Vortices and chirality in multi-band superconductors

We investigate several important properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The BCS (Bardeen-Cooper-Schrieffer) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg-Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken time-reversal symmetry, that is, a chiral solution. The Ginzburg-Landau equation for three-component superconductors leads to a double sine-Gordon model. A kink solution exists to this equation as in the conventional sine-Gordon model. In the chiral region of the double sine-Gordon model, an inequality of Bogomol'nyi type holds, and fractional-$\pi$ kink solutions exist with the topological charge Q. This yields multi-vortex bound states in three-band superconductors.