Polarons in two-dimensional polar materials: All-coupling variational theory

We present a detailed and self-contained theoretical study of polarons in two-dimensional (2D) polar materials, which extends the classical macroscopic theory of Fr\"ohlich polarons to the 2D case. The theory is fully determined by experimentally accessible parameters, the static and optical 2D polarizabilities of a monolayer, the frequency of transverse optical phonons, and the effective mass of charge carriers. We define a single dimensionless parameter, which characterizes the coupling of electrons with longitudinal optical phonons, analyze both weak- and strong-coupling regimes, and adopt the Feynman variational path-integral approach for a high-quality interpolation between these limits. Our results provide insight into the ground-state energy and effective mass of polarons in the new generation of 2D polar monolayers.