Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Abstract

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the MonteCarlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard-Jones and 1/r 12 repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.

Geometrical defects in two-dimensional melting of many-particle Yukawa systems

“…According to Figure 6, at this temperature the system slowly switches between high and low values of the order parameter, corresponding to the defect configurations depicted in parts (a) and (c) of Figure 5. Therefore, there is a range of temperatures, in which ordered and disordered states are unstable and have approximately the same probabilities to be observed, as reported in [31,32], and no hysteresis should occur in the limit of infinite simulation time. Let us now turn to the analysis of the polygon construction.…”

“…Previous studies of similar systems [31] suggest that the effect of hysteresis might be caused by the finite rate of heating and cooling. We test this hypothesis by analysing the evolution of topological defect fraction at the constant prescribed temperature of kT ref = 0.00243, starting from either liquid or solid initial state.…”

Electrostatics in soft matter

“…• Whereas the two known extreme limits of zero [163,162,160] and infinite [172,173,174] screening strength λ are recovered by lattice sum calculations [158], † Note that in the ground state, i.e. at rigorously zero temperature, the value of V 0 is irrelevant.…”

Buckling of two-dimensional plasma crystals with nonreciprocal interactions

“…Meanwhile, several theoretical and numerical studies have systematically examined the instability of the hexagonal monolayer Yukawa crystal in the context of complex plasma [30][31][32][33][34][35][36], classical Wigner crystals [37][38][39][40][41] and charged colloids [42][43][44][45][46][47][48][49][50][51][52]. It has been shown that under harmonic confinement, for a decreasing confinement strength or increasing density, the hexagonal monolayer is expected to buckle first to a hexagonal triple layer crystal and subsequently to a bilayer square [4].…”