Angular dependence of the Josephson critical current in c -axis twist junctions of high-temperature superconductors

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 φ₀ about the c axis. This work was motivated by recent high-quality c-axis twist Josephson junctions prepared with Bi₂Sr₂CaCu₂O_8+δ by Li et al. Our interest lies in studying whether the Josephson critical voltage IcRₙ measured along the c axis in high-temperature superconductors as a function of φ₀ 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_x²-y²-wave order parameters, a dominant d_x²-y² and subdominant dxy mixed order parameter, and a dominant d_x²-y² 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.