1. General Seminars

Accurate calculations of optical spectra for large systems

by Dr Margherita Marsili

Aula Conversi (Laboratori Nazionali di Frascati)

Aula Conversi

Laboratori Nazionali di Frascati

Many-body perturbation theory (MBPT) is the natural framework for the description of electronic excited state properties of materials. For istance, within MBPT, single-particle excitation energies (as probed by photoemission and STS experiments) are found at the poles of the single particle Green's function. Response functions, describing the optical spectra, can be expressed in terms of the two-particle Green's function and are calculated via the solution of the Bethe-Salpeter equation (BSE), which explicitly contains the electron-hole interaction. When electron-hole interactions are neglected, the neutral excited state is described, starting from the ground state, by the promotion of an electron from an occupied state to an available empty one. Such single-particle transitions concur, independently one to the other, to the construction of the optical absorption spectrum. †In this approximation, absorption spectra are often in bad agreement with the experiments both concerning the peak positions and the lineshape. The agreement with experiment is restored when the electron-hole interactions are included. Excited states are in this case described as linear combinations of independent-particle transitions. The description of the optical spectra, for both finite and extended systems, is in this case very reliable, but the calculations are computationally extremely expensive. One of the main limitations to the system-size derives from the presence of summations on empty states. In this seminar I will first review the theoretical framework and derivation of the MBPT-BSE approach, and then show a new formulation of the BSE solution, where the summation over empty states is exactly avoided. In our scheme, implemented in the Quantum Espresso Package, the screened interaction between the excited electron and hole is described using an optimal basis set [1], and the electron-hole Hamiltonian is an operator acting on the conduction states manifold. Large system sizes should be moreover achievable thanks to the use of Wannier functions that strongly reduce the amount of terms to be calculated. As a consequence we are able to determine, not only the excitation spectra, as possible within a recently proposed formalism {2], but also, directly, each excited state. [1] P. Umari, et al Phys. Rev. B 79, 201104 (2009) [2] D.Rocca, et al. Phys. Rev. B 85, 045116 (2012)