Electron-Phonon Coupling: I

Excitons and phonons in materials are well understood by ab initio methods, but just recently exciton-phonon coupling (EPC) has been studied by first principles methods. It plays a key role in phenomena including Stokes shifts, Raman spectra, and ultrafast optical experiments.

To study EPC, we combine results from GW/BSE and DFPT and calculate excited-state forces, which are the gradient of the excited-state energy surface. With those forces, we can relax excited states using optimization algorithms as is done in common DFT routines. We show results for two cases: (1) self-trapped excitons in LiF and (2) coherent phonon generation in bilayer MoS₂ (2LMoS₂).

For the first case, using relaxations from two different starting points in a supercell with 128 atoms, we found the relaxed structure to be a polaronic exciton centered on a fluoride ion, which has anisotropic optical absorption. For this supercell calculation, we developed a rule to properly choose the BSE Hamiltonian size to minimize the computational expense. For the second case, we study five different stackings of 2LMoS₂. While the AA’ stacking is the most stable stacking in the ground state, the AB and AB’ stackings are more stable in the excited state than AA’ in the high exciton concentration limit. We found that absorption of light may excite not only the A’₁ phonon mode but also layer breathing modes, and this EPC is stacking-dependent.

Our results provide meaningful insights about EPC effects in an atomistic scale.