The fundamental properties of recently synthesized single- and bilayer ${\mathrm{PdSe}}_{2}$ are investigated using accurate many-body perturbation GW theory to quantitatively examine their electronic structure and explain the insufficiency of previously reported experimental and theoretical results. Including electron-hole interactions responsible for exciton formation, we solve the Bethe-Salpeter equation on top of the ${\mathrm{GW}}_{0}$ approximation to predict the optical properties. The fundamental quasiparticle band gaps of single- and bilayer ${\mathrm{PdSe}}_{2}$ are 2.55 and 1.89 eV, respectively. The optical gap of monolayer ${\mathrm{PdSe}}_{2}$ reduces significantly due to a large excitonic binding energy of 0.65 eV comparable to that of ${\mathrm{MoSe}}_{2}$, while an increase of the layer number decreases the excitonic binding energy to 0.25 eV in bilayer ${\mathrm{PdSe}}_{2}$. The giant band gap renormalization of \ensuremath{\sim}36--38% in the bilayer (BL) ${\mathrm{PdSe}}_{2}$/graphene heterostructure has a high impact on the construction of ${\mathrm{PdSe}}_{2}$-based devices and explains the experimentally observed band gap. The small value of the experimental optical gap of single-layer (SL) ${\mathrm{PdSe}}_{2}$ (1.3 eV) can be explained by the presence of Se vacancies, which can drop the Tauc-estimated optical gap to \ensuremath{\sim}1.32 eV. The absorption spectra of both mono- and bilayer ${\mathrm{PdSe}}_{2}$ cover a wide region of photon energy, demonstrating promising application in solar cells and detectors. These findings provide a basis for a deeper understanding of the physical properties of ${\mathrm{PdSe}}_{2}$ and ${\mathrm{PdSe}}_{2}$-based heterostructures.
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