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

Abstract 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. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006