Unconventional bright ground-state excitons in monolayer TiI$_2$ from first-principles calculations

TL;DR

This work demonstrates a bright ground-state exciton in a monolayer TiI$_2$ via ab initio screened configuration interaction and Bethe–Salpeter calculations, driven by SOC-induced $K$-valley conduction-band splitting and a weak electron–hole exchange which keeps the bright state lowest. The A exciton binds with $E_b^A\approx 441\ \mathrm{meV}$ and lies $\Delta_{DA}\approx +3\ \mathrm{meV}$ below the dark state D, with the B exciton at $\approx 105\ \mathrm{meV}$ higher; trions show a similar bright-ground-state behavior with $E_b^{\text{trion}}\approx 32\ \mathrm{meV}$ and a charge-dependent $\Delta_{DA}$ in the $12$–$18\ \mathrm{meV}$ range. The bright ground state persists under in-plane strains of $\pm 1\%$, and trions inherit brightness, suggesting TiI$_2$ as a promising platform for fast radiative recombination and optoelectronic applications. The findings illuminate a framework for discovering other materials with bright ground-state excitons, emphasizing the roles of halogen-driven SOC and weak exchange, and highlight the central influence of many-body Coulomb interactions in determining exciton fine structure.

Abstract

Based on \textit{ab initio} screened configuration interaction calculations we find that TiI$_2$ has a bright exciton ground state and identify two key mechanisms that lead to this unprecedented feature among transition metal dichalcogenides. First, the spin-orbit induced conduction band splitting results in optically allowed spin-alignment for electrons and holes across a significant portion of the Brillouin zone around the $\mathbf{K}$-valley, avoiding band crossings seen in materials like monolayer MoSe$_2$. Second, a sufficiently weak exchange interaction ensures that the bright exciton remains energetically below the dark exciton state. We further show that the bright exciton ground state is stable under various mechanical strains and that trion states (charged excitons) inherit this bright ground state. Our findings are expected to spark further investigation into related materials that bring along the two key features mentioned, as bright ground-state excitons are crucial for applications requiring fast radiative recombination.

Figures (5)

• Figure 1: Unit cell and band structure of monolayer TiI$_2$. (a) TiI$_2$ in top and side view with the in-plane lattice constant $a$ and $\mathrm{I}-\mathrm{I}$ distance $d$. (b) The band structure computed within DFT. The color indicates the spin expectation value along $z$. The inset shows the spin-orbit coupling induced conduction band splitting at $\mathbf{K}$.
• Figure 2: Low-energy excitonic states (a) Energetic positions of many-body optical dipoles are indicated by grey (black) vertical lines for the bright (dark) excitons. (b),(c) Configurational weights at $\mathbf{K}$ of the first bright (A) and first dark (D) exciton. The color of the bands indicates the spin expectation value along $z$ and the thickness of the bands corresponds to the excitonic weights.
• Figure 3: Low-energy trion states (a) Absorption spectrum of positive (red) and negative (blue) trions relative to the bright ground-state exciton A (grey). Energetic positions of many-body optical dipoles are indicated by vertical lines. The dark states, characterized by negligible dipole moments, are not visible at this scale. However, we use small vertical dark lines to indicate their energetic positions. (b),(c) Configurational weights at $\mathbf{K}$ of the first bright positively (A$^{+}_{\mathbf{K}}$) and negatively (A$^{-}_{\mathbf{K}}$) charged trion species. The color of the bands indicates the spin expectation value along $z$ and the thickness of the lines encodes the configurational weight.
• Figure 4: Dark-bright splitting under the influence of strain The in-plane lattice constant $a$ and the I-I distance $d$ have been varied within the interval $[-1, +1] \, \%$ from their equilibrium values.
• Figure 5: Dark-bright splitting analysis (a) Energetic splitting in meV between the dark (D) and the bright state (A) in monolayer TiI$_2$ (black/grey) and MoSe$_2$ (light-orange/orange) calculated at different levels in the exciton calculations: using only single-particle energies (IP), including diagonal electron-hole interactions (eh diag.) and including all interactions (eh) in \ref{['eq:BSE_matrix_elements']}. (b) Dark-bright splitting ($\Delta_{\mathrm{DA}}$) for TiI$_2$ and MoSe$_2$ as a function of the number of configurations (given by the radius around $\mathbf{K}$). The inset shows the conduction bands for both materials around $\mathbf{K}$ and the orange vertical lines indicate the radius $r_{\times}$ for which the spin-split conduction bands cross in MoSe$_2$.