Trion polaron problem in bulk and two-dimensional materials

We develop a microscopic theoryof the trion polaron: a bound state of two electrons and one hole, dressed by longitudinal optical (LO) phonons. Starting from the Frohlich Hamiltonian, which describes the interaction of charged particles with LO phonons in three-dimensional (bulk) and two-dimensional (monolayer) polar crystals, we adopt the intermediate coupling variational approximation of Lee, Low, and Pines, and generalize it for the three-body problem. This yields an effective three-particle Hamiltonian with renormalized electron-electron and electron-hole interactions, similar to those obtained for exciton polaron and bipolaron problems. We compute the binding energies for a family of bulk perovskite materials and several atomic monolayer materials characterized by pronounced polar effects, providing quantitative benchmarks for spectroscopic measurements.