Magnetic flux transitions in two-band single-junction superconductors with time-reversal symmetry breaking

Based on Ginzburg-Landau theory, we investigate the electromagnetic properties of two-band superconductors with broken time-reversal symmetry. We propose an apparatus of superconducting ring integrated with microbridge structure to probe the peculiar topological excitations in the chiral system. The phase difference of two order parameters in the superconductor satisfies the double sine-Gordon equation, and a linear relationship between the phase difference at both ends of the junction and total magnetic flux in the ring can be obtained. Then with the Josephson current-phase relation, we establish the dependence of the circulating current and magnetic flux on the applied external magnetic field. Our results show that this single-junction system will exhibit the irreversible behaviors and two different types of fractional flux transitions can clearly manifest the time-reversal symmetry breaking in two-component superconductors.