Exciton States in Monolayer ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$ Probed by Upconversion Spectroscopy

Transitions metal dichalcogenides (TMDs) are direct gap semiconductors in the monolayer (ML) limit with fascinating optical and spin-valley properties. The strong optical absorption of up to 20% for a single ML is governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited exciton states in ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$ monolayers have so far been elusive because of their low oscillator strength and strong inhomogeneous broadening. Here, we show that encapsulation in hexagonal boron nitride results in an emission line width of the $\mathrm{A}:1s$ exciton below 1.5 meV and 3 meV in our ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$ monolayer samples, respectively. This allows us to investigate the excited exciton states by photoluminescence upconversion spectroscopy for both monolayer materials. The excitation laser is tuned into resonance with the $\mathrm{A}:1s$ transition, and we observe emission of excited exciton states up to 200 meV above the laser energy. We demonstrate bias control of the efficiency of this nonlinear optical process. We discuss the origin of the upconversion effect. Our model calculations suggest an exciton-exciton (Auger) scattering mechanism specific to TMD MLs involving an excited conduction band, thus generating high-energy excitons with small wave vectors. The optical transitions are further investigated by white light reflectivity, photoluminescence excitation, and resonant Raman scattering, confirming their origin as excited excitonic states in monolayer thin semiconductors.

Popular Summary

When thinned to sheets just one atom thick, transition metal dichalcogenides behave as semiconductors, offering potential applications in a wide range of thin, flexible optics and electronics. Their strong absorption of visible light is due to excitons, bound pairs of electrons, and positively charged holes. At high densities, excitons can scatter off one another, leading to the annihilation of one exciton as a second exciton absorbs its energy and enters a higher energy state (a process known as upconversion). Here, we show experimentally and theoretically that these types of interactions are qualitatively different in transition metal dichalcogenides when compared to conventional semiconductors.

First, we develop a theory that goes beyond usual analyses of excitons to show that exciton upconversion is an efficient, resonant process. This opens exciting new possibilities that we explore in our experiments. We use upconversion photoluminescence spectroscopy to study the excited exciton states in ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$ monolayers, which have so far not been accessible in conventional samples using standard techniques. These experiments reveal many firsts, including electrical control of exciton upconversion in ${\mathrm{MoSe}}_2$, identification of particular exciton excited states, and scattering between excitons in ${\mathrm{MoTe}}_2$.

These nonlinear optical effects give insights into exciton-exciton interactions, relevant physical processes at the heart of population inversion, and other density-dependent phenomena for devices such as lasers.

Figure 1

Upconversion spectroscopy in TMD monolayers. We present, for four different monolayer materials, resonant excitation experiments of the $\mathrm{A}:1s$ exciton at $T=4\mathrm{K}$, which result in PL emission at higher energy. The laser energy—equal to the $\mathrm{A}:1s$ transition energy—is marked by a vertical arrow. The upconversion emission peaks are labeled $\mathrm{A}:2s$ and $\mathrm{B}:1s$, where the origin of these peaks is confirmed in complementary experiments such as reflectivity and PLE. The results for ${\mathrm{WSe}}_2$ are reproduced from Ref. [16], and the ${\mathrm{MoS}}_2$ results from Ref. [31]. The inset in panel (a) shows a scheme of the sample. The inset in panel (b) shows the exciton-exciton Auger process, where one exciton annihilates and another one acquires total momentum and energy of the two particles.

Figure 2

Control of upconversion in ML ${\mathrm{MoSe}}_2$ for $T=4\mathrm{K}$. Sample No. 1: (a) Scanning a Ti-Sa laser across the $\mathrm{A}:1s$ transition, which results in upconversion emission of the A:$2s$ and $\mathrm{B}:1s$ transitions (black curve for excitation exactly at resonance). Blue symbols give the integrated upconversion intensity as a function of laser energy. (b) Reflection contrast for the same sample spot, confirming the energy positions of $\mathrm{A}:1s$, $\mathrm{A}:2s$, and $\mathrm{B}:1s$ transitions. (c) The power dependence of the upconversion signal shows an increase with a slope of roughly 1.64 (black symbols), as compared to the standard $\mathrm{A}:1s$ exciton emission with a slope of roughly half (0.88—red symbols) using a HeNe laser for excitation. (d) Contour plot (blue—below 50 counts; red—greater than 2000 counts) of upconversion PL intensity as the excitation laser is swept across the $\mathrm{A}:1s$ resonance. Sample No. 2: (e) Schematics of the charge tunable device. (f) Voltage control of upconversion. The signal is maximal in the neutral regime and gets weaker as the $n$-type regime favors trion and not neutral exciton absorption; the $\mathrm{B}:1s$ and $\mathrm{A}:2s$ emission are marked; a third emission peak of yet-to-be-determined origin appears at lower energy.

Figure 3

Exciton spectroscopy in ${\mathrm{MoTe}}_2$ monolayers encapsulated in hBN for $T=4\mathrm{K}$. (a) Differential reflectivity spectrum. The energy positions of the exciton transitions $\mathrm{A}:1s$, $\mathrm{A}:2s$, and $\mathrm{B}:1s$ are marked. (b) Excitation with a HeNe laser at 1.96 eV, resulting in hot PL of the $\mathrm{A}:2s$ state and PL for the $\mathrm{A}:1s$ state. The low-energy peak labeled “$T$” might be related to the trion or phonon replica. (c) Photoluminescence excitation measurements detecting the emission from the $\mathrm{A}:1s$ exciton. Peaks related to the resonant excitation of the $\mathrm{A}:2s$ and $\mathrm{B}:1s$ are marked. (d) Upconversion PL. The laser tuned into resonance with the $\mathrm{A}:1s$ state results in emission of about 120 meV higher energy, same as in Fig. 1.

Figure 4

Model of exciton upconversion—single-particle picture. Filled circles denote electrons; open circles denote unoccupied states in the valence band. Dashed arrows show real electronic transitions. (a) Intraband process enabled by excitonic effects. The resulting high-energy exciton involves carriers in bands $c$ and $v$; the final momentum ${\mathit{K}}_f={\mathit{K}}_1+{\mathit{K}}_2$ is large. (b) Resonant Auger process resulting in high-energy, low-wave-vector ${\mathit{K}}_f$ excitons involving the excited conduction band $c^{\prime }$.

Figure 5

Dependence of the coefficient $|A_n{|}^2$ on $n$ for $r_0=3a_B$. The red line shows the approximation $|A_n{|}^2=2.47\times {10}^{-7}/n^3$. The inset shows dependences $|A_1{|}^2$ (red), $|A_2{|}^2$ (blue), and $|A_3{|}^2$ (green) on the screening radius $r_0$. Dashed lines are fits $|A_1{|}^2=0.015(a_B/r_0{)}^2$, $|A_2{|}^2=3.46\times {10}^{-5}(a_B/r_0{)}^4$, and $|A_3{|}^2=6.63\times {10}^{-6}(a_B/r_0{)}^4$.

Figure 6

Charge tunable device. In differential reflectivity on the charge tunable device of Figs. 2 and 2, we identify the $\mathrm{A}:1s$ state and, at more negative bias, the charged exciton state (marked T for trion).

Figure 7

Raman spectroscopy in ML ${\mathrm{MoTe}}_2$, $T=4\mathrm{K}$. (a) Nonresonant Raman scattering using a HeNe laser. (b) Single-resonant Raman scattering as the excitation laser energy is one phonon energy $A_1^{\prime }$ above the $\mathrm{A}:1s$ state. (c) Double-resonant Raman experiments, as a phonon multiple ensures efficient relaxation from the optically excited $\mathrm{A}:2s$ state to the emitting $\mathrm{A}:1s$ state.