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Quantum statistical analysis of superconductivity, fractional quantum Hall effect, and aromaticity
Author(s) -
Böhm Michael C.,
Saal Christoph
Publication year - 2000
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/1097-461x(2000)79:3<125::aid-qua1>3.0.co;2-1
Subject(s) - superconductivity , condensed matter physics , physics , fractional quantum hall effect , pairing , quantum mechanics , pauli exclusion principle , hamiltonian (control theory) , quantum , cooper pair , chemistry , quantum hall effect , electron , quantum spin hall effect , mathematics , mathematical optimization
The phenomena of superconductivity and fractional quantum Hall effect (FQHE) as well as the well‐known chemical concepts of aromaticity and antiaromaticity are analyzed on the basis of quantum statistical considerations. We suggest that the superconducting transition is caused by a first‐order interaction between the charge carriers which does not necessarily involve a second‐order coupling of the electron–phonon type. For molecular model systems it is demonstrated that the formation of superconducting Cooper pairs can lead to an attenuation of destabilizing quantum constraints of the intersite type, i.e., constraints due to the Pauli antisymmetry principle (PAP). We suggest that this attenuation is the driving force for the superconducting transition. Such a reduction of the PAP influence on the quantum ensemble is also the key element of the present explanation of the FQHE. Analogies between the superconducting transition and the plateaus in the Hall conductance are emphasized. Both phenomena can be interpreted in terms of an electronic phase transition which shifts the original fermionic (fe) system towards a hard core bosonic (hcb) boundary. hcb ensembles are characterized by on‐site anticommutativity and intersite commutativity. The collective solid‐state phenomena superconductivity and FQHE are correlated with the popular chemical concepts of aromaticity and antiaromaticity. Numerical results for the superconducting pairing are derived by the two‐parameter Hubbard Hamiltonian. In order to express physically transparent interrelations between fe and hcb ensembles, the so‐called statistical transmutation is adopted. Arguments on the basis of experimental results are summarized which support the present PAP‐driven superconducting pairing formalism. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 125–162, 2000