Electric displacement as the fundamental variable in electronic-structure calculations

TL;DR

This paper introduces a new formalism for electronic-structure calculations where electric displacement D is the fundamental variable, simplifying the treatment of ferroelectric systems and boundary conditions in periodic insulators.

Contribution

The authors develop a novel approach fixing electric displacement D instead of E or P, providing clearer conceptual understanding and practical advantages for first-principles calculations of ferroelectric materials.

Findings

Enables full control over electrical variables in density functional calculations.

Simplifies the treatment of stresses and strains in ferroelectric systems.

Demonstrated with PbTiO3 example.

Abstract

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.