Calculations of quasi-particle spectra of semiconductors under pressure

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 (CuAlO2) 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 spin-orbit 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. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim