Electric displacement as the fundamental variable in electronic-structure calculations

Details Electric displacement as the fundamental variable in electronic-structure calculations Electric displacement as the fundamental variable in electronic-structure calculations

2008-06-04

arxiv.org/abs/0806.0844v2

Nature Physics 5, 304-308 (2009)

Physics

Condensed Matter

Materials Science

6 pages, 4 figures. Added new results for the non-linear piezoelectric response of PbTiO3. For associated supplementary notes,

Scientific paper

10.1038/nphys1185

Finite-field calculations in periodic insulators are technically and conceptually challenging, due to fundamental problems in defining polarization in extended solids. While significant progress has been made recently with the establishment of techniques to fix the electric field E or the macroscopic polarization P in first-principles calculations, both methods lack the ease of use and conceptual clarity of standard zero-field calculations. Here we develop a new formalism in which the electric displacement D, rather than E or P, is the fundamental electrical variable. Fixing D has the intuitive interpretation of imposing open-circuit electrical boundary conditions, which is particularly useful in studying ferroelectric systems. Furthermore, the analogy to open-circuit capacitors suggests an appealing reformulation in terms of free charges and potentials, which dramatically simplifies the treatment of stresses and strains. Using PbTiO3 as an example, we show that our technique allows full control over the electrical variables within the density functional formalism.

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