Phonon softening in triangular lattice

We have numerically studied the phonon softening in a triangular lattice system with Su-Schrieffer-Heeger's (SSH) type interaction and with a three-quarter-filled electronic band. When the temperature is lowered, the simultaneous softening of multiple phonon modes is observed at a critical temperature. These softened modes have momenta parallel to the vectors connecting neighboring vertices of the hexagonal structure of the Fermi surface, being irrelevant to nesting vectors. Therefore, this phenomenon that occurs when the temperature is lowered is not a conventional Peierls transition. It is found that the Fermi surface composed of straight lines is a necessary condition for the simultaneous phonon softening. Multi-mode states are realized below the critical temperature. However, all of the softened modes are not necessarily condensed at the lowest free-energy state.