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Electric displacement as the fundamental variable in electronic-structure calculations


Finite-field calculations in periodic insulators are technically and conceptually challenging, owing to fundamental problems in defining polarization in extended solids. Although 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 enables full control over the electrical variables within the density functional formalism.

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Figure 1: Electrical boundary conditions within different methods.
Figure 2: Potential step and internal energy as a function of d.
Figure 3: Dielectric properties.
Figure 4: Lattice-dynamical and piezoelectric properties.


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This work was supported by the Department of Energy SciDac program on Quantum Simulations of Materials and Nanostructures, grant number DE-FC02-06ER25794 (M.S. and N.A.S.), and by ONR grant N00014-05-1-0054 (D.V.).

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Correspondence to Massimiliano Stengel.

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Stengel, M., Spaldin, N. & Vanderbilt, D. Electric displacement as the fundamental variable in electronic-structure calculations. Nature Phys 5, 304–308 (2009).

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