Polaron relaxation and charge dynamics near the mobility edge of a possible Wigner lattice of polarons

Abstract

We performed impedance spectroscopy and optical investigations below the reported mobility edge of two models systems (${X}_{n}$/${X}_{1.95\ensuremath{-}\ensuremath{\delta}}{\mathrm{Al}}_{1.95}{\mathrm{Si}}_{2.05}{\mathrm{O}}_{8.00}$; $X=\mathrm{K}$ or Rb, $n$ is the doping density of guest atoms) used to explore the metal-insulator transition in a deformable lattice. The bulk ac conductivity and imaginary dielectric permittivity of insulating samples near the mobility edge in both systems show a power-law behavior and variable-range hopping (VRH) conduction that is indeed related to the proposed polaron relaxation and conduction. We show that polaron relaxation and VRH occur simultaneously above a particular density of an interacting gas of small (bi)polarons, which is commensurate with the electron-lattice coupling strength and the intersite electron transfer energy. Based on our experimental results, we propose a rich phase diagram for the charge dynamics in a deformable lattice from the perspective of a Wigner lattice of small (bi)polarons.