio Perroni

Abstract

We investigate superconductivity in KTaO$_3$ (KTO)-based two-dimensional electron gases for the (001), (110), and (111) crystallographic orientations within a unified microscopic framework. Using a self-consistent tight-binding slab model, we determine the confinement potential, electronic structure, and orbital composition for each orientation, explicitly including inversion-symmetry-induced orbital Rashba couplings. Using a local spin-singlet s-wave pairing interaction, we find that the pronounced orientation dependence of the superconducting critical temperature primarily originates from differences in the spatial extent of the two-dimensional electron gas and the associated redistribution of the density of states at the Fermi level, rather than from changes in the pairing interaction. Our results provide a microscopic explanation for the experimentally observed orientation dependence of superconductivity at KTO-based interfaces.

Inhomogeneous superconductivity in (001), (110) and (111) KTaO$_3$ two-dimensional electronic gas: $T_c$ driven from electronic confinement

Abstract

We investigate superconductivity in KTaO (KTO)-based two-dimensional electron gases for the (001), (110), and (111) crystallographic orientations within a unified microscopic framework. Using a self-consistent tight-binding slab model, we determine the confinement potential, electronic structure, and orbital composition for each orientation, explicitly including inversion-symmetry-induced orbital Rashba couplings. Using a local spin-singlet s-wave pairing interaction, we find that the pronounced orientation dependence of the superconducting critical temperature primarily originates from differences in the spatial extent of the two-dimensional electron gas and the associated redistribution of the density of states at the Fermi level, rather than from changes in the pairing interaction. Our results provide a microscopic explanation for the experimentally observed orientation dependence of superconductivity at KTO-based interfaces.
Paper Structure (26 sections, 80 equations, 11 figures)

This paper contains 26 sections, 80 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Electrostatic potential and electronic band structure
  3. Superconducting instability and critical temperature
  4. Phonon-mediated pairing mechanism
  5. Instantaneous pairing mechanism
  6. Conclusions and discussion
  7. Orbital Rashba terms for different orientations
  8. (001) direction
  9. Nearest neighbors.
  10. Next-to-nearest neighbors.
  11. Slab decomposition.
  12. (110) direction
  13. Nearest neighbors.
  14. Next-to-nearest neighbors.
  15. Rotation to the (110) slab coordinates.
  16. ...and 11 more sections

Figures (11)

  • Figure 1: (a) Cubic structure of KTO; $t_D$ and $t_I$ denote the tight-binding hopping amplitudes. (b–d) Top view of crystalline KTO along the (001) (b), (110) (c), and (111) (d) directions. The cubic lattice constant is $a_0=3.988$ Å.
  • Figure 2: (a-c) Potential barrier $\varphi$ as a function of the layer position using different benchmark values of the positive charge density $n_{2D}$ for the (001) (a), (110) (b) and (111) (c) directions. (d-f) Interfacial electric field $F_0$ as a function of $n_{2D}$ for (001) (d), (110) (e) and (111) (f) directions.
  • Figure 3: Electron 2D density $n_z$ for different benchmark values of $n_{2D}$ at the (001) (a), (110) (b) and (111) (c) interfaces. The insets show the details close to the interfaces.
  • Figure 4: Band structure of the KTO-based heterostructure along the (a,d,g) (001), (b,e,h) (110), and (c,f,i) (111) directions for positive charge densities (a–c) $n_{2D}=0.8\times10^{14},\mathrm{cm}^{-2}$, (d–f) $n_{2D}=1.0\times10^{14},\mathrm{cm}^{-2}$, and (g–i) $n_{2D}=1.6\times10^{14},\mathrm{cm}^{-2}$. The quasi-momentum $k_i$ is expressed in units of the corresponding in-plane lattice constant. The energy zero ($E=0$) is set to the self-consistent Fermi level obtained from the electrostatic screening simulations at each $n_{2D}$.
  • Figure 5: (a-c) Local layered-resolved density of states at the self-consistent value of the chemical potential for (001) (a), (110) (b) and (111) (c) directions.
  • ...and 6 more figures