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Maximally-localized generalized Wannier functions for composite energy bands

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arxiv cond-mat/9707145 v1 pith:IC4QD4QT submitted 1997-07-14 cond-mat.mtrl-sci

Nicola Marzari , David Vanderbilt (Department of Physics , Astronomy , Rutgers University) This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords functionswannierbandsblochgeneralizedmethodspacetotal
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We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ <r^2>_n - <r>_n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^k describing the rotation among the Bloch bands at each k-point. The method is thus suitable for use in connection with conventional electronic-structure codes. The procedure also returns the total electric polarization as well as the location of each Wannier center. Sample results for Si, GaAs, molecular C2H4, and LiCl will be presented.

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Cited by 2 Pith papers

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  1. Quantum Metric Bound State of Light

    cond-mat.mes-hall 2026-06 unverdicted novelty 7.0 of 10

    Defect-induced bound states in flat bands have exponential decay length lower-bounded by the quantum metric when kinetic energy and CLS protection are absent.

  2. Effects of the Hubbard interaction on the quantum metric

    cond-mat.str-el 2024-12 conditional novelty 6.0 of 10

    On a fermionic Creutz ladder, the dressed quantum metric matches exact diagonalization results better than the generalized quantum metric, and Hubbard interactions suppress the quantum metric.

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