Atomic theory model free#

The black lines denote the exciton band structure of LiF, and the yellow discs are the contribution | A s Q | 2 of each exciton to the formation of the excitonic polaron.

Atomic theory model free#

(a) The contribution of each free exciton state to the formation of excitonic polarons. Reuse & PermissionsĮxciton band structure, convergence of the formation energy of excitonic polarons with Brillouin zone sampling, and charge densities of polarons and excitonic polaron in LiF. This observation provides us with a strategy to initialize the iterative minimization of the ab initio excitonic polaron equations. In this example, the electron-phonon coupling matrix element g c c ′ ν ( k + Q, q ) in Eq. ( 26) is manually set to zero.

(c) Wannier exciton with artificially enhanced Fröhlich exciton-phonon interaction. With the help of short-range Holstein-type interactions, localized solutions emerge when there is a significant difference in electron-phonon coupling and hole-phonon coupling (in this example, 50 meV and 200 meV, respectively). (b) Wannier exciton with both Fröhlich electron-phonon and Holstein electron-phonon interactions. This observation indicates that a large difference in effective masses between electrons and holes favors the formation of the excitonic polaron. When the hole mass is much larger ( m h = 15 m e), the minimum energy corresponds to a localized solution (dashed line). When m h = 5 m e, the minimum energy solution corresponds to a fully delocalized exciton (solid line). (a) Wannier exciton with Fröhlich electron-phonon interactions. Reuse & Permissionsįormation energy of the excitonic polaron relative to the total energy of the free exciton, for various model systems. Accordingly, the free excitons are fully delocalized in the center-of-mass coordinate, and localized in the relative coordinate. The components of the eigenstates in the center-of-mass coordinate are plane waves, whose energies are indicated by the black parabola (for the 1 s exciton). Upon changing the electron and hole coordinates into the center-of-mass reference frame, the components of the eigenstates in the relative coordinate are hydrogenic wave functions, whose energies are indicated by grey horizontal lines. (b) The Wannier model for excitons is analytically solvable. Both bands are described by the effective mass approximation, and there is attractive Coulomb interaction between electrons and holes screened by the electronic dielectric constant ε ∞. (a) In the Wannier model, there is one parabolic valence band and one parabolic conduction band, separated by the quasiparticle band gap E g. Schematic illustration of the Wannier model for excitons. This work constitutes the first step toward a complete ab initio many-body theory of excitonic polarons in real materials. The key advantage of the present approach is that it does not require supercells, therefore it can be used to study a variety of materials hosting either small or large excitonic polarons. Then, we apply this theory to calculating excitonic polarons in lithium fluoride ab initio. We find that, in the case of Fröhlich interactions, excitonic polarons only form when there is a significant difference between electron and hole effective masses. We first apply this theory to model Hamiltonians for Wannier excitons experiencing Fröhlich or Holstein electron-phonon couplings. In this manuscript, we present a theory of excitonic polarons that is amenable to first-principles calculations. However, quantitative ab initio calculations of these effects are exceedingly rare. Excitonic polarons have long been thought to exist in a variety of materials, and are often invoked to explain the Stokes shift between the optical absorption edge and the photoluminescence peak. The quasiparticle thus formed by the exciton and the surrounding lattice distortion is called excitonic polaron. The electron and the hole forming the exciton also interact with the underlying atomic lattice, and this interaction can lead to a trapping potential that favors exciton localization. Excitons are neutral excitations that are composed of electrons and holes bound together by their attractive Coulomb interaction.