Eur. Phys. J. B (2016) 89: 60
https://doi.org/10.1140/epjb/e2016-60448-5

Regular Article

Role of confinements on the melting of Wigner molecules in quantum dots

¹ Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, 741246 Mohanpur, India
² Christian-Albrechts-Universität zu Kiel, Institut für Theoretische Physik und Astrophysik, Leibnizstrasse 15, 24098 Kiel, Germany
³ Joint Institute for High Temperatures RAS, Izhorskaya Str. 13, 125412 Moscow, Russia

^a e-mail: filinov@theo-physik.uni-kiel.de
^b e-mail: ghosal@iiserkol.ac.in

Received: 5 June 2015
Received in final form: 18 September 2015
Published online: 2 March 2016

Abstract

We explore the stability of a Wigner molecule (WM) formed in confinements with different geometries emulating the role of disorder and analyze the melting (or crossover) of such a system. Building on a recent calculation [D. Bhattacharya, A. Ghosal, Eur. Phys. J. B 86, 499 (2013)] that discussed the effects of irregularities on the thermal crossover in classical systems, we expand our studies in the untested territory by including both the effects of quantum fluctuations and of disorder. Our results, using classical and quantum (path integral) Monte Carlo techniques, unfold complementary mechanisms that drive the quantum and thermal crossovers in a WM and show that the symmetry of the confinement plays no significant role in determining the quantum crossover scale n_X. This is because the zero-point motion screens the boundary effects within short distances. The phase diagram as a function of thermal and quantum fluctuations determined from independent criteria is unique, and shows “melting” from the WM to both the classical and quantum “liquids”. An intriguing signature of weakening liquidity with increasing temperature, T, is found in the extreme quantum regime. The crossover is associated with production of defects. However, these defects appear to play distinct roles in driving the quantum and thermal “melting”. Our analyses carry serious implications for a variety of experiments on many-particle systems − semiconductor heterostructure quantum dots, trapped ions, nanoclusters, colloids and complex plasma.