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Excitonic Bose-Einstein condensation (EBEC) has drawn increasing attention recently with the emergence of 2D materials. A general criterion for EBEC, as expected in an excitonic insulator (EI) state, is to have negative exciton formation energies in a semiconductor. Here, using exact diagonalization of multi-exciton Hamiltonian modelled in a diatomic Kagome lattice, we demonstrate that the negative exciton formation energies are only a prerequisite but insufficient condition for realizing an EI. By a comparative study between the cases of both a conduction and valence flat bands (FBs) versus that of a parabolic conduction band, we further show that the presence and increased FB contribution to exciton formation provide an attractive avenue to stabilize the EBEC, as confirmed by calculations and analyses of multi-exciton energies, wave functions and reduced density matrices. Our results warrant a similar many-exciton analysis for other known/new candidates of EIs, and demonstrate the FBs of opposite parity as a unique platform for studying exciton physics, paving the way to material realization of spinor BEC and spin-superfluidity.

The thermal discrete dipole approximation (T-DDA) is a numerical approach for modeling near-field radiative heat transfer in complex three-dimensional geometries. In this work, the convergence of the T-DDA is investigated by comparison against the exact results for two spheres separated by a vacuum gap. The error associated with the T-DDA is reported for various sphere sizes, refractive indices and vacuum gap thicknesses. The results reveal that for a fixed number of subvolumes, the accuracy of the T-DDA degrades as the refractive index and the sphere diameter to gap ratio increase. A converging trend is observed as the number of subvolumes increases. The large computational requirements associated with increasing the number of subvolumes, and the shape error induced by large sphere diameter to gap ratios, are mitigated by using a nonuniform discretization scheme. Nonuniform discretization is shown to significantly accelerate the convergence of the T-DDA, and is thus recommended for near-field thermal radiation simulations. Errors less than 5% are obtained in 74% of the cases studied by using up to 82712 subvolumes. Additionally, the convergence analysis demonstrates that the T-DDA is very accurate when dealing with surface polariton resonant modes dominating radiative heat transfer in the near field., Comment: 46 pages, 12 figures, 3 tables