Josephson effects in twisted cuprate bilayers

Tarun Tummuru; Stephan Plugge; Marcel Franz

doi:10.1103/PhysRevB.105.064501

paper

Josephson effects in twisted cuprate bilayers

arXiv:2108.13457 · doi:10.1103/PhysRevB.105.064501

Abstract

Twisted bilayers of high- $T_{c}$ cuprate superconductors have been argued to form topological phases with spontaneously broken time reversal symmetry $T$ for certain twist angles. With the goal of helping to identify unambiguous signatures of these topological phases in transport experiments, we theoretically investigate a suite of Josephson phenomena between twisted layers. We find an unusual non-monotonic temperature dependence of the critical current at intermediate twist angles which we attribute to the unconventional sign structure of the $d$ -wave order parameter. The onset of the $T$ -broken phase near $4 5^{\circ}$ twist is marked by a crossover from the conventional $2 π$ -periodic Josephson relation $J (φ) ≃ J_{c} sin φ$ to a $π$ -periodic function as the single-pair tunneling becomes dominated by a second order process that involves two Cooper pairs. Despite this fundamental change, the critical current remains a smooth function of the twist angle $θ$ and temperature $T$ implying that a measurement of $J_{c}$ alone will not be a litmus test for the $T$ -broken phase. To obtain clear signatures of the $T$ -broken phase one must measure $J_{c}$ in the presence of an applied magnetic field or radio-frequency drive, where the resulting Fraunhofer patterns and Shapiro steps are altered in a characteristic manner. We discuss these results in light of recent experiments on twisted bilayers of the high- $T_{c}$ cuprate superconductor Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8 + δ}$ .

arXiv comment14 pages, 9 figures (including appendices)

Josephson effects in twisted cuprate bilayers

Abstract

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