Two - dimensional electron crystals in single and dou - ble layers

We present results of Monte-Carlo simulations for finite 2D single and bilayer systems. Strong Coulomb correlations lead to arrangement of particles in configurations resembling a crystal lattice. For binary layers, there exists a particularly rich variety of lattice symmetries which depend on the interlayer separation d. We demonstrate that in these mesoscopic lattices there exist two fundamental types of ordering: radial and orientational. The dependence of the melting temperature on d is analyzed, and a stabilization of the crystal compared to a single layer is found. Introduction. The properties of a finite number of charged particles (N ∼ 10) in a single " two-dimensional " layer have been the subject of intensive threoretical and experimental investigation in the last decade [1]-[5]. In particular, if at low temperature the density parameter r s is increased, transitions from a Fermi liquid to a so-called Wigner molecule [4] and, further, to a Wigner crystal have been found [5]. The interplay between the long-range Coulomb interaction and a shallow confinement potential plays in these systems a prominent role making conventional effective single-particle approximations unreliable. In this connection the predictions of both classical and quantum Monte Carlo methods which treate N-body correlations rigorously, are of great importance, in particular for the theoretical understanding of the solid-liquid crossover. Recently, a new 2D system has attracted the attention of several groups, namely, bilayer structures. The phase diagram of bilayer systems is far more rich compared to single layers. In particular, the formation of Wigner lattices in electronic or ionic bilayers has been predicted, both by classical [6] and quantum-mechanical [7] studies and revealed the existence of distinct structural phases: rectangular, square, rhombic and triangular staggered lattices. The transition between these phases takes place at specific values of the interlayer distance d, when one of the phases becomes energetically favorable and may proceed in continuous or discontinuous manner. However , these predictions have been made for macroscopic systems. Here, we extend the analysis of bilayer stuctures to finite-size systems (e.g. electrons or ions in quantum dots and radio frequency traps, respectively). Our previous inverstigation of finite single layer structures [5] has revealed that these mesoscopic systems have a richer phase diagram than their macroscopic counterpart, and that the phase diagram strongly depends on the particle number. In this paper, we demonstrate that different crystalline structures are stable in different ranges of the interlayer distance. Moreover, we find that …