Current induced magnetic flux response in frustrated three-band superconductors as a bulk probe of broken time reversal symmetry (BTRS) ground states

Within the Ginzburg-Landau formalism we provide a classification of all possible ground states (GS) of a three-band superconductor (3BSC) where either frustrated states with BTRS or a single non-BTRS GS with unconventional/conventional s-wave symmetry, respectively, exist. The necessary condition for a BTRS GS in general cannot be reduced to a ''-''sign of the product of all interband couplings (IBC) valid in the case of 3 equivalent bands with repulsive equal IBC, only. It corresponds to a maximal IBC frustration. We show that with increasing diversity of the parameter space this frustration is reduced and the regions of possible BTRS GS start to shrink. We track possible evolutions of a BTRS GS of a 3BSC based doubly-connected system in an external magnetic field. Depending on its parameters, a magnetic flux can induce various current density leaps, connected with adiabatic or non-adiabatic transitions from BTRS to non-BTRS states and vice versa. The current induced magnetic flux response of samples with a doubly-connected geometry e.g. as a thin tube provides a suitable experimental tool for the detection of BTRS GS.