Accurate calculation of excitonic signatures in the absorption spectrum of BiSBr using semiconductor Bloch equations

In order to realize the significant potential of optical materials such as metal halides, computational techniques which give accurate optical properties are needed, which can work hand-in-hand with experiments to generate high efficiency devices. In this work a computationally efficient technique based on semiconductor Bloch equations (SBEs) is developed and applied to the material BiSBr. This approach gives excellent agreement with the experimental optical gap, and also agrees closely with the excitonic stabilisation energy and the absorption spectrum computed using the far more computationally demanding ab initio Bethe-Salpeter approach. The SBE method is a good candidate for theoretical spectroscopy on large- or low-dimensional systems which are too computationally expensive for an ab initio treatment.

Figure 1

(a) View down the b axis of the BiSBr $Pnma$ crystal structure, showing the “cluster” shape of the chains which make up the crystal. Bismuth atoms are green, bromine atoms are brown, and sulfur atoms are yellow. (b) Side view of one of the cluster chains of the previous perspective showing that the bismuth atoms are arranged in an effectively one-dimensional structure.

Figure 2

Optical properties of BiSBr calculated using various techniques described in the text. (a) Optical gaps computed using BSE, SBE, TDDFT, TDDFT with a scissor operator, and TDDFT using the HSE06 functional, with the experimental gap plotted as a dashed line. (b) Corresponding simulated absorption spectra not including the SBE approach. (c) Absorption spectrum of SBE compared with BSE. (d) Excitonic stabilization energies of the five approaches. (e) SBE imaginary part of the dielectric matrix for the direction along atomic chains computed with (solid line) and without (dashed line) local field effects, and with free particles (dotted line) compared to BSE (shaded blue curve). Comparing the free particle spectrum and excitonic spectrum gives an estimate of the exciton binding energy: $E_b=305$ meV.

Figure 3

(a) Coulomb coupling $V_{|k-k^{\prime }|}^{ij}$ between microscopic polarization operators $P_k^{ij}$ and $P_{k^{\prime }}^{ij}$ for Wannier-Mott excitons with Bohr radii much larger than a lattice constant couples electrons and holes with different quasimomenta belonging to one pair of energy bands. (b) Coulomb coupling for the Frenkel excitons that couples microscopic polarizations for different pairs of bands.