Revisitation of the Lock-In Transition in One-Dimensional Charge-Density Waves

We studied the lock-in transition of charge-density waves of one-dimensional conductors.Though this phenomenon has been known for decades, there are still discrepancies between the theories and the experiments.We focused on the pioneering study of this phenomenon by McMillan and revisited, in particular, his numerical calculations.We first reproduced his results by providing unwritten information in the article.The obtained critical point was in good agreement with the previous study, as well as the analytical solution proposed later.We found a simple power-law behavior of the free energy in the critical regime, leading to the power-law divergence of the specific heat.We also introduced the concept of stiffness, equivalent to helicity modulus, which also showed a power-law behavior.These results allowed us to propose a new perspective on the lock-in transition.][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] The wavelength of a CDW λ CDW is determined by the nesting vector connecting over the Fermi surfaces, independent of the lattice constants of the pristine lattice.Hence the ratio M = λ CDW /a does not have to be an integer, where a denotes any of the lattice constants. When is close to an integer, the CDW may be locked by the pristine lattice at low temperatures so that λ CDW shifts to an integral multiple of a.This phenomenon is called the lock-in transition.One of the distinguished features in the lock-in transition is the emergence of solitons.