Chiral p-wave superconductors have complex coherence and magnetic field penetration lengths

We show that in superconductors that break time-reversal symmetry and have anisotropy, such as p+ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa. Correspondingly, the long-range decay of the magnetic field and order parameter is in general given by the same exponent. Thus, one cannot characterize p+ip superconductors by the usual coherence and magnetic field penetration lengths. Instead, the system has normal modes that are associated with linear combinations of magnetic fields, moduli of and phases of the order-parameter components. Each such normal mode has its own decay length that plays the role of a hybridized coherence/magnetic field penetration length. On a large part of the parameter space, these exponents are complex. Therefore, the system in general has damped oscillatory decay of the magnetic field accompanied by damped oscillatory variation of the order-parameter fields.