Radzihovsky L, Frey E, Nelson D R
Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Mar;63(3 Pt 1):031503. doi: 10.1103/PhysRevE.63.031503. Epub 2001 Feb 27.
We investigate two-dimensional (2D) melting in the presence of a one-dimensional (1D) periodic potential as, for example, realized in recent experiments on 2D colloids subjected to two interfering laser beams. The topology of the phase diagram is found to depend primarily on two factors: the relative orientation of the 2D crystal and the periodic potential troughs, which selects a set of Bragg planes running parallel to the troughs, and the commensurability ratio p=a(')/d of the spacing a(') between these Bragg planes to the period d of the periodic potential. The complexity of the phase diagram increases with the magnitude of the commensurabilty ratio p. Rich phase diagrams, with "modulated liquid," "floating," and "locked floating" solid and smectic phases are found. Phase transitions between these phases fall into two broad universality classes, roughening and melting, driven by the proliferation of discommensuration walls and dislocations, respectively. We discuss correlation functions and the static structure factor in these phases, and make detailed predictions about the universal features close to the phase boundaries. We predict that for charged systems with highly screened short-range interactions, these melting transitions are generically reentrant as a function of the strength of the periodic potential, a prediction that is in accord with recent 2D colloid experiments. Implications of our results for future experiments are also discussed.
我们研究了存在一维周期势时的二维熔化现象，例如在近期对二维胶体施加两束干涉激光束的实验中所实现的那样。发现相图的拓扑结构主要取决于两个因素：二维晶体与周期势谷的相对取向，它选择了一组平行于势谷的布拉格平面，以及这些布拉格平面之间的间距(a(')与周期势的周期(d)的可公度比(p = a('/d)。相图的复杂性随着可公度比(p)的增大而增加。发现了具有“调制液体”、“浮动”以及“锁定浮动”固体和近晶相等丰富的相图。这些相之间的相变分为两大类普适性类别，分别由失配壁和位错的增殖驱动的粗糙化和熔化。我们讨论了这些相中的关联函数和静态结构因子，并对靠近相界的普适特征做出了详细预测。我们预测，对于具有高度屏蔽短程相互作用的带电系统，这些熔化转变通常会随着周期势强度的变化而出现重入现象，这一预测与近期的二维胶体实验结果一致。还讨论了我们的结果对未来实验的影响。
