Many-body theory of optical absorption in doped two-dimensional semiconductors

Abstract

In this article, we use a many-body approach to study the absorption spectra of electron-doped two-dimensional semiconductors. Optical absorption is modeled by a many-body scattering Hamiltonian which describes an exciton immersed in a Fermi sea. The interaction between electron and exciton is approximated by an effective scattering potential, and optical spectra are calculated by solving for the exciton Green's function. From this approach, a trion state can be assigned as a bound state of an electron-exciton scattering process, and the doping-dependent phenomena observed in the spectra can be attributed to several many-body effects induced by the interaction with the Fermi sea. While the many-body scattering Hamiltonian can not solved exactly, we reduce the problem to two limiting solvable situations. The first approach approximates the full many-body problem by a simple scattering process between the electron and the exciton, with a self-energy obtained by solving a Bethe-Salpeter equation (BSE). An alternate approach assumes an infinite mass for the exciton, such that the many-body scattering Hamiltonian reduces to a Mahan-Noziéres-De Dominicis (MND) model. The exciton Green's function can then be solved numerically exactly by a determinantal formulation, and the optical spectra show signatures of the Fermi-edge singularity at high doping densities. The full doping dependence and temperature dependence of the exciton and trion lineshapes are simulated via these two approximate approaches, with the results compared to each other and to experimental expectations.

Band nesting and exciton spectrum in monolayer MoS2

“…For example, contradictory results of DFT studies of MoS 2 ground state have been reported 35,39,[60][61][62] , some suggesting that MoS 2 has a ground exciton state that is indirect in exciton center-of-mass momentum 61,62 . In addition, excitonic spectrum depends heavily on screening of interactions due to dielectric environment [63][64][65] and carriercarrier screening for doped samples 66,67 .…”

Excitonic theory of doping-dependent optical response in atomically thin semiconductors

“…Ab initio calculations of the trion binding energy are commonly available for monolayer TMDCs [30][31][32][33][34]. In contrast, a complete fully microscopic theory of the doping-dependent absorption spectra has not been provided so far: Available theoretical studies are based on phenomenological approaches which start from approximate variational exciton and trion states [35][36][37][38][39][40][41][42][43]. Most of these studies also rely on phenomenological momentumindependent contact Coulomb potentials [35,36,38,39] or unscreened two-dimensional Coulomb potentials neglecting the influence of the dielectric environment [43].…”

“…In some works, excitons and doping densities are also composed of independent electrons [39,43]. Moreover, available theoretical studies assume either equal electron and hole masses [36, 38-40, 42, 43] or infinite hole masses [37,43].…”

Doping-induced non-Markovian interference causes excitonic linewidth broadening in monolayer WSe$_2$

“…Due to the lack of exactly calculated scattering continua, previous theories only explained specific aspects of the experimentally observed features like doping-dependent excitonic and trionic oscillator strengths [35][36][37]. Predicted exciton-trion energy separations already spanned from values comparable to experiments [33,35,[37][38][39] to overestimates [36]. However, no description could quantitatively explain the interplay of measured exciton-trion energy separation and simultaneously occurring exciton linewidth broadening, which was underestimated in previous theories [36][37][38]40] compared to experiments [19][20][21].…”