Nonlinear electronic excitations in crystalline solids using meta-generalized gradient approximation and hybrid functional in time-dependent density functional theory

TL;DR

This paper develops and applies advanced real-time density functional theory methods with meta-GGA and hybrid functionals to study nonlinear electron excitations in crystalline solids, highlighting the importance of accurate band gap potentials.

Contribution

It introduces numerical techniques for stable time evolution with TB-mBJ and HSE functionals, including a new method to evaluate excitation energy without an energy functional.

Findings

Electronic excitations are sensitive to band gap energies at low laser intensities.

Results using TB-mBJ and HSE are similar at high laser intensities.

LDA predicts more intense excitations at low laser intensities.

Abstract

We develop numerical methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta generalized gradient approximation (meta-GGA) proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt a predictor-corrector step for stable time-evolution. Since energy functional is not known for the TB-mBJ potential, we propose a method to evaluate electronic excitation energy without referring to the energy functional. Calculations using the HSE hybrid functional is computationally expensive due to the nonlocal Fock-like term. We develop a computational method for the operation of the Fock-like term in Fourier space, for which we employ massively parallel computers equipped with graphic processing units. To demonstrate significances of utilizing potentials providing correct band gap energies, we compare electronic excitations induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: results using TB-mBJ and HSE are close to each other, while the excitation of the LDA calculation is more intensive than the others. At high laser intensities close to a damage threshold, we have found that electronic excitation energies are similar among the three cases.