More than fifty years ago, hypotheses about the spontaneous Bose condensation of excitons in matter, i.e. without external optical excitation, were done [1]. This new theorized phase shows formal analogies with the superconductor ground state, albeit the nature of the order is different, and it may exhibit effects like macroscopic quantum coherence and exotic low-energy excitations [2].In this work we performed an high-throughput search for possible excitonic instability among thousands of recently discovered 2D monolayer materials, as obtained by computational exfoliation in 2018 [3] and contained in the Material Cloud 2D materials database (MC2D) [4]. We developed a dedicated screening protocol in order to discriminate candidates by applying state-of-the-art ab-initio methods, in particular many-body perturbation theory [5]. We accurately evaluated quasiparticle band structures and excitonic states via GW and BSE approaches, respectively. Robust computational workflows are implemented in the aiida-yambo plugin [6], a crucial tool needed in this work to perform the simulations in an automated high-throughput fashion.Preliminary but pushed convergence tests reveal that AsCuLi2, a topological insulator [7] isostructural to hexagonal Boron Nitride, may present spontaneous excitonic formation in its true ground state. Calculations are still ongoing, challenging the evaluation of excitonic states of AsCuLi2 within very high numerical accuracy (few meV, i.e. the accuracy of the method). A kp model Hamiltonian of the system has been developed consistently with the ab-initio findings, in order to describe the low-energy band structure in the neighborhood of the Gamma point and possibly derive a gap equation. [1] D. Sherrington and W. Kohn, Speculations about Grey Tin. Reviews of Modern Physics, 40(4):767-769, October (1968).[2] T. Portengen, Ostreich, and L. J. Sham, Theory of electronic ferroelectricity.Phys. Rev. B, 54:17452{17463, Dec (1996).[3] Mounet et al., Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nature Nanotechnology, 13(3):246-252 (2018).[4] Mounet et al., Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Materials Cloud Archive, 2020.158(3) (2020).[5] Sangalli et al., Many-body perturbation theory calculations using the yambo code. J. Phys.: Condens. Matter, 31(32):325902 (2019).[6] Bonacci et al., Towards high-throughput many-body perturbation theory: efficient algorithms and automated workflows. arXiv:2301.06407 (2023).[7] Marrazzo et al., Relative Abundance of Z2 Topological Order in Exfoliable Two-Dimensional Insulators. Nano Letters, 19(12):8431-8440 (2019).
