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Register a new userJosephson effects in twisted nodal superconductors
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Added by
Pavel Volkov Andreevich
Publication date
2021
fields
Physics
and research's language is
English
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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 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 $I_csim cos(2theta_0)$ with $cos(6theta_0)$ corrections. Furthermore, strong disorder at the interface is demonstrated to suppress the time-reversal breaking superconducting phase near $theta_0=45^circ$. Last, we provide a comprehensive theoretical analysis of experiments that can reveal the full current-phase 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.
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Twisted bilayers of high-$T_c$ cuprate superconductors have been argued to form topological phases with spontaneously broken time reversal symmetry ${cal T}$ 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 ${cal T}$-broken phase near $45^circ$ twist is marked by a crossover from the conventional $2pi$-periodic Josephson relation $J(varphi)simeq J_csin{varphi}$ to a $pi$-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 $theta$ and temperature $T$ implying that a measurement of $J_c$ alone will not be a litmus test for the ${cal T}$-broken phase. To obtain clear signatures of the ${cal T}$-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$_{8+delta}$.
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