Modulation of the superconducting critical temperature due to quantum confinement at the LaAlO${}_3$/SrTiO${}_3$ interface

Abstract

Superconductivity develops in bulk doped SrTiO${}_3$ and at the LaAlO${}_3$/SrTiO${}_3$ interface with a dome-shaped density dependence of the critical temperature $T_c$, despite different dimensionalities and geometries. We propose that the $T_c$ dome of LaAlO${}_3$/SrTiO${}_3$ is a shape resonance due to quantum confinement of superconducting bulk SrTiO${}_3$. We substantiate this interpretation by comparing the exact solutions of a three-dimensional and quasi-two-dimensional two-band BCS gap equation. This comparison highlights the role of heavy bands for $T_c$ in both geometries. For bulk SrTiO${}_3$, we extract the density dependence of the pairing interaction from the fit to experimental data. We apply quantum confinement in a square potential well of finite depth and calculate $T_c$ in the confined configuration. We compare the calculated $T_c$ to transport experiments and provide an explanation as to why the optimal $T_c$'s are so close to each other in two-dimensional interfaces and the three-dimensional bulk material.

6 pages, 5 figures

References in corpus (7)

• Electric Field Control of the LaAlO${}_3$/SrTiO${}_3$ Interface Ground State
• Electron-phonon interaction and charge carrier mass enhancement in SrTiO3
• Topological superconductivity and unconventional pairing in oxide interfaces
• Intrinsic instability of electronic interfaces with strong Rashba coupling
• Large modulation of the Shubnikov-de Haas oscillations by the Rashba interaction at the LaAlO${}_3$/SrTiO${}_3$ interface
• Rise and fall of shape resonances in thin films of BCS superconductors
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• Theory of superconductivity in doped quantum paraelectrics
• Implicit renormalization approach to the problem of Cooper instability
• Ionic gating in metallic superconductors: A brief review
• Anomalous screening of an electrostatic field at the surface of niobium nitride
• Interplay between singlet and triplet pairings in multi-band two-dimensional oxide superconductors
• Probing Quantum Confinement and Electronic Structure at Polar Oxide Interfaces
• Orientation-dependent electric transport and band filling in hole co-doped epitaxial diamond films
• Upper critical magnetic field and multiband superconductivity in artificial high-Tc superlattices of nano quantum wells
• Superconducting dome in doped 2D superconductors with broken inversion symmetry
• Periodicity of superconducting shape resonances in thin films
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Quantized conductance in a one-dimensional ballistic oxide nanodevice
• Origin of the dome-shaped superconducting phase diagram in ${\mathrm{SrTiO}}_3$-based interfaces