Population Pulsation Resonances of Excitons in Monolayer ${\mathrm{MoSe}}_2$ with Sub-$1\mu \mathrm{eV}$ Linewidths

Monolayer transition metal dichalcogenides, a new class of atomically thin semiconductors, possess optically coupled 2D valley excitons. The nature of exciton relaxation in these systems is currently poorly understood. Here, we investigate exciton relaxation in monolayer ${\mathrm{MoSe}}_2$ using polarization-resolved coherent nonlinear optical spectroscopy with high spectral resolution. We report strikingly narrow population pulsation resonances with two different characteristic linewidths of 1 and $<0.2\mu \mathrm{eV}$ at low temperature. These linewidths are more than 3 orders of magnitude narrower than the photoluminescence and absorption linewidth, and indicate that a component of the exciton relaxation dynamics occurs on time scales longer than 1 ns. The ultranarrow resonance ($<0.2\mu \mathrm{eV}$) emerges with increasing excitation intensity, and implies the existence of a long-lived state whose lifetime exceeds 6 ns.

Figure 1

(a) Depiction of the dispersion relation for delocalized excitons, where the $x$ axis represents the exciton center of mass momentum. In this picture, only excitons inside of the light cone can efficiently radiatively recombine. (b) Depiction of pump and probe fields interacting with a ${\mathrm{MoSe}}_2$ monolayer. A narrow bandwidth pump laser selectively excites excitons of a particular energy (shown here as green). The interference of the pump and probe laser fields gives rise to a population pulsation resonance. (c) In an inhomogeneous distribution of two-level systems composed of states ($|0⟩$ and $|+⟩$), both hole-burning and population pulsation effects can contribute to a ${\chi }^{(3)}$ response. Here, we show two examples of the perturbation sequence up to third order in the applied fields. $E_1$ and $E_2$ are the probe and pump fields at frequencies ${\omega }_1$ and ${\omega }_2$, respectively. $P_{+}$ is the polarization, and $n_{+}$ is the excited state population. The superscripts label the perturbation order. The population pulsation effect results in a modulation of the state populations at the pump-probe difference frequency.

Figure 2

(a) Degenerate DR spectrum showing the exciton and trion resonance, consistent with low temperature photoluminescence (PL) measurements (inset). The colored lines indicate the spectral positions of the nondegenerate DR spectra shown on the right. (b)–(d) High resolution nondegenerate DR measurements as a function of pump position [as indicated in inset (a)], showing narrow DR resonances for different pump energies (cross-linearly polarized pump and probe). Linewidths are extracted from fits of a weighted contribution from both the real and imaginary parts of the same complex Lorentzian function. (e) The linewidth is observed to increase linearly with increasing pump power revealing a zero power intercept of $1.53\pm 0.04\mu \mathrm{eV}$ and a slope of $8.3\pm 0.6\mathrm{neV}/\mu \mathrm{W}$ (for $20\mu \mathrm{W}$ probe power at pump position $c$).

Figure 3

Polarization dependent differential reflectivity. (a) The low power ($2\mu \mathrm{W}$ pump and probe) DR response has a linewidth of $0.8\mu \mathrm{eV}$ FWHM for cross-linearly polarized pump and probe (blue). The negligible resonance for cross-circularly polarized pump and probe (red) is a consequence of the valley-dependent optical selection rules. The pump energy is 1.655 eV. (b) Energy level diagram of the valley exciton system. Direct exciton transitions occur at $K$ valleys forming two exciton subsystems with $\sigma \pm$ polarized optical selection rules. We model the exciton as a single state for each valley. The exciton relaxation rate (${\mathrm{\Gamma }}_r$), intervalley relaxation rate (${\mathrm{\Gamma }}_v$), nonradiative decay rate to long-lived state (${\mathrm{\Gamma }}_{\mathrm{nr}}$), and long-lived state decay rate (${\mathrm{\Gamma }}_{\mathrm{ll}}$) are shown.

Figure 4

Power dependent cross-linear and co-circular differential reflectivity. The reflected pump and probe are simultaneously detected and the two powers are increased together. $P_0$ corresponds to $10\mu \mathrm{W}$. At $P_0$, the cross-linearly (a) and co-circularly (b) polarized spectra have similar linewidths of 1.8 and $2.5\mu \mathrm{eV}$, respectively. The amplitude of each spectrum is normalized, and the data are stacked to highlight the changes of line shape with power. The cross-linearly polarized data show a power dependent broadening, consistent with an increase of the nonradiative decay rate, ${\mathrm{\Gamma }}_{\mathrm{nr}}$. At higher powers a narrow peak emerges in the co-circularly polarized spectra whose width is related to the decay rate of the long-lived states, ${\mathrm{\Gamma }}_{\mathrm{ll}}$.