We investigated the lock-in transition of charge density waves (CDWs) in quasi-one-dimensional conductors, based on McMillan's free energy. The higher-order umklapp terms play an essential role in this study. McMillan's theory was extended by Nakanishi and Shiba to treat multiple CDW vectors. Although their theories were aimed at understanding CDWs in quasi-two-dimensional conductors, we applied them to the quasi-one-dimensional conductors, including ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_3, {\mathrm{NbSe}}_3$, and $m-{\mathrm{TaS}}_3$, and confirmed its validity for these cases. Then we discussed our previous experimental result of $o-{\mathrm{TaS}}_3$, which revealed the coexistence of commensurate and incommensurate states. We found that the coexistence of multiple CDW vectors is essential for the lock-in transition to occur in $o-{\mathrm{TaS}}_3$. The even- and odd-order terms in the free energy play roles for amplitude development and phase modulation, respectively. Moreover, consideration of the condition of being commensurate CDWs allowed us to relate it with that of the weak localization in random media.

中文翻译：

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准一维导体中电荷密度波的锁定跃迁：麦克米兰理论的重新解释

基于麦克米兰的自由能，我们研究了准一维导体中电荷密度波（CDW）的锁定跃迁。高阶umklapp术语在这项研究中起着至关重要的作用。Nakanishi和Shiba扩展了McMillan的理论，以治疗多种CDW载体。尽管他们的理论旨在理解准二维导体中的CDW，但我们将其应用于准一维导体，包括${\mathrm{ķ}}_{0.3}{O}_3， {\mathrm{铌硒}}_3$， 和 $米-{钽}_3$，并确认其在这些情况下的有效性。然后我们讨论了之前的实验结果$Ø-{钽}_3$，揭示了相称国家和不相称国家的并存。我们发现，多个CDW向量的共存对于在系统中发生锁定过渡至关重要。$Ø-{钽}_3$。自由能中的偶数和奇数项分别对振幅发展和相位调制起作用。此外，考虑到相称CDW的条件，使我们可以将其与随机介质中弱定位的条件联系起来。