H D Cornean et al 2008 J. Phys. A: Math. Theor. 41 125202 doi:10.1088/1751-8113/41/12/125202
Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators
H D Cornean1, A Nenciu1 and G Nenciu2,3
Show affiliationsIt is proved that for general, not necessarily periodic, quasi one-dimensional systems the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial localization as the corresponding spectral projection. As a consequence, an eigenbasis of the band position operator provides a basis of optimally localized (generalized) Wannier functions for quasi one-dimensional systems, and this proves the strong Marzari–Vanderbilt conjecture. If the system has some translation symmetries (e.g. usual translations, screw transformations), they are 'inherited' by the Wannier basis.
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Issue 12 (28 March 2008)
Received 21 September 2007, in final form 13 February 2008
Published 10 March 2008
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Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators
H D Cornean et al 2008 J. Phys. A: Math. Theor. 41 125202
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2008 J. Phys.: Conf. Ser. 192 011002
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