The photoluminescence (PL) spectra of monolayer (1L) semiconductors feature peaks ascribed to different charge-carrier complexes. We perform diffusion quantum Monte Carlo simulations of the binding energies of these complexes and examine their response to electric and magnetic fields. We focus on quintons (charged biexcitons), since they are the largest free charge-carrier complexes in transition-metal dichalcogenides (TMDs). We examine the accuracy of the Rytova-Keldysh interaction potential between charges by comparing the binding energies of charge-carrier complexes in 1L-TMDs with results obtained using $\textit{ab initio}$ interaction potentials. Magnetic fields$<8$T change the binding energies (BEs) by$\sim0.2$ meV,T$^{-1}$, in agreement with experiments, with the BE variations of different complexes being very similar. Our results will help identify charge complexes in the PL spectra of 1L-semiconductors

Density functional theory (DFT) is widely used to study defects in monolayer graphene with a view to applications ranging from water filtration to electronics to investigation of radiation damage in graphite moderators. To assess the accuracy of DFT in such applications, we report diffusion quantum Monte Carlo (DMC) calculations of the formation energies of some common and important point defects in monolayer graphene: monovacancies, Stone-Wales defects, and silicon substitutions. We find that standard DFT methods underestimate monovacancy formation energies by around 1 eV. The disagreement between DFT and DMC is somewhat smaller for Stone-Wales defects and silicon substitutions. We examine vibrational contributions to the free energies of formation for these defects, finding that vibrational effects are non-negligible. Finally, we compare the DMC atomization energies of monolayer graphene, monolayer silicene, and bulk silicon, finding that bulk silicon is significantly more stable than monolayer silicene by 0.7522(5) eV per atom.

Excitonic complexes in type-II quantum-ring heterostructures may be considered as artificial atoms due to the confinement of only one charge-carrier type in an artificial nucleus. Binding energies of excitons, trions, and biexcitons in these nanostructures are then effectively ionization energies of these artificial atoms. The binding energies reported here are calculated within the effective-mass approximation using the diffusion quantum Monte Carlo method and realistic geometries for gallium antimonide rings in gallium arsenide. The electrons form a halo outside the ring, with very little charge density inside the central cavity of the ring. The de-excitonization and binding energies of the complexes are relatively independent of the precise shape of the ring.