Fig. 2: PL, absorption and ab initio calculations of the A exciton and its sideband.
From: Unconventional excitonic states with phonon sidebands in layered silicon diphosphide
a, PL spectrum (grey solid line) measured at 5.5 K and its fitted results using two Gaussian peaks plus a background. The fitted peaks are assigned as A (green solid line) and Aʹ (yellow solid line). b, The second derivative of the reflectance contrast (d-RC) spectrum (orange solid line) measured at 5.5 K. The arrows indicate the absorption peaks associated with the band edge (yellow) and the A exciton (red). c, Calculated absorption spectra of SiP2 by using the GW–BSE (dark blue) and GW–RPA (cyan) methods. The yellow dashed line represents the band-edge transition, the red dashed line represents the A exciton, and the binding energy is 140 meV. d, Left: schematic diagram for excitons bound by the Coulomb interaction and electronic band structures for bulk SiP2. Right: schematic diagram of the quasiparticle band for excitonic states, which includes the exciton peak A (2.12 eV) and the sideband A′. e, Calculated absorption spectrum of SiP2 with (blue solid line) and without (red dotted line) ex–ph interactions and the experimental PL spectrum (orange dashed line). The main A exciton peak of the blue line is obtained from GW–BSE calculations. The green and yellow shaded Gaussian peaks are A and Aʹ, respectively, as defined in a. f, Energy shifts of the band gap at the X point \(E_{\mathrm{g}}^{{{\mathrm{X}}}}\) individually induced by each optical phonon mode with momentum q = 0 at a temperature of zero. L0 represents the lattice structure without displacement of phonon modes. ±Lshift stands for atomic displacements of phonon modes. The change in the band gap is estimated by averaging the energy shifts of the band gap \(E_{\mathrm{g}}^{{{\mathrm{X}}}}\) with positive (red bar) and negative (dark blue bar) atomic displacements. Black circles denote energies of the corresponding phonon modes. g, The phonon density of states (DOS) for optical phonon modes, which is projected to the PB atoms in the embedded PB–PB chains (top) and their neighbouring silicon atoms (bottom). Insets: the PB atoms and their neighbouring silicon atoms.
