Capillary waves on ferroelastic domain walls as a pairing mechanism in strontium titanate

While it has long been known that strontium titanate is a superconductor, with a transition temperature of ~300 mK, the pairing mechanism that leads to superconductivity remains a mystery. We gather insight from recent experiments on superconductivity in the two-dimensional gas formed in lanthanum aluminate/strontium titanate heterostructures. These experiments provide evidence that superconductivity is localized to the edge of the electron gas, which is also associated with a ferroelastic domain wall between an out-of-plane deformation associated with the high electron density region and an in-plane deformation associated with the electron poor region. While the energy scales associated with bulk ferroelastic domains are quite large, on the order of 100 K, we show that capillary waves on domain walls can have much lower energy scales. Further, we argue that these capillary waves are strongly coupled to charge, making them a compelling candidate for an intermediate boson that mediates pairing interaction. We put these notions together in a model of ferroelastic domain walls that supports electron pairing.