Elucidating Na$_2$KSb band structure: near-band-gap photoemission spectroscopy and DFT calculations
The electronic band structure of Na$_{2}$KSb was studied by a combination of low-energy photoemission spectroscopy and density functional theory (DFT) calculations. The optical and photoemission quantum efficiency (QE) spectra, along with longitudinal energy distribution curves (EDCs) of multialkali Na$_{2}$KSb(Cs,Sb) photocathodes were measured in the temperature range of 80--295 K. The thresholds of various band-to-band transition in Na$_{2}$KSb were observed in the optical and QE spectra of Na$_{2}$KSb(Cs,Sb) photocathodes. The evolution of EDC derivatives with varying photon energy reveals a fine structure related to the emission of two types of electrons: (i) ballistic electrons, which are excited from heavy hole, light hole and split-off valence bands, and (ii) photoelectrons, that are captured in the side valleys of Na$_{2}$KSb conduction band. The analysis of EDCs and QE spectra allowed us to determine the band structure parameters of Na$_{2}$KSb at $T = 80$ K, including the band gap $E_{\text{g}} = 1.52 \pm 0.02$ eV, spin-orbit splitting $Δ_{\text{SO}} = 0.59 \pm 0.04$ eV and the energy separations between $Γ$ and side valleys of the conduction band: $Δ_{Γ-\text{X}1} = 0.41 \pm 0.05$ eV and $Δ_{Γ-\text{X}2} = 0.65 \pm 0.05$ eV. The experimentally determined band gaps and side valley positions, as well as the energies of the final electronic states of optical transitions are in good agreement with the DFT calculations. The obtained data on the hot electron dynamics and electronic band structure of Na$_{2}$KSb are crucial to improve the understanding of the photoemission processes in this material and will contribute to the development of the robust spin-polarized electron sources with multialkali photocathodes.