Induced discommensurations in the lock-in transition of charge-density waves

TL;DR

This study investigates the lock-in transition in charge-density waves using numerical methods, revealing discommensurations' role in transitioning between commensurate and incommensurate states, consistent with experimental diffraction results.

Contribution

It introduces a numerical annealing approach to reproduce wave profiles and demonstrates how discommensurations can be excited in the commensurate state, linking topological invariants to these phenomena.

Findings

Discommensurations are present near the critical value of the lock-in transition.

Discommensurations can be excited in the commensurate state, leading to incommensurate states.

The excitation of discommensurations aligns with previous diffraction studies of $o$-TaS$_3$.

Abstract

We studied McMillan's free energy of the lock-in transition in charge-density waves. The wave profiles near the critical value were obtained by numerical annealing. First, we demonstrated that our method reproduces the previous studies. The obtained wave profiles include discommensurations near the critical value. Then, we calculated possible wave profiles in the commensurate state. We found that discommensurations are able to be excited in the commensurate state, leading the system to turn out to an incommensurate state. We proposed that these wave profiles result from topological invariants. Moreover, excitation of the discommensurations is favorable for the direction to the original wavelength of the incommensurate state. This is attributed to the nature of McMillan's free energy. The current-induced incommensurations, which we discovered with the diffraction study of $o$-TaS$_3$ [Inagaki \textit{et al.}, J. Phys. Soc. Jpn. 77, 093708 (2008)], is consistent with this study.