Josephson effects in twisted nodal superconductors
Abstract
Motivated by the recent proposals for unconventional emergent physics in twisted bilayers of nodal superconductors, we study the peculiarities of the Josephson effect at the twisted interface between $d$wave superconductors. We demonstrate that for clean interfaces with a twist angle $\theta_0$ in the range $0^\circ<\theta_0<45^\circ$ the critical current can exhibit nonmonotonic temperature dependence with a maximum at a nonzero temperature as well as a complex dependence on the twist angle at low temperatures. The former is shown to arise quite generically due to the contributions of the momenta around the gap nodes, which are negative for nonzero twist angles. It is demonstrated that these features reflect the geometry of the Fermi surface and are sensitive to the form of the momentum dependence of the tunneling at the twisted interface. Close to $\theta_0=45^\circ$ we find that the critical current does not vanish due to Cooper pair cotunneling, which leads to a transition to a timereversal breaking topological superconducting $d+id$ phase. Weak interface roughness, quasiperiodicity, and inhomogeneity broaden the momentum dependence of the interlayer tunneling leading to a critical current $I_c\sim \cos(2\theta_0)$ with $\cos(6\theta_0)$ corrections. Furthermore, strong disorder at the interface is demonstrated to suppress the timereversal breaking superconducting phase near $\theta_0=45^\circ$. Last, we provide a comprehensive theoretical analysis of experiments that can reveal the full currentphase relation for twisted superconductors close to $\theta_0=45^\circ$. In particular, we demonstrate the emergence of the Fraunhofer interference pattern near $\theta_0=45^\circ$, while accounting for realistic sample geometries, and show that its temperature dependence can yield unambiguous evidence of Cooper pair cotunneling, necessary for topological superconductivity.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.13456
 Bibcode:
 2021arXiv210813456V
 Keywords:

 Condensed Matter  Superconductivity;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons