Exciton dynamics in equilibrium and nonequilibrium regimes

TL;DR

This work offers a first-principles account of exciton physics in 2D insulators across equilibrium and nonequilibrium regimes, leveraging DFT, GW, and BSE to predict exciton binding energies, quasiparticle gaps, and optical spectra. It reveals a redshift–blueshift crossover of exciton energies with increasing photoexcited density in MoSi$_2$Z$_4$ monolayers and demonstrates the significant role of exciton–phonon coupling in temperature-dependent spectra and lifetimes, particularly in AlN. By coupling many-body theory with finite-temperature effects, it shows that strong Coulomb interactions in 2D platforms stabilize an electron–hole liquid phase at temperatures well above cryogenic limits, with MoSi$_2$Z$_4$ series offering room-temperature EHL under experimentally accessible densities. The findings highlight how dimensionality enhances Coulomb effects, enabling robust excitonic states and collective phases that could underpin future optoelectronic and quantum technologies. Collectively, the thesis provides a comprehensive ab-initio framework and concrete material candidates for observing and exploiting nontrivial exciton dynamics in 2D systems.

Abstract

The bound electron-hole pairs known as excitons govern the optical properties of insulating solids. While their behavior in equilibrium is well-understood theoretically, the nonequilibrium regime at high excitation densities-where phenomena like electron-hole liquids emerge - is less explored. This thesis presents a first-principles study of excitons in two-dimensional materials. We use the GW approximation and the Bethe-Salpeter equation to investigate their properties from equilibrium to nonequilibrium conditions. We first demonstrate how increasing photo-excited carrier density leads to a redshift-blueshift crossover of excitons. We then show that electron-phonon interactions critically modify optical spectra and exciton lifetimes at finite temperatures. Finally, we unify these effects to demonstrate the formation of an electron-hole liquid phase above a critical carrier density and below a critical temperature. Our work identifies how enhanced Coulomb interactions in two dimensions can stabilize this phase at significantly higher temperatures, proposing promising material candidates for observing these collective states.

Figures (35)

• Figure 1: Illustration of exciton formation in an insulating material. (a) Optical excitation of an electron from the valence band to the conduction band via an external pump with photon energy ($\hbar\omega$), and (b) exciton formation with binding energy $E_b$. (c) The energy levels $e_1$, $e_2$, and so on, of the bound excitons below the quasiparticle band gap ($E^{QP}$). (d) Optical absorption spectrum in an insulating material with excitonic effects (red) and without electron-hole interaction (EHI) in blue color.
• Figure 2: Schematic representation of a (left) tightly bound Frenkel exciton that has a radius of around the size of the unit cell; (right) Wannier-Mott exciton has a large radius that exceeds the unit cell size.
• Figure 3: Illustration of exciton types and optical transitions. (a) and (b) depict direct excitons with vertical optical transitions with conservation of momentum for excited electron-hole pairs. (c) Represents an indirect exciton, where an electron (or it could be a hole) has a lattice momentum $\hbar q$ with respect to its counterpart. The optical selection rules classify excitons into bright and dark types based on the spin configuration of the conduction electron and valence hole. Bright excitons, shown in (a), have the same spin, allowing them to absorb photons with zero momentum linear polarized light. Dark excitons, illustrated in (b), have opposite spins, leading to spin-forbidden optical transitions for linearly polarized light.
• Figure 4: A schematic representation of exciton formation in 3D (left) and 2D (right) dielectric material. The electric field lines between the quasi-electron and quasi-hole in a 3D system are screened by the dielectric environment of the material, However, in a 2D system, the electric field lines are relatively very less screened by the material's dielectric environment. This leads to a strong EHI between the quasiparticles in 2D materials and large binding energy of the excitons.
• Figure 5: Schematic representation of intralayer exciton (localized in the Layer BX$_2$), and interlayer exciton with the electron being localized in one layer (Layer BX$_2$), and the hole localized in another layer (Layer AX$_2$).