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The recent discovery of iron pnictide superconductors has resulted in arapidly growing interest in multiband models with more than two bands. In thiswork we specifically focus on the properties of three-band Ginzburg-Landaumodels which do not have direct counterparts in more studied two-band models.First we derive normal modes and characteristic length scales in theconventional U(1) three-band Ginzburg-Landau model as well as in its timereversal symmetry broken counterpart with $U(1)\times Z_2$ symmetry. We showthat in the latter case, the normal modes are mixed phase/density collectiveexcitations. A possibility of the appearance of a massless phase-differencemode associated with fluctuations of the phase difference is also discussed.Next we show that gradients of densities and phase differences can beinextricably intertwined in vortex excitations in three-band models. This canlead to very long-range attractive intervortex interactions and appearance oftype-1.5 regimes even when the intercomponent Josephson coupling is large. Insome cases it also results in the formation of a domain-like structures in theform of a ring of suppressed density around a vortex across which one of thephases shifts by $\pi$. We also show that field-induced vortices can lead to achange of broken symmetry from U(1) to $U(1)\times Z_2$ in the system. In thetype-1.5 regime, it results in a semi-Meissner state where the system has amacroscopic phase separation in domains with broken U(1) and $U(1)\times Z_2$symmetries.

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