Ginzburg-Landau action and polarization current in an excitonic insulator model of electronic ferroelectricity

In comparison to transport of spin polarization in ferromagnets, transport of electric polarization in ferroelectrics remains less explored. Taking an excitonic insulator model of electronic ferroelectricity as a prototypical example, we theoretically investigate the low-energy dynamics and transport of electric polarization by microscopically constructing the Ginzburg-Landau action. We show that, because of the scalar nature of the excitonic order parameter, only the longitudinal fluctuations are relevant to the transport of electric polarization. We also formulate the electric-polarization diffusion equation, in which the electric-polarization current is defined purely electronically without recourse to the lattice degrees of freedom.