Peierls transition refers to the phenomena in which metals undergo phase changes associated with Fermi surface instability and periodic lattice distortion due to the interaction of electrons and phonons at k = 2k_F. R. E. Peierls proposed the mechanism in his famous Quantum Theory of Solids (1955) in order to elucidate why low-symmetry structures are stabilized in crystalline Sb and Bi. Later, phase transitions found in 1970s in materials with low-dimensional Fermi surfaces have shown to be driven by this mechanism.

Owing to intensive studies, it has been established that the qualitative behaviour of the Peierls transition is well characterized by the strength of electron-phonon coupling as a dominant parameter. Thus the transitions are more often categorised simply into two classes: weak-coupling and strong-coupling types.

Our study have shown that the classification scheme is not appropreate...

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