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 θ0 in the range 0 • < θ0 < 45 • 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 θ0 = 45 • we find that the critical current does not vanish due to Cooper pair cotunneling, which leads to a transition to a time-reversal 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 Ic ∼ cos(2θ0) with cos(6θ0) corrections. Furthermore, strong disorder at the interface is demonstrated to suppress the time-reversal breaking superconducting phase near θ0 = 45 • . Last, we provide a comprehensive theoretical analysis of experiments that can reveal the full current-phase relation for twisted superconductors close to θ0 = 45 • . In particular, we demonstrate the emergence of the Fraunhofer interference pattern near θ0 = 45 • , while accounting for realistic sample geometries, and show that its temperature dependence can yield unambiguous evidence of Cooper pair cotunneling, necessary for topological superconductivity.

Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

“…In addition, more recently single layer cuprates exhibiting critical temperatures close to their bulk values have been fabricated [96], opening an avenue for realizing twisted cuprate moiré systems with square lattices for which our model may be directly applicable. Such twisted heterostructures have recently been studied theoretically [97][98][99][100][101], with few-layer twisted interfaces already realized in experiment [102,103]. It remains to be seen whether Hofstadter physics can be realized in twisted cuprates, but, if it is, a reentrant HSC phase may be possible in this system.…”

Twisted multilayer nodal superconductors

“…Their physics is therefore similar to that of a twisted bilayer [21,35,36]. Nevertheless, in view of the estimates for the tunneling strength g ∼ 5 − 10meV inferred from recent transport studies [24,29,30], such a renormalization might help stabilize T -broken superconductivity. In contrast, the problem posed by CT multilayers cannot be simplified in this way.…”

“…Transport measurements find that close to 45 • twist angle, the interlayer Josephson current is dominated by its second harmonic, which signals co-tunneling of Cooper pairs [24]. While indicative of a non-trivial phase difference between the two superconducting layers, and hence T breaking, this does not directly reveal the topological nature of the state [29,30]. Along similar lines, Ref.…”

Doping a moiré Mott Insulator: A t-J model study of twisted cuprates

“…Note added-During the finalization of the manuscript, we are aware of two preprints [36,37] which also study the twisted cuprate bilayer and discusses the critical Josephson current.…”