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 CrX3 have been characterized as being localized (Frenkel) excitons that emerge from the atomic d − d transitions between the Cr-3d-t2g and eg 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.

Strongly Correlated Exciton‐Magnetization System for Optical Spin Pumping in CrBr3 and CrI3.

“…It does not follow, however, that the energy scales generating the excitons are similar. On the contrary, the GW calculations [ 52,53 ] demonstrate that the bulk single‐particle band gap yields 3.8 eV for CrBr 3 and 2.4 eV for CrI 3 with the ground exciton binding energy of 2.5 eV for CrBr 3 and 1.2 eV for CrI 3 . Our calculations of the excitonic wave function in CrBr 3 and CrI 3 (Figure 1e,f) indicate that the ground excitonic state exhibits strong Frenkel and charge‐transfer characteristics.…”

“…That signifies that the excitonic excitation occurs virtually within CrX 3 molecule. Multiple valence and conduction bands contribute to the ground excitonic states, [ 53 ] which are made mostly of d ‐orbitals of chromium atom: e g for the conduction band and t 2g for the valence band. The minority contribution originates from the p ‐states or the halide atom (Br or I).…”

“…As such, the contributions to the excitonic ground state wave functions originate from the entire Brillouin zone and multiple sub‐bands rather than from the band edges at the specific points of the reciprocal lattice. [ 53 ] As such, there is no clear physical distinction between the electron and hole states that would favor the localization of any type of carrier. Therefore, we calculated the atomically‐resolved ground excitonic wave functions for CrBr 3 and CrI 3 in a general case as demonstrated in Figure a,b.…”

Possible realization of hyperbolic plasmons in a few-layered rhenium disulfide

“…When calculating the dielectric response within BSE, the valence and conduction states that form the two-particle Hamiltonian are increased until the two-particle eigenvalues converge within an accuracy of 10 meV. For ReS 2 the excitons are essentially Wannier-Mott [21] in nature and only the states at the valence band top and conduction band bottom contribute to their formation, so the convergence in the two-particle Hamiltonian size is much faster compared to the cases of CrX 3 [22] where the excitons have Frenkel character and many valence and conductions bands over several electron volts form them. However, for the present work, our focus is the plasmonic response, while we will note the excitonic binding energies in different layered variants later.…”

Dynamical correlations in single-layer CrI3

“…However, quasiparticle self-consistent GW calculations for both bulk and ML CrI 3 predict instead much larger values, around 2.0-3.0 eV depending on the computational scheme and the presence or absence of spin-orbit coupling [35,36]. Recent GW calculations combined with Bethe-Salpeter calculations propose an alternative description, suggesting that there are in-gap states in the infrared range associated with strongly bound excitons [37][38][39]. These clear differences demonstrate that the electronic correlations are essentially strong in this material and that they have to be addressed in detail.…”