Length scales, collective modes, and type-1.5 regimes in three-band superconductors

Abstract

The recent discovery of iron pnictide superconductors has resulted in a rapidly growing interest in multiband models with more than two bands. In this work we specifically focus on the properties of three-band Ginzburg-Landau models which do not have direct counterparts in more studied two-band models. First we derive normal modes and characteristic length scales in the conventional $U(1)$ three-band Ginzburg-Landau model as well as in its time-reversal symmetry-broken counterpart with $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry. We show that, in the latter case, the normal modes are mixed phase-density collective excitations. A possibility of the appearance of a massless mode associated with fluctuations of the phase difference is also discussed. Next we show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to very long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. In some cases it also results in the formation of a domainlike structure in the form of a ring of suppressed density around a vortex across which one of the phases shifts by $\ensuremath{\pi}$. We also show that field-induced vortices can lead to a change of broken symmetry from $U(1)$ to $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ in the system. In the type-1.5 regime, it results in a semi-Meissner state where the system has a macroscopic phase separation in domains with broken $U(1)$ and $U(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetries.