Calculations of quasi-particle spectra of semiconductors under pressure

Abstract

Different approximations in calculations of electronic quasi-particle states in semiconductors are compared and evaluated with respect to their validity in predictions of optical properties. The quasi-particle self-consistent GW (QSGW) approach yields values of the band gaps which are close to experiments and represents a significant improvement over single-shot GW calculations using local density approximation (LDA) start wavefunctions. The QSGW approximation is compared to LDA bands for a wide-gap material (CuAlO 2 ) and materials with very small gaps, PbX (X=S, Se, and Te). For wide-gap materials QSGW overestimates the gaps by 0.3―0.8 eV, an error which is ascribed to the omission of vertex corrections. This is confirmed by calculations of excitonic effects, by solving the Bethe-Salpeter equation. The LDA error in predicting the binding energy of the Cu-3d states is examined and the QSGW and LDA + U approximations are compared. For PbX the spinorbit coupling is included, and it is shown that although LDA gives a reasonable magnitude of the gap at L, only QSGW predicts the correct order of the L + 6 and L ― 6 states and thus the correct sign (negative) of the gap pressure coefficient. The pressure-induced gap closure leads to linear (Dirac-type) band dispersions around the L point.