Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory

By Xifan Wu, D. Vanderbilt, D. V. D. O. Physics, Astronomy, Rutgers University Bell Laboratories, Lucent Technologies, M. Hill, Nj. 2005

611 citations recorded by the source corpus.

The methods of density-functional perturbation theory may be used to calculate various physical response properties of insulating crystals including elastic, dielectric, Born charge, and piezoelectric tensors. These and other important tensors may be defined as second derivatives of an appropriately defined energy functional with respect to atomic-displacement, electric-field, or strain perturbations, or as mixed derivatives with respect to two of these perturbations. The resulting tensor quantities tend to be coupled in complex ways in polar crystals, giving rise to a variety of variant definitions. For example, it is generally necessary to distinguish between elastic tensors defined under different electrostatic boundary conditions, and between dielectric tensors defined under different elastic boundary conditions. Here, we describe an approach for computing all of these various response tensors in a unified and systematic fashion. Applications are presented for two materials, hexagonal ZnO and rhombohedral $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$, at zero temperature.

Subfields: Condensed Matter Physics, Geophysics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/0cb676924067e0daf975908a96b153e80e2e7499

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Citations in the corpus

Electric displacement as the fundamental variable in electronic-structure calculations (2008, background): “[8] can be similarly defined in terms of the second derivatives of U({d}, u, η).”
Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk (2018, background): “(5).(35) χαβ 1⁄4 ~χαβ þ Ω 1 0 ZmαðK (1)ÞmnZnβ: (5)”
Stability and strength of atomically thin borophene from first principles calculations (2016, methodology): “We calculate the elastic tensor coefficients including ionic relaxations using the finite differences method [64,65].”
Quantum‐mechanical condensed matter simulations with CRYSTAL (2018, background): “The H matrix in Equation (19) has to be considered a pseudoinverse of H where translational degrees of freedom are projected out, as discussed in detail elsewhere (Wu et al., 2005).”
Identifying defect-tolerant semiconductors with high minority-carrier lifetimes: beyond hybrid lead halide perovskites (2015, methodology): “ included at the level of first order perturbation to the DFT results. Ionic dielectric tensors are computed from the interatomic force constants obtained using density functional perturbation theory.[94] The dielectric constants reported in Table 1 are computed as one third of the trace (Tr(ε)/3) o”