Benchmarking exchange-correlation potentials with the mstar60 dataset: Importance of the nonlocal exchange potential for effective mass calculations in semiconductors

The accuracy of effective masses predicted by density functional theory\ndepends on the exchange-correlation functional employed, with nonlocal hybrid\nfunctionals giving more accurate results than semilocal functionals. In this\narticle, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE),\nTran-Blaha modified Becke-Johnson (TB-mBJ), and the hybrid\nHeyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentials\nfor the calculation of effective masses with perturbation theory. We introduce\nthe mstar60 dataset, which contains 60 effective masses derived from 18\nsemiconductors. The ratio between experimental and calculated effective masses\nis $1.70 \\pm 0.20$ for PBE, $0.76 \\pm 0.04$ for TB-mBJ, $0.99 \\pm 0.04$ for\nHSE06. We reveal that the nonlocal exchange in HSE06 enlarges the optical\ntransition matrix elements leading to the superior accuracy of the hybrid\nfunctional in the calculation of effective masses. The omission of nonlocal\nexchange in the transition operator for HSE leads to serious errors. For the\nsemilocal PBE functional, the errors in the bandgap and the optical transition\nmatrix elements partially cancel out in the calculation of effective masses.\nThe TB-mBJ functional yields PBE-like matrix elements paired with realistic\nbandgaps leading to a consistent overestimation of effective masses. However,\nif only limited computational resources are available, experimental masses can\nbe estimated by multiplying TB-mBJ masses with the factor of 0.76. We then\ncompare effective masses of transition metal dichalcogenide bulk and monolayer\nmaterials: we show that changes in the matrix elements are important in\nunderstanding the layer-dependent effective mass renormalization.\n