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

## TL;DR

This paper demonstrates that chiral p-wave superconductors with broken time reversal symmetry exhibit coupled magnetic and order parameter modes, leading to complex, hybridized decay lengths and oscillatory magnetic field behavior.

## Contribution

It reveals that in anisotropic, time-reversal-breaking superconductors, magnetic and order parameter excitations are mixed, resulting in unique decay modes not characterized by traditional lengths.

## Key findings

- Magnetic and order parameter modes are coupled in p+ip superconductors.
- Decay lengths are hybridized and can be complex, causing oscillatory decay.
- Normal modes have their own distinct decay lengths, differing from conventional superconductors.

## Abstract

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 are 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.