Influence Functional Approach to Non-Perturbative Exciton Binding Renormalization from Phonons

Abstract

We construct a many-body model Hamiltonian to capture how phonons renormalize exciton binding as a function of temperature. By using the GW approximation and density functional perturbation theory, we are able to parameterize this Hamiltonian completely from first principles. To capture static quasiparticle properties non-perturbatively, we evolve this Hamiltonian in imaginary time with path integral Monte Carlo using an influence functional based approach. For a class of Wannier-Mott type excitons, our binding energies are in quantitative agreement with experiment. We find that in addition to long-range dipolar interactions from longitudinal optical modes, short-ranged deformation potentials from acoustic modes and transverse optical modes can significantly renormalize electron and hole polaron binding energies at elevated temperature. However, exciton binding energies are only appreciably renormalized by coupling to optical phonons.

Figures (8)

• Figure 1: Workflow of PIMC framework with first principles parameterization. For the PIMC step, black dashed lines represent the screened Coulomb interaction between the electron and hole from the phonons. Red and blue lines represent the induced self-attraction from the phonons for an electron and hole, respectively.
• Figure 2: (a) MgO electronic band structure with effective mass fits at the valence band maximum and conduction band minimum, (b) MgO phonon band structure with dashed lines illustrating the long-wavelength mode behaviors, (c) MgO LO mode interactions fits in the $\Gamma-X$ direction, and (d) MgO acoustic mode interactions fits in the $\Gamma-X$ direction.
• Figure 3: (a) CdS electronic band structure with effective mass fits at the valence band maximum and conduction band minimum, (b) CdS phonon band structure with dashed lines illustrating the long-wavelength mode behaviors, (c) CdS optical mode interactions fits in the $\Gamma-X$ direction, and (d) CdS acoustic mode interactions fits in the $\Gamma-X$ direction.
• Figure 4: (a) AgCl electronic band structure with effective mass fits at the valence band maximum and conduction band minimum, (b) AgCl phonon band structure with dashed lines illustrating the long-wavelength mode behaviors, (c) AgCl optical mode interactions fits in the $\Gamma-X$ direction, and (d) AgCl acoustic mode interactions fits in the $\Gamma-X$ direction.
• Figure 5: (a) CsPbBr$_3$ electronic band structure with effective mass fits at the valence band maximum and conduction band minimum, (b) CsPbBr$_3$ phonon band structure with dashed lines illustrating the long-wavelength mode behaviors, (c) CsPbBr$_3$ LO mode interactions fits in the $\Gamma-X$ direction, and (d) CsPbBr$_3$ acoustic mode interactions fits in the $\Gamma-X$ direction. In panel (c), we note that we have not plotted the charge-phonon matrix elements for mode LO$_3$, but we have included them in the PIMC calculations.