Revisiting the Modern Theory of Electric Polarization via a Density-Based Approach

The modern theory of electric polarization is one of the greatest successes of electronic structure theory, providing an elegant formulation of electric polarization as a bulk property in terms of a geometric/Berry phase, playing important roles in areas such ferro-, piezo-, and flexo- electric systems. However, as pointed out by by Resta in J. Chem. Phys. 154, 050901 (2021), the theory, which applies to bulk crystals/periodic systems, bears little/no formal resemblence to the dipole moment of a finite sized sample. In addition, the theory provides a quantum mechanical solution to a problem that can be formulated independently of classical/quantum considerations. In this talk I will propose an alternative formulation that addresses these tensions via a density-based approach, and discuss some progress on establishing its correspondence to the Berry phase formulation in the case of bulk crystals.