Angular dependence of the Josephson critical current in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math>-axis twist junctions of high-temperature superconductors

Abstract

We have investigated theoretically the case of a highly anisotropic layered superconductor consisting of two identical parts that are twisted with respect to each other by an angle ${\ensuremath{\varphi}}_{0}$ about the $c$ axis. This work was motivated by recent high-quality $c$-axis twist Josephson junctions prepared with ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ by Li et al. Our interest lies in studying whether the Josephson critical voltage ${I}_{c}{R}_{n}$ measured along the $c$ axis in high-temperature superconductors as a function of ${\ensuremath{\varphi}}_{0}$ could give valuable information regarding the orbital symmetry of the superconducting order parameter. We assume both coherent and incoherent interlayer tunneling processes, and ordinary intralayer impurity scattering. We have derived and studied the effective Lawrence-Doniach model appropriate for the cases of pure $s$-wave and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave order parameters, a dominant ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and subdominant ${d}_{\mathrm{xy}}$ mixed order parameter, and a dominant ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ with a subdominant $s$-wave mixed order parameter. Our results suggest that Josephson tunneling across the $c$-axis twist junctions can indeed be a useful tool for probing the superconducting order-parameter symmetry. Further experiments to clarify the situation are suggested.