Energy renormalizations of resident carriers and excitons in transition metal dichalcogenide monolayers

Abstract

Energy renormalizations of resident carriers and excitons are studied theoretically, and compared with recent experiments of electrostatically-doped WSe$_2$ monolayers. The calculated energy renormalization of resident carriers, subjected to strong out-of-plane magnetic field, reveals the importance of dynamical screening in transition metal dichalcogenides. The energy renormalization of tightly bound excitons is analyzed through the exchange interaction between the electron (or hole) component of the exciton and resident carriers that share the same spin and valley quantum numbers. Our theory explains the weak energy shift of excitonic resonances despite the strong energy renormalization of resident carriers. We identify the dependence of the energy renormalization on the envelope function of a tightly-bound exciton, showing that unlike free electron-hole pairs, this energy renormalization is not the added renormalizations of a resident electron and resident hole.

Figures (8)

• Figure 1: The measured bandgap energy (filled symbols) and excitonic resonance energies (open circles) of WSe$_2$ monolayers as a function of CB electron density. Taken from Ref. Nguyen_Nat19. The inset shows photoluminescence spectra of WSe$_2$ monolayers.
• Figure 2: (a) Magneto-optical reflectance spectra from $K$ valley of a charge tunable WSe$_2$ monolayer at 4 K. Taken from Ref. Liu_PRL20. The out-of-plane magnetic field is 17.5 T. (b) Optical transition of the negative trion when resident electrons only populate the bottom CB valley at $K$'. (c) Optical transition of the exciton when resident holes only populate the VB valley at $K$.
• Figure 3: Color maps of helicity-resolved magneto-optical absorption spectra of an electrostatically hole-doped WSe$_2$ monolayer as a function of magnetic field and photon energy at 4 K. Taken from Ref. Dery_PRX25. The measured signal is $(1 - T/T_0)^\pm$, where $T$$(T_0)$ is the transmission (reference) spectrum, and $\pm$ refers to light with $\sigma_\pm$ polarization. The hole density is $1.7 \times 10^{12}$ cm$^{-2}$ in (a),(b) and $4.6 \times 10^{12}$ cm$^{-2}$ in (c),(d). (e) Schemes of optical excitations in valley-polarized WSe$_2$ monolayer with hole LLs in the VB valley at $K$.
• Figure 4: Energy renormalization and screening effects of resident holes in the static regime. The calculations simulate hBN-encapsulated WSe$_2$ monolayers at $B = 17.5\,$T (see Appendix \ref{['app:num']} for parameters). (a) Total energy per particle as a function of filled LLs in the valley at $K$. The calculations are performed for $N = \{6,8,10,12,14, 16\}$ filled LLs in the two valleys. The calculated values are marked by open symbols, among which the minimum values are marked by filled symbols. (b) The screening factor $F_{K}({x_q}) + F_{K'}({x_q})$ for several cases of $N_K$ when $N=14$.
• Figure 5: Energy renormalization of WSe$_2$ monolayers in the dynamical regime at $B = 17.5\,$T. (a) Same as in Fig. \ref{['fig:BGRe']}(a) but with inclusion of the Coulomb-hole energy. (b) Same as in (a) but for an electron-doped WSe$_2$ monolayer. (c) Screened exchange and Coulomb-hole energies of the lowest LL in a fully valley-polarized hole system with $N$ filled LLs. The self-energy of holes $\Sigma(0) = \Sigma_\text{sx}(0) + \Sigma_\text{Ch}(0)$ and the bandgap renormalization of free e-h pairs $\Delta E_\text{g} = \Sigma_\text{sx}(0) + 2 \Sigma_\text{Ch}(0)$ are shown by the green diamond and blue triangle symbols, respectively. The parameters used in the calculations are detailed in Appendix \ref{['app:num']}.