Berry-phase treatment of the homogeneous electric field perturbation in insulators
By R. W. Nunes, Xavier Gonze. 2001
204 citations recorded by the source corpus.
A perturbation theory of the static response of insulating crystals to homogeneous electric fields that combines the modem theory of polarization (MTP) with the variation-perturbation framework is developed at unrestricted order of perturbation. First, we address conceptual issues related to the definition of such a perturbative approach. In particular, in our definition of an electric-field-dependent energy functional for periodic systems, the position operator appearing in the perturbation term is replaced by a Berry-phase expression, along the lines of the MTP. Moreover, due to the unbound nature of the perturbation, a regularization of the Ferry-phase expression for the polarization is needed in order to define a numerically stable variational procedure. Regularization is achieved by means of discretization, which can be performed either before or after the perturbation expansion. We compare the two possibilities and apply them to a model tight-binding Hamiltonian. Lowest-order as well as generic formulas are presented for the derivatives of the total energy, the normalization condition, the eigenequation, and the Lagrange parameters.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/8a9cf06028bc99d4c055f3123cd0a659656e32f7
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Theory of Polarization: A Modern Approach (2007, background): “Transforming back to Bloch functions, Nunes and Gonze showed in 2001 [38] how the known perturbative treatments could be obtained (and, in some cases, extended) by deriving them from a variational principle based on minimizing an energy functional F of the form”
- Recent developments in the ABINIT software package (2016, methodology): “The Modern Theory of Polarization provides a formula for the electronic part Pel as Pel · bi = fe Ω 1 N i⊥ Ni⊥∑ Im ln Ni‖∏ detMki,ki+∆ki .”
- Maximally-localized Wannier Functions: Theory and Applications (2011, background): “(89) (Nunes and Vanderbilt, 1994) or via the equivalent Berry-phase expression (Nunes and Gonze, 2001; Souza et al., 2002; Umari and Pasquarello, 2002).”
- Berry phase effects on electronic properties (2009, background): “On the computational side, calculating polarization in finite electric fields has been addressed, which has a deep influence on density functional theory in extended systems (Nunes and Gonze, 2001; Nunes and Vanderbilt, 1994; Souza et al., 2002).”