Quasiparticle electronic structure and optical spectra of single-layer and bilayer ${\mathrm{PdSe}}_2$: Proximity and defect-induced band gap renormalization

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 ∼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 ∼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.

Figure 1

(a) The top and side views of single-layer ${\mathrm{PdSe}}_2$. The yellow and gray atoms represent Se and Pd, respectively. (b) The band structure of single-layer ${\mathrm{PdSe}}_2$ calculated within optPBE (blue) and HSE06 (red) levels of theory. The Fermi level is set to 0 eV. (c) Spatial distribution of electron density in VBM (left panel, $0.0002\mathrm{e}/{\AA }^3$), CBM and CBM1 (middle and right panels, $0.005\mathrm{e}/{\AA }^3$) states. (d) The electron localization function of monolayer ${\mathrm{PdSe}}_2$ renormalized between 0.0 and 1.0. Delocalized and localized electrons are represented by values of 0.5 and 1.0, respectively.

Figure 2

Quasiparticle ${\mathrm{G}}_0{\mathrm{W}}_0$ (dotted black) and ${\mathrm{GW}}_0$ (solid blue) band structures of single-layer (left) and bilayer (right) ${\mathrm{PdSe}}_2$. The black and grey arrows correspond to indirect and direct band gaps.

Figure 3

(a) The equilibrium geometry of simulated heterostructure and (b) partial DOS of BL ${\mathrm{PdSe}}_2$/graphene calculated within optPBE functional. The Fermi level is set to 0 eV.

Figure 4

(a) Convergence of the imaginary part of the dielectric function (top) and the QP band gap (bottom). (b) Schematic illustration of an optical transition. (c),(d) Optical properties of ML and BL ${\mathrm{PdSe}}_2$: imaginary part of dielectric function (top panels); absorption coefficient (middle panels), the most prominent oscillator strengths are plotted by black bars, the grey line corresponding to the incident AM1.5G solar flux is given for view; Tauc plots (bottom panels), the dashed lines are linear fitting the curves.

Figure 5

The comparative DOS of perfect and defective monolayer ${\mathrm{PdSe}}_2$.