Exciton and trion formation in systems with van Hove singularities

TL;DR

This work analyzes how van Hove singularities (VHS) and higher-order VHS (HOVHS) in a valence band with a Mexican-hat dispersion shape exciton and trion bound states in two-dimensional semiconductors. Using a variational framework with the Rytova-Keldysh Coulomb interaction, it demonstrates that increasing the Mexican-hat width enhances binding energies, while deeper hats reduce them; notably, narrowing the hat can make trion formation more favorable than exciton formation. Introducing a monkey-saddle HOVHS to the valence band induces a power-law DOS and transmits singular features into the bound-state dispersions, including energy-degeneracy lifting and potential momentum-dark exciton/trion states. The results offer design rules for engineering 2D materials (e.g., InSe, Bernal-stacked graphene) to tailor bound-state spectra and optical properties for advanced optoelectronic applications.

Abstract

We investigate the role of van-Hove singularities (VHS) in a system's electronic band structure on the formation and properties of excitons and trions. We consider (i) the different parameters of a Mexican-hat-type dispersion of the valence band, which hosts a VHS at the band edge, and (ii) the presence of regular VHS or higher-order VHS (HOVHS). We find that for a given spin-degenerate Mexican-hat-shaped valence band, where a trion and exciton can form, trion formation becomes more favourable as the Mexican-hat dispersion becomes narrower. Also, we show that if the electronic band structure contains an HOVHS, then both the exciton and trion dispersion will also contain such a singularity. Therefore, a HOVHS in the valence band can suitably change the density of states (DOS) of the bound-state particle and lead to the generation of new states, which could impact the optical properties of the system. Our work provides a pathway to how 2D quantum materials, which host such singularities, can be engineered to favour a particular bound-state thus opening new avenues for these materials into potential applications.

Figures (12)

• Figure 1: Example of (inverted) Mexican-hat dispersion of form $A\bm{k}^2-B\bm{k}^4$. (Left) Surface plot, (right) plot along $k_x$, where the VHS points are indicated in red and the divergent effective mass is indicated in blue.
• Figure 2: (a) Valence band dispersion of the inverted Mexican-hat shaped dispersion described in Eq.(\ref{['Eq:val123']}). (b) Plot of changing Mexican-hat width $k_{max}$ for a fixed $\Delta M$ of $0.021$ eV.
• Figure 3: (a) Valence band dispersion of the Mexican-hat forms in Eq.(\ref{['eq:456-1']}). (b) Continuous binding energies line of the exciton and trion (total) binding energies of the system, where the ratio $A/B$ is equal to 0.035 throughout.
• Figure 4: Valence band dispersion (a) and DOS (b) of the Mexican-hat dispersion with monkey saddle term added, see Eq.(\ref{['Eq:val-mh-ms']}). The units of $D$ are eVÅ$^3$.
• Figure 5: (a) Excitonic dispersion of Mexican-Hat valence band dispersion with monkey saddle term added. From the system described in Fig. \ref{['fig:valwms']} and Eq.(\ref{['Eq:val-mh-ms']}). (b) Density of states of the excitonic dispersion. The units of $D$ are eVÅ$^3$.