Efficient Computation of Spontaneous Polarization Using Wannier Center Displacements

A widely-used approach to computing the spontaneous polarization of a crystalline ferroelectric is to calculate the Berry-phase polarization for structures along a deformation path between the centrosymmetric and polar structures and use continuity of the polarization to resolve the ambiguity arising from the fact that the polarization of a bulk crystal is only defined modulo a lattice. In this work we formulate an alternative symmetry-based method to obtain the spontaneous polarization {\it using only one self-consistent calculation} by inferring the displacements of Wannier centers between oppositely polarized states. This method gives the same result as the first, while avoiding the inefficiency involved in construction of a deformation path and computation for multiple hypothetical structures. We present applications to a wide variety of ferroelectric structures. In addition, we will discuss how this formulation provides a natural framework for the physics of the switching polarization in more exotic cases, such as charge-ordered ferroelectrics.