Optical absorption study by ab initio downfolding approach: Application to GaAs

We examine whether the essence and quantitative aspects of electronic excitation spectra are correctly captured by an effective low-energy model constructed from an ab initio downfolding scheme. A global electronic structure is first calculated by ab initio density-functional calculations with the generalized gradient approximation. With the help of constrained density-functional theory, the low-energy effective Hamiltonian for bands near the Fermi level is constructed by the downfolding procedure in the basis of maximally localized Wannier functions. The excited states of this low-energy effective Hamiltonian ascribed to an extended Hubbard model are calculated by using a low-energy solver. As the solver, we employ the Hartree–Fock approximation supplemented by the single-excitation configuration-interaction method considering electron-hole interactions. The present three-stage method is applied to GaAs, where eight bands are retained in the effective model after the downfolding. The resulting spectra well reproduce the experimental results, which indicate that our downfolding scheme offers a satisfactory framework of the electronic-structure calculation, particularly for the excitations and dynamics as well as for the ground state.

Figure 1

(Top) A global ab initio band structure of GaAs at [$-15\text{eV}$:$+30\text{eV}$]. (Bottom) Ab initio original (solid line) and interpolated (dots) bands. Energy zero is set to the top of the valence bands. The energy window is set to [$-15\text{eV}$:$+10\text{eV}$].

Figure 2

(Color online) Maximally localized Wannier functions of Ga (top) and As (bottom). The amplitudes of the contour surface are $+0.5/\sqrt{v}$ (dark shaded balls) and $-0.5/\sqrt{v}$ (lightly shaded balls), where $v$ is the volume of the primitive cell. The shaded sheet represents a $3\times 3\times 3$ fcc lattice and Ga and As nuclei are illustrated as gray and blue dots.

Figure 3

Schematic diagram for CNDO-HF band calculation.

Figure 4

Self-consistent GaAs CNDO-HF band structure (solid line) and ab initio interpolated band structure (dots). Energy zero is set to the top of the valence bands.

Figure 5

(Color online) Calculated SECI (thick red line) and IPA (thin green line) optical absorption spectrum of GaAs. The closed blue and open blue circles represent experimental data taken from Refs. 30, 31, respectively.

Figure 6

(Color online) Dependence of SECI spectra (red lines) on scaling factor $x$; (a) $x=0.8$, (b) $x=1.0$, and (c) $x=1.2$. The closed blue and open blue circles represent experimental data taken from Refs. 30, 31, respectively.