Polarons and Exciton Polarons in Two-Dimensional Polar Materials

We propose a macroscopic theory of optical phonons, Fröhlich polarons, and exciton polarons in two-dimensional (2D) polar crystalline monolayers. Our theory extends the classical macroscopic formulation of the electron-phonon problem in three-dimensional (3D) polar crystals to the new generation of 2D materials. Similarly to the 3D case, in our approach, the effective electron-phonon Hamiltonian is parametrized solely in terms of macroscopic experimentally accessible quantities-2D polarizabilities of the monolayer at low and high frequencies. We derive the dispersion of long wave length longitudinal optical (LO) phonons, which can be viewed as a 2D form of the Lyddane-Sachs-Teller relation, and study the formation of 2D Fröhlich polarons by adopting the intermediate coupling approximation. Finally, we apply this approach to excitons in polar 2D crystals and derive an effective potential of the electron-hole interaction dressed by LO phonons. Because of a specific dispersion of LO phonons, polarons and exciton polarons in 2D materials exhibit unique features not found in their 3D counterparts. As an illustration, the polaron and exciton polaron binding energies are computed for a representative set of 2D polar crystals, demonstrating the interplay between dimensionality, polarizability of materials, and electron-phonon coupling.