Quantum fluctuation of ferroelectric order in polar metals

Polar metallic phase, a metallic phase with long-range ferroelectric (FE) order, has been widely observed in FE materials since the last decade. While it is less conventional, FE order as a spontaneous inversion symmetry breaking actually does not require a global FE polarization that can be effectively screened by merely a couple of percents of metallic carriers. Strangely, FE order is found to be strongly suppressed by metallic carriers and completely destroyed at moderate ~12% carrier density. Here, we propose a general mechanism, carrier-induced quantum fluctuation, to explain this effective destruction of FE order in polar metals. In essence, owing to the virtual kinetic effect of quantum particles, carriers are always dressed by polarizable medium to form larger polarons. Since the local FE correlation inside the polaron is disrupted, the long-range FE order can thus be destroyed when the size of polarons breach the percolation threshold. We demonstrate such polaron formation and its size growth via kinetic strength with a simple model using exact diagonalization, perturbation and quantum Monte Carlo approaches. This proposed quantum mechanism not only provides an intuitive picture for many experimental findings, but also advocates the importance of quantum physics in polar metals, which enables new possibilities in designing FE-based electronic devices.