First-Principles Calculations at Constant Polarization

TL;DR

This paper introduces an exact formalism for first-principles calculations at fixed electric polarization, improving upon previous approximate methods and demonstrating its effectiveness on various polar materials.

Contribution

The paper presents a new exact method for first-principles calculations at fixed polarization, enhancing accuracy over prior approximate approaches.

Findings

Improved description for materials with complex polarization contributions

Accurate energy landscape mapping at fixed polarization

Enhanced physical insights into polar material behavior

Abstract

We develop an exact formalism for performing first-principles calculations for insulators at fixed electric polarization. As shown by Sai, Rabe, and Vanderbilt (SRV) [N. Sai, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B {\bf 66}, 104108 (2002)], who designed an approximate method to tackle the same problem, such an approach allows one to map out the energy landscape as a function of polarization, providing a powerful tool for the theoretical investigation of polar materials. We apply our method to a system in which the ionic contribution to the polarization dominates (a broken-inversion-symmetry perovskite), one in which this is not the case (a III-V semiconductor), and one in which an additional degree of freedom plays an important role (a ferroelectric phase of KNO$_3$). We find that while the SRV method gives rather accurate results in the first case, the present approach provides important improvements to the physical description in the latter cases.