Superfluidity and superconductivity only occur on the Earth in special materials at extremely low temperatures. By contrast, these exotic states of matter are expected to be commonplace in neutron stars: the neutrons form a superfluid and the protons a superconductor. In 'normal' matter - main-sequence stars, white dwarfs and most material on Earth - the magnetic force that acts on charged particles is the familiar Lorentz force. For superconducting matter the magnetic force is quite different - but most work on neutron stars still uses the Lorentz force anyway, for simplicity.
Here we lay some foundations for including proton superconductivity in neutron star models. We derive a single equation governing an equilibrium magnetic field in a superconductor and solve it numerically. Our solutions show qualitative differences from earlier models that assumed normal matter.
Phys. Rev. Letters, 110, 1101 (2013) arXiv e-print (arXiv:1211.3912)