Real- and Momentum-Space Description of the Excitons in Bulk and Monolayer Chromium Tri-Halides: Article No. 33

Excitons with large binding energies ~2–3 eV in CrX₃ have been characterized as being localized (Frenkel) excitons that emerge from the atomic d − d transitions between the Cr-3d-t_2g and e_g orbitals. 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 the dp hybridization 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-d orbital manifold, nevertheless, the fractions of the spectral weight shared with the ligand halogen states increases as the dp hybridization enhances. The hybridization enhances as the halogen atom becomes heavier, bringing the X-p states closer to the Cr-d states 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-p hybridization, 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 CrCl₃ and CrBr₃ and acquires mixed Frenkel–Wannier character in CrI₃, making the excitons in CrI₃ most susceptible to environmental screening and spin–orbit coupling.