Correlation-induced inhomogeneity in circular quantum dots

Properties of the 'electron gas'—in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected—change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood¹. For very weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and order into a Wigner crystal phase. The physics at intermediate densities, however, remains a subject of fundamental research^{2,3,4,5,6,7,8}. Here, we study the intermediate-density electron gas confined to a circular disc, where the degree of confinement can be tuned to control the density. Using accurate quantum Monte Carlo techniques⁹, we show that the electron–electron correlation induced by an increase of the interaction first smoothly causes rings, and then angular modulation, without any signature of a sharp transition in this density range. This suggests that inhomogeneities in a confined system, which exist even without interactions, are significantly enhanced by correlations.