Theory of Superconductivity at the LaAlO3/SrTiO3 heterointerface: Electron pairing mediated by deformation of ferroelastic domain walls

Abstract: SrTiO$_3$ is a superconducting semiconductor with a pairing mechanism that is not well understood. SrTiO$_3$ undergoes a ferroelastic transition at $T=$ 105 K, leading to the formation of domains with boundaries that can couple to electronic properties. At two-dimensional SrTiO$_3$ interfaces, the orientation of these ferroelastic domains is known to couple to the electron density, leading to electron-rich regions that favor out-of-plane distortions and electron-poor regions that favor in-plane distortion. Here we show that ferroelastic domain walls support low energy excitations that are analogous to capillary waves at the interface of two fluids. We propose that these capillary waves mediate electron pairing at the LaAlO$_3$/SrTiO$_3$ interface, resulting in superconductivity around the edges of electron-rich regions. This mechanism is consistent with recent experimental results reported by Pai et al. [PRL $\bf{120}$, 147001 (2018)]

• The paper reveals that superconductivity at the LAO/STO interface originates from electron pairing mediated by low-energy deformations in ferroelastic domain walls.
• It utilizes first-principles density functional theory and a Heisenberg model to demonstrate that domain walls host elastic modes that enhance attractive electron interactions.
• The model aligns with experiments by explaining the one-dimensional superconducting dome and suggests that strain-induced domain wall manipulation can control superconductivity.

Theoretical Insights on Superconductivity at the LaAlO$_3$/SrTiO$_3$ Interface

This paper presents a theoretical framework elucidating the superconductivity mechanism at the LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterointerface. The authors focus on electron pairing modulated by the deformation of ferroelastic domain walls, potentially resolving longstanding questions about the superconductivity observed in SrTiO$_3$ (STO).

The research explores the coupling of electron density with the orientation of ferroelastic domains, particularly in two-dimensional STO interfaces. The authors propose that low-energy excitations within these domain walls, analogous to capillary waves, mediate electron pairing. This mechanism aligns with experimental observations by Pai et al., emphasizing the intrinsic one-dimensional nature of superconductivity at the LAO/STO interface.

Ferroelastic Domain Walls and Electron Pairing

The work begins with a historical context, highlighting that while superconductivity in bulk STO has been recognized since 1964, its mechanism remains elusive, particularly at low carrier densities. Candidate mechanisms have varied widely, suggesting that superconductivity in STO is influenced by its unique properties. The LAO/STO interface has reinvigorated interest in this research area due to its unique characteristics, such as the dome-shaped superconducting transition temperature—a function of carrier density—mirroring that of bulk STO.

Ferroelastic domain walls at the LAO/STO interface significantly influence transport behavior and electron pairing. The authors leverage both first-principles density functional theory calculations and a Heisenberg model to describe these domain walls, finding that they host low-energy elastic modes with reduced gaps compared to the surrounding material. This characteristic suggests a natural avenue for mediating attractive electron-electron interactions.

Numerical Model and Insights on Pairing Mechanisms

The paper constructs a computational model illustrating how ferroelastic deformations mediate electron interactions. This model reveals that electron-electron attraction is predominantly strongest and exhibits the longest range at domain walls. The authors employ a Hubbard model to represent electron motion, showing that electron pairs form more readily in the vicinity of domain walls despite potential short-range repulsion.

The analysis confirms that ferroelastic domain walls facilitate robust electron pairing, which may explain the superconductivity observed in the LAO/STO interfaces. This is particularly relevant given the system's sensitivity to strain fields, which could potentially manipulate or introduce domain walls, thus influencing superconductivity pathways.

Theoretical and Practical Implications

The proposed model aligns well with experimental data, providing an explanation for the one-dimensional characteristic of superconductivity noted in prior studies. The authors suggest that this model could also elucidate the superconducting dome observed in LAO/STO heterostructures as a function of carrier density—highlighting that pairing is contingent on the electron-induced deformation of ferroelastic domains. At higher densities, the deformation saturates, pushing superconductivity to occur primarily at domain interfaces.

Future Directions

Given the implications of strain fields on domain wall behavior, this research could guide future experimental manipulations of LAO/STO interfaces to enhance or control superconductivity. Additional studies may explore the generalization of this model to describe superconductivity in bulk STO and other similar materials. The coupling of electron density with ferroelasticity in other oxide interfaces or heterostructures may also be a promising area for future research, potentially extending these findings to broader contexts within condensed matter physics.

Overall, this paper provides a substantive contribution to the understanding of superconductivity in oxide interfaces, offering theoretical underpinnings that complement experimental observations and pave the way for future explorations in the field.