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Hamiltonian for the spin quantum Hall effect solution and derivation based on an SU (2) gauge field
Author(s) -
Bracken Paul
Publication year - 2010
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/qua.22326
Subject(s) - hamiltonian (control theory) , physics , quantum hall effect , eigenfunction , quantum spin hall effect , wave function , quantum mechanics , gauge theory , eigenvalues and eigenvectors , quantum electrodynamics , condensed matter physics , electron , mathematics , mathematical optimization
A Hamiltonian to describe a spin quantum Hall effect with two types of spin‐orbit coupling is introduced and the eigenfunctions and eigenvalues are obtained for it. It is shown that this Hamiltonian also results by gauging a kinetic energy Hamiltonian by an SU (2) gauge field. The Berry phase is obtained from the model wavefunction for the model and used to define a filling factor. This allows for the calculation of the spin Hall conductivity. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010