Quantum statistics of charged particles and fingerprints of Wigner crystallization in D dimensions

摘要

After a brief summary of the physical arguments underlying Wigner's original concept in 1934 of a quantal electron crystal, theoretical interpretation of a number of experimental findings are presented. These include (i) low-density carriers in semiconductors in applied magnetic fields in both three, and recently two, dimensions; and (ii) low-temperature phase diagram of underdoped high T-c cuprates; fullerides with relatively low T-c are also referred to in a related context. Interpretation of areas (i) and (ii) focuses on the relevance of both Fermi-Dirac and anyonic (fractional) statistics, the latter in relation to the proposed melting curve of the two-dimensional (2D) magnetically induced Wigner solid into the Laughlin liquid phase, which is the seat of the fractional quantum Hall effect. A brief discussion follows of crystalline phases additional to the Wigner solid, namely Skyrmion and Hall crystals. Bose-Einstein statistics is then referred to, but now in relation to finite-size confined quantal assemblies, with fingerprints of Wigner molecules the focus. Finally, quasi-1D lattices are considered, both in Bechgaard salts and in the very recent single-electron counting experiment of Bylander et al. (c) 2006 Wiley Periodicals, Inc.