Multivalley 3D Electronic Structure of PbSe from Soft-X-Ray ARPES and First-Principles Calculations

Abstract

PbSe is a narrow-gap IV-VI semiconductor, whose multivalley valence bands, with maxima at the L, $Σ$, and $Δ$ points, underpin its intermediate-temperature thermoelectric properties. We combine soft-X-ray angle-resolved photoemission spectroscopy (SX-ARPES) with first principles simulations to study the valence band structure of bulk PbSe. High resolution measurements are conducted at photon energies of 400-900 eV to map the valence manifold along X$Γ$X, WXW, and K$Γ$K, and iso-energy surfaces are collected in the $k_z=0$ plane. Comparison to ARPES enables a rigorous assessment of the performance of density functional theory (DFT), using semi-local and hybrid functionals, as well as many-body perturbation theory within the quasiparticle self-consistent $GW$ approximation. We find that the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and QP$GW$ reproduce the measured band dispersions to within 0.1-0.2 eV over the entire valence band. In contrast, the semi-local Perdew-Burke-Ernzerhof (PBE) functional compresses the band width and deviates from experiment by up to 0.6 eV. We further show that an accurate band structure and band gap are vital to obtaining a correct description of the dependence of the Seebeck coefficient of p-type PbSe on the hole concentration (Pisarenko relation). This has implications for computational efforts to discover thermoelectric materials.