Tightly Bound Excitons in Monolayer ${\mathrm{WSe}}_2$

Exciton binding energy and excited states in monolayers of tungsten diselenide (${\mathrm{WSe}}_2$) are investigated using the combined linear absorption and two-photon photoluminescence excitation spectroscopy. The exciton binding energy is determined to be 0.37 eV, which is about an order of magnitude larger than that in III–V semiconductor quantum wells and renders the exciton excited states observable even at room temperature. The exciton excitation spectrum with both experimentally determined one- and two-photon active states is distinct from the simple two-dimensional (2D) hydrogenic model. This result reveals significantly reduced and nonlocal dielectric screening of Coulomb interactions in 2D semiconductors. The observed large exciton binding energy will also have a significant impact on next-generation photonics and optoelectronics applications based on 2D atomic crystals.

Figure 1

(a) Optical reflection image of ${\mathrm{WSe}}_2$ flakes on a Si substrate covered by a 300-nm ${\mathrm{SiO}}_2$ layer. A monolayer sample (middle) is outlined by dashed blue lines. (b) PL spectrum of monolayer ${\mathrm{WSe}}_2$ excited by a cw HeNe laser at 1.96 eV. (c) Emission spectrum of monolayer ${\mathrm{WSe}}_2$ under the excitation of femtosecond IR pulses centered at 1.07 eV. It consists of two features corresponding to the SHG (blue) and two-photon PL (red). The latter is magnified by 15 times. The PL excited by the cw HeNe laser (green) is included for comparison. (d) Excitation power dependence of the integrated SHG and two-photon PL.

Figure 2

(a) Linear absorption (red line, right axis) and 2PPL excitation spectrum (blue symbols, left axis) measured on monolayer ${\mathrm{WSe}}_2$ at room temperature. Each data point of the 2PPL excitation spectrum corresponds to an integrated PL (1.664–1.687 eV) normalized by the reference SHG signal from a $z$-cut quartz crystal according to Eq. (1). The uncertainty corresponds to the spectral resolution, determined by the bandwidth of the excitation pulse. $A$ and $B$ correspond to the fundamental exciton resonances arisen from transitions from the two highest energy spin-orbit split-off valance bands and the lowest energy conduction bands at the $K(K^{\prime })$ point of the Brillouin zone. $A^{\prime }$ and $A^{\prime \prime }$ denote the $2s$ state and a broad $p$ peak observed in one- and two-photon absorption, respectively. (b) Second-order numerical derivative of the linear absorption spectrum of (a). Black dashed line denotes the band edge energy of 2.02 eV determined from the fit described in the text.

Figure 3

(a) Representative PL spectra of monolayer ${\mathrm{WSe}}_2$ excited by femtosecond IR pulses centered at 0.85–1.1 eV. The spectra were normalized by the SHG intensity from a $z$-cut single crystal quartz plate recorded under identical experimental conditions. (b) Experimental 2PPL excitation spectrum (symbols) and fit (green line) including contributions from both excitons and band-to-band transitions (dotted red lines) as described in the text.

Figure 4

Exciton excitation spectrum of monolayer ${\mathrm{WSe}}_2$ determined experimentally in this work (left panel) is compared with the 2D hydrogenic model (right panel). Red lines denote the one-photon active states and the blue box is the unresolved two-photon active states. The exciton binding energy and the bottom of the continuum in the 2D hydrogenic model are chosen to match the values obtained from experiment.