Real- and momentum-space description of the excitons in bulk and monolayer chromium tri-halides

Abstract Excitons with large binding energies ~2–3 eV in CrX₃have been characterized as being localized (Frenkel) excitons that emerge from the atomicd − dtransitions between the Cr-3d-t_2gande_gorbitals. The argument has gathered strength in recent years as the excitons in recently made monolayers are found at almost the same energies as the bulk. The Laporte rule, which restricts such parity forbidden atomic transitions, can relax if a symmetry-breaking mechanism is present. While what can be classified as a purely Frenkel exciton is a matter of definition, we show using an advanced first principles parameter-free approach that these excitons in CrX₃, in both its bulk and monolayer variants, have band origin and it is thedphybridization between Cr and X that primarily acts as the symmetry-breaking mechanism that relaxes the Laporte rule. We show that the character of these excitons is mostly determined by the Cr-dorbital manifold, nevertheless, the fractions of the spectral weight shared with the ligand halogen states increases as thedphybridization enhances. The hybridization enhances as the halogen atom becomes heavier, bringing the X-pstates closer to the Cr-dstates in the sequence Cl → Br → I, with an attendant increase in exciton intensity and a decrease in binding energy. By applying a range of different kinds of perturbations that qualitatively mimics the effects originating from the missing vertex in self-energy, we show that moderate changes to the two-particle Hamiltonian that essentially modifies the Cr-d-X-phybridization, can alter both the intensities and positions of the exciton peaks. A detailed analysis of several deep-lying excitons, with and without strain, elucidates the fact that the exciton is most Frenkel-like in CrCl₃and CrBr₃and acquires mixed Frenkel–Wannier character in CrI₃, making the excitons in CrI₃most susceptible to environmental screening and spin–orbit coupling.