  Two-dimensional (2D) post-transition metal chalcogenides (PTMC) have
attracted attention due to their suitable band gaps and lower exciton binding
energies, making them more appropriate for electronic, optical and
water-splitting devices than graphene and monolayer transition metal
dichalcogenides (TMDs). Of the predicted 2D PTMCs, GaSe has been reliably
synthesized and experimentally characterized. Despite this fact, quantities
such as lattice parameters and band character vary significantly depending on
which density functional theory (DFT) functional is used. Although many-body
perturbation theory (GW approximation) has been used to correct the electronic
structure and obtain the excited state properties of 2D GaSe, and solving the
Bethe-Salpeter equation (BSE) has been used to find the optical gap, we find
that the results depend strongly on the starting wavefunction. In attempt to
correct these discrepancies, we employed the many-body Diffusion Monte Carlo
(DMC) method to calculate the ground and excited state properties of GaSe
because DMC has a weaker dependence on the trial wavefunction. We benchmark
these results with available experimental data, DFT [local-density
approximation, Perdew-Burke-Ernzerhof (PBE), strongly constrained and
appropriately normed (SCAN) meta-GGA, and hybrid (HSE06) functionals] and
GW-BSE (using PBE and SCAN wavefunctions) results. Our findings confirm
monolayer GaSe is an indirect gap semiconductor (Gamma-M) with a quasiparticle
electronic gap in close agreement with experiment and low exciton binding
energy. We also benchmark the optimal lattice parameter, cohesive energy and
ground state charge density with DMC and various DFT methods. We aim to present
a terminal theoretical benchmark for pristine monolayer GaSe, which will aide
in the further study of 2D PTMCs using DMC methods.
