Frustrated multiband superconductivity

We show that a clean multiband superconductor may display one or several phase transitions with increasing temperature from or to chiral superconducting states with broken time-reversal symmetry with continuous evolution of the relative phases of the superconducting order parameters. These transitions may occur when more than two bands are involved in the formation of the superconducting phase and when the number of repulsive interband interactions is odd. These transitions are signalled by slope changes in the temperature dependence of the superconducting gaps. In the case of quasi-2D superconductors, such transitions also occur with increasing in-plane magnetic field.