Nonlinear behavior of the band gap of Pb1−xEuxSe (0≤x≤1) from first principles

We present an ab initio investigation of the band gap of the Pb1-xEuxSe (0<=x<=1) alloy using the special quasirandom structure approach proposed by Wei [Phys. Rev. B 42, 9622 (1990)]. Due to the complexity of this particular system, i.e., (i) the narrow-band gap of the parent compound PbSe, (ii) spin-orbit coupling induced by relativistic effects in the Pb atoms, and (iii) the strongly localized f electrons of Eu, an accurate description of its properties represents a serious challenge to density-functional theory. We discuss results obtained from Perdew, Burke, and Ernzerhof density functional and Heyd, Scuseria, and Ernzerhof Hartree-Fock hybrid functional calculations, both with and without an additional Hubbard U treatment of the Eu f electrons. At low Eu concentrations (x<0.13) the HSE functional gives a good description of the band gap of Pb1-xEuxSe . At high Eu concentrations an additional Hubbard U treatment of the Eu f electrons is mandatory.