Valley-Polarized Exciton-Polaritons in a Monolayer Semiconductor

TL;DR

This paper reports the experimental observation of valley-polarized exciton-polaritons in monolayer MoS2 embedded in a microcavity, demonstrating room-temperature valley polarization in hybrid light-matter quasiparticles for potential valleytronic applications.

Contribution

It introduces the first evidence of valley-polarized exciton-polaritons in monolayer transition metal dichalcogenides within a microcavity, enabling polarization-sensitive control at room temperature.

Findings

Valley-polarized exciton-polaritons emit polarized light with spectral Rabi splitting.

Valley polarization persists at room temperature due to cavity effects and intervalley dynamics.

This work enables polarization-sensitive polaritonic devices operating at ambient conditions.

Abstract

Single layers of transition metal dichalcogenides are two-dimensional direct bandgap semiconductors with degenerate, but inequivalent, `valleys' in the electronic structure that can be selectively excited by polarized light. Coherent superpositions of light and matter, exciton-polaritons, have been observed when these materials are strongly coupled to photons, but these hybrid quasiparticles do not harness the valley-sensitive excitations of monolayer transition metal dichalcogenides. Here, we demonstrate evidence for valley polarized exciton-polaritons in monolayers of MoS$_2$ embedded in a dielectric microcavity. Unlike traditional microcavity exciton-polaritons, these light-matter quasiparticles emit polarized light with spectral Rabi splitting. The interplay of cavity-modified exciton dynamics and intervalley relaxation in the high-cooperativity regime causes valley polarized exciton-polaritons to persist to room temperature, distinct from the vanishing polarization in bare monolayers. Achieving polarization-sensitive polaritonic devices operating at room temperature presents a pathway for manipulating novel valley degrees of freedom in coherent states of light and matter.

Figures

Equations

$$p=\frac{\left(I_{+}-I_{-}\right)}{\left(I_{+}+I_{-}\right)}$$

$$p_{\text{bare}}=\frac{A_{\mathrm{bare}}}{1+\frac{2{\Gamma }_{\mathrm{v}}}{{\Gamma }_{\mathrm{ex}}}}$$

$$p_{\text{MC}}=\frac{A_{\mathrm{MC}}}{1+\frac{2{\Gamma }_{\mathrm{v}}}{{\Gamma }_{\mathrm{ex}}+{\Gamma }_{\mathrm{c}}}}$$

Full text

Confining photons to small volumes, such as between two mirrors, can enhance light-matter interactions and lead to coherent superpositions of light and matter, or polaritons Purcell (1946); Haroche and Kleppner (1989). This framework of cavity quantum electrodynamics (QED) is the foundation for strong, coherent interactions with light in both atoms Kimble (1998) and two-level solid state systems Reithmaier et al. (2004); Yoshie et al. (2004); Wallraff et al. (2004). Translating this approach to bosonic exciton-polariton quasiparticles in semiconductors Weisbuch et al. (1992); Houdré et al. (1994) enables new many-body coherent phenomena such as Bose-Einstein condensation in the solid-state Deng et al. (2010), with potential opto-electronic applications in ‘polaritonics’ Amo et al. (2010); Sanvitto and Kéna-Cohen (2016). Although the cavity QED parameter regimes vary greatly across these implementations, they generally share the spectral selectivity of high-quality resonators.

More recently, polarization selectivity has brought a new dimension to cavity QED. For example, accessing specific sublevels using polarized light can merge time-reversal symmetry breaking into chiral photonics Lenferink et al. (2014); Sayrin et al. (2015); Söllner et al. (2015). Although individual atoms allow strong coupling in circularly-polarized cavity QED Junge et al. (2013), the degenerate valley-specific excitons of transition metal dichalcogenides (TMDs) are a model material system for achieving polarization selectivity with bosonic exciton-polaritons (Fig. 1a).

TMDs are layered two-dimensional (2D) semiconductors that have a direct band gap in their monolayer form Mak et al. (2010); Splendiani et al. (2010). Inversion asymmetry in TMDs leads to strong spin-orbit splitting at the direct bandgap of the $K$ and $K^{\prime}$ valleys. Monolayer TMDs such as MoS2 or WSe2 can therefore support two different classes of energy degenerate excitons, identical in most properties, but with opposite Berry curvature and distinct response to light of opposite helicity depending on their valley pseudospin index Xiao et al. (2012) (Fig. 1b). The selectivity of valley phenomena has been exploited for polarization-dependent opto-electronics Mak et al. (2012); Zeng et al. (2012); Cao et al. (2012); Kioseoglou et al. (2012); Wang et al. (2012); Sallen et al. (2012), correlated spin-electron motion Mak et al. (2014), and proposed mechanisms for coherent information processing Rohling and Burkard (2012); Behnia (2012); Jones et al. (2013); Wang et al. (2016). Controlling the dynamics of valley-polarized excitons with polarization-sensitive cavity QED is an exciting possibility not yet understood.

Monolayer TMD materials can be interfaced with photonic cavities Gan et al. (2013); Wu et al. (2014); Schwarz et al. (2014); Wei et al. (2015) to enhance radiative coupling. As with excitons in semiconductor quantum wells, strongly coupled 2D exciton-polaritons have been observed by embedding monolayer TMDs in planar microcavities (MCs) Liu et al. (2015). The tightly bound excitons and large oscillator strengths in TMDs allow these quasiparticles to persist at room temperature Liu et al. (2015); Dufferwiel et al. (2015); Flatten et al. (2016); Lundt et al. (2017). Marrying the valley structure of excitons in TMD monolayers with cavity QED will extend polaritonics to a new regime in which two species of degenerate exciton-polariton quasiparticles can spatially co-exist in separate regions of momentum space and can be selectively excited by helical cavity fields. Understanding this polarization-sensitive cavity QED regime would make possible new explorations of coherent optical phenomena in 2D semiconductors and their layered heterostructures Low et al. (2016); Basov et al. (2016).

Here, we report the observation of valley-polarized exciton-polaritons in monolayer MoS2 embedded in a planar microcavity (Fig. 1a). These distinct degenerate light-matter quasiparticles are selectively coupled to circularly-polarized cavity modes. In contrast to excitons in bare monolayers, the MC exciton-polaritons preserve valley polarization at room temperature, which is explained by the competition between the exciton valley decay time and the cavity-enhanced total decay rate of the exciton-polaritons in the cavity QED system. The ability to manipulate pseudospin dynamics in hybrid optical devices with 2D materials opens new opportunities for valley-sensitive 2D material photonics with engineered chiral light-matter interactions.

Results

The monolayer MoS2 microcavity (MC-MoS2) samples consist of a single layer of monolayer MoS2 embedded in a distributed Bragg reflector (DBR) microcavity (MC), as illustrated in Fig. 1a. The DBRs are made from alternating silicon dioxide and silicon nitride layers grown on top of a Si substrate. Separate MCs were fabricated both with the cavity on resonance with and detuned from the MoS2 $A$-exciton for use in different experiment configurations, as we will describe. The monolayer flakes of MoS2 are synthesized by chemical vapor deposition and transferred on top of the bottom DBR before the top DBR is deposited so they are at the center of the inner cavity. Both as-grown and transferred monolayer MoS2 show $A$-exciton photoluminescence (PL) peak centered at 1.855 eV with an inhomogeneously broadened full width half-maximum linewidth $\Gamma_{\rm ex}=64$ meV when collected with a microscope objective. Measured with a lens instead, the $A$-exciton PL is centered at 1.81 eV with linewidth of 90 meV due to the increased inhomogeneous broadening of the larger spot.

We first confirm the presence of strongly coupled light-matter quasiparticles in the MC-MoS2 by observing Rabi splitting in both reflectivity and PL spectra. In regions of the MC where there is no monolayer MoS2, the reflectivity spectrum shows only a single dip with width $\Gamma_{\rm c}\approx 10$ meV, which is somewhat broadened by the non-zero collection angle from the cavity (Fig. 2a top). In regions with monolayer MoS2, the MC reflectivity (PL) spectrum shows two dips (peaks) (Fig. 2b). These resonance features are signatures of the upper polariton (UP) and lower polariton (LP) quasiparticle eigenstates in the MC.

Exciton-polariton behavior at room temperature is verified from an anti-crossing in the energy dispersion obtained from angle-resolved white light reflectivity (Fig. 2c). As the angle $\theta$ is swept, the cavity resonance changes energy and detunes from the exciton absorption. For this measurement, the MC is designed to be red detuned from the MoS2 exciton so that the modes are resonant at a non-zero angle ($\theta\approx$$$) and the modified MC-MoS2 dispersion is clearly visible.

For the MC-MoS2 sample shown in Fig. 2d, for \theta<$$$, the UP energy is nearly constant and the LP energy blue-shifts with angle. For \theta>$$$, the UP and LP behavior reverses, but the dispersion curves do not touch. This anti-crossing between the UP and LP branches is a feature of the strong light-matter coupling in which the coherent exchange rate dominates the incoherent losses. Under these conditions, a resonant excitation creates exciton-polariton quasiparticles that are nearly equal superpositions of material exciton and cavity photon. The Rabi splitting, $\hbar\Omega$, between the UP and LP on resonance is $39\pm 5$ meV (Fig. 2d). The interaction coupling constant, $g$, between 2D excitons and cavity photons was calculated from a two-mode coupled oscillator model Savona et al. (1995) as $g=28\pm 2$ meV. This room temperature measurement is consistent with the value reported for strongly coupled monolayer MoS2 exciton-polaritons in a MC Liu et al. (2015). The dispersion and mode splitting structure verify that the MC at room temperature is populated by exciton-polaritons in a regime dominated by coherent exchange between light and matter excitations.

The polariton energies do not blue-shift at lower temperatures in contrast to excitons in bare MoS2 on thermally grown SiO2. This feature has been explained in previous reports as due to compressive strain at the interface from the different thermal expansion coefficients of the SiO2 substrate and monolayer MoS2 Liu et al. (2015). MoS2 covered with other oxides such as HfO2 and Al2O3 also show reduced temperature-dependent shifts in band gap Plechinger et al. (2012).

With the hybrid light-matter quasiparticles established in MC-MoS2, the valley pseudospin polarization of the exciton-polaritons was explored using polarized photoluminescence. For this measurement, the DBR layer thicknesses were chosen so the cavity dispersion is resonant with the MoS2 exciton at normal incidence. Polarized PL was first measured with near resonant pump energy $E_{\textrm{ph}}$ ($E_{\textrm{ph}}=1.938$ eV for MC-MoS2 and $E_{\textrm{ph}}=1.987$ eV for bare MoS2) at cryogenic temperatures (8 K) to maximize the valley polarization Mak et al. (2012); Zeng et al. (2012); Cao et al. (2012); Kioseoglou et al. (2012); Sallen et al. (2012). $E_{\textrm{ph}}$ was selected to have the same energy differences with the MC-MoS2 and the bare MoS2 emission at room temperature to obtain similar pumping efficiency to the valley-specific MoS2 excitons. Excitons with in-plane wavevector $k_{\parallel}\neq 0$ are pumped in the monolayer with an off-resonant beam at an oblique angle. Momentum relaxation will populate the $k_{\parallel}=0$ exciton-polaritons in the MC-MoS2, which will emit light collected at normal incidence. If the excitation of exciton-polaritons is valley-sensitive, then the emission from right- and left-circularly polarized cavity modes will be asymmetric. Circular polarization of $k_{\parallel}=0$ normal emission from Rabi-split UP and LP modes indicates that the optical properties of the MC-MoS2 are determined by exciton-polariton quasiparticles with definite valley character.

The emission spectrum in Fig. 3a shows the Rabi-split UP and LP resonances at 1.805 eV and 1.825 eV, respectively. Circular polarization of the cavity emission is evident. As described in the Supplementary Information, care is taken that the off-resonant circularly polarized excitation from the pump at angle \theta=$$$ creates nearly equal s$and$p$ linear polarized electric field components in the DBR MC so the circular polarization of the total pumped cavity field is preserved.

To quantify the measurements, the total PL polarization $p$ is defined as

[TABLE]

where $I_{+}$ and $I_{-}$ are the helicity-resolved PL intensities. At 8 K, both UP and LP show significant polarizations of 19$\%$ and 29.5$\%$, respectively (Fig. 3a). For bare MoS2 at the same temperature (Fig. 3d), we observe $p=40\%$ for the $A$-exciton, a typical MoS2 polarization at cryogenic temperatures Cao et al. (2012); Zeng et al. (2012); Kioseoglou et al. (2012). A low-temperature defect state Tongay et al. (2013) (labeled as $D$) is present in the bare MoS2 which does not exhibit polarization, confirming the polarization arises from the valley-pumped exciton-polaritons and not measurement bias. The polarization for both UP and LP modes increases for $E_{\rm ph}$ closer to the exciton resonance, following the behavior of bare MoS2 Mak et al. (2012); Zeng et al. (2012); Cao et al. (2012); Kioseoglou et al. (2012); Sallen et al. (2012) (see Supplementary Information). The emission polarization of the cavity polariton modes in the strong coupling regime confirms the presence of valley polarized exciton-polaritons in MoS2 microcavities.

At a temperature of 8 K, both MC-MoS2 and bare MoS2 exhibit significant and comparable polarizations. Increasing to room temperature, $p$ in bare MoS2 decreases close to 0$\%$ (Fig. 3e, f). The MC-MoS2, on the other hand, retains a non-zero polarization of 7.5$\%$ and 13$\%$ for the UP and LP. (Fig. 3b, c).

Because emission polarization from valley states is determined by the relative exciton relaxation and intervalley scattering rates Mak et al. (2012); Kioseoglou et al. (2012), the evolution of $p$ with temperature probes valley scattering dynamics. Fig. 4a shows the temperature dependence $p(T)$ from both bare MoS2 and MC-MoS2. In bare MoS2, the low-temperature valley polarization $p$ of $A$-exciton vanishes quickly as the temperature is raised above 100 K. This behavior originates from the ratio of the exciton and valley relaxation rates, as predicted by a rate equation model (see Supplementary Information) Mak et al. (2012); Kioseoglou et al. (2012):

[TABLE]

where $A_{\rm bare}$ is a constant depending on optical pumping, $\Gamma_{\rm ex}$ is the exciton relaxation rate, and $\Gamma_{\rm v}$ is the intervalley scattering rate. The temperature evolution of $p$ can therefore be interpreted as a measurement of the ratio $\Gamma_{\rm v}/\Gamma_{\rm ex}$. At elevated temperatures, $\Gamma_{\rm v}$ increases due to thermally-activated phonon-assisted intervalley scattering Kioseoglou et al. (2012); Zeng et al. (2012) and emission polarization is suppressed.

The temperature-dependent emission polarization for exciton-polaritons in MC-MoS2 is very different from bare MoS2. The low-temperature UP and LP polarizations $p_{\rm UP}$ and $p_{\rm LP}$ are slightly smaller than that in bare MoS2, which is expected due to the non-perfect circular polarization of the cavity field from oblique incidence (see Supplementary Information), the differential shift of the exciton energy with temperature, and the inhomogeneity of the MoS2 flakes in the collection region of the cavity. At room temperature, the polarizations $p_{\rm UP}(T)$ and $p_{\rm LP}(T)$ decrease smoothly to 7.5$\%$ and 13$\%$, in contrast to the vanishing polarization in bare MoS2.

We explain this difference using a valley-sensitive cavity rate model accounting for coherent exchange and incoherent scattering (Fig. 4b). Our phenomenological model is a generalization of the standard steady state master equation approach for interacting boson modes in cavity QED Laussy et al. (2009), modified to include two distinct MC photon modes (of different polarization) coupled to two distinct exciton modes (for $K$ and $K^{\prime}$ valleys). The cavity QED rate equations are augmented with incoherent intervalley scattering between each bosonic valley mode with rate $\Gamma_{\rm v}$ proportional to the exciton population of the other valley, and the exciton and photon modes relax with rates $\Gamma_{\rm ex}$ and $\Gamma_{\rm c}$, respectively. Details of the valley-sensitive cavity QED model are in the Supplementary Information. In the high cooperativity regime ($4g^{2}\gg\Gamma_{\rm c}\Gamma_{\rm ex}$), which is necessarily satisfied for the strong coupling regime for the MoS2 MCs, the polarization of the steady state cavity emission takes a convenient form:

[TABLE]

Eq. (3) has the same structure as Eq. (2) describing a bare monolayer, but relaxation now occurs equally through both exciton and cavity channels. Importantly, only the excitonic part of the exciton-polariton quasiparticle experiences the intervalley scattering while the polarized photonic amplitudes do not couple for a good cavity with negligible mode mixing. The ratio in the denominator of Eq. (3) is therefore reduced compared to the bare MoS2. Radiative decay of the exciton-polaritons through cavity emission occurs before incoherent valley scattering, and the polarization of the output field persists even at elevated temperatures. Additional details of this model are in the Supplementary Information.

This picture is confirmed from the temperature dependence $p(T)$. Although the homogeneous exciton radiative lifetime is highly temperature dependent Moody et al. (2015); Robert et al. (2016), the total exciton decay time in MoS2 has been found to be nearly temperature independent $\tau_{\rm ex}=\hbar/\Gamma_{\rm ex}=4$ ps Lagarde et al. (2014); Palummo et al. (2015). The intervalley scattering rate is proportional to the phonon thermal population $\Gamma_{\rm v}\sim\exp\left(-E/k_{\rm B}T\right)$ Zeng et al. (2012). These assumptions allow $p_{\rm bare}$ to be well-fit by Eq. (2) with $A_{\rm bare}=0.413\pm 0.009$ and $E=35\pm 4$ meV.

Using this same phonon model parameters as inputs to Eq. (2) yields a two-parameter fit for $p_{\rm MC}$ with the amplitude $A_{\rm MC}$ and $\Gamma_{\rm c}$ the only free parameters (Fig. 4a). The extracted $\Gamma_{\rm c}=4.2$ meV (UP) and 5.2 meV (LP) are consistent with the intrinsic linewidth (4 meV without angle broadening) of our MC, demonstrating that this valley-sensitive cavity model is a self-consistent description of the exciton-polariton polarization. The good agreement of the valley-sensitive cavity model with the emission polarization verifies the observation of valley polarized exciton-polaritons with modified dynamics distinct from typical valley excitations in monolayer semiconductors.

The preservation of the polarized emission from light-matter quasiparticles in MoS2 implies that the two classes of exciton-polariton with distinct valley index presented in Fig. 1 can be selectively excited. It is therefore necessary to treat the TMD exciton-polariton system as a having two classes of exciton-polariton, each with upper and lower branches. The optical coherence possible between these distinct, spatially co-existing polaritonic quasiparticles is determined by both the dynamics of intervalley scattering and the photonic cavity.

In summary, we have established the existence of strongly-coupled exciton-polaritons with polarized valley pseudospin in a 2D TMD semiconductor. These hybrid light-matter quasiparticles can be selectively pumped and probed in photonic microcavities using circularly polarized light. The dynamics of these polarization-sensitive quasiparticles are distinct from valley excitons in TMD monolayers due to the cavity photon, representing ‘half’ of the hybrid quasiparticle, being insensitive to intervalley scattering, resulting in preservation of appreciable exciton-polariton valley polarization at room temperature. The capability to select distinct valley-polarized light-matter quasiparticles in cavity QED with circular polarization makes possible a platform to bring the valley and spin degrees of freedom to two-dimensional semiconductor polaritonics Low et al. (2016); Basov et al. (2016).

Methods

Sample preparation. The DBR is fabricated by depositing alternating layers of SiO2 and Si3N4 on a silicon wafer substrate using plasma-enhanced chemical vapor deposition (PECVD). The top DBR has fewer pairs than the bottom to favor emission in the detector direction. The thickness of the inner cavity region of SiO2 between the DBRs corresponds to $\lambda/2n$, with $\lambda$ near the MoS2 $A$-exciton transition wavelength and $n\approx 1.45$ the index of refraction of SiO2. Monolayer MoS2 is grown onto a SiO2/Si wafer by chemical vapor deposition (CVD) at atmospheric pressure Lee et al. (2012). The physical and optical properties of the MoS2 monolayers are characterized through atomic force microscopy, optical microscopy, Raman spectroscopy, and PL measurements (see Supplementary Information). The CVD-grown monolayer was transferred using a polycarbonate film Lin et al. (2011); Park et al. (2010) onto the bottom DBR, and the system was then encapsulated by growing a top DBR using PECVD. Both as-grown and polycarbonate-transferred monolayer MoS2 have a direct-gap transition of the $A$-exciton at 1.855 eV with linewidth around 64 meV. Details of CVD procedures, sample structure, and characterization can be found in the supplementary information.

Optical measurement. For the MC-MoS2, angle-resolved reflectivity measurements were performed using a goniometer with angular resolution of [math]. A stabilized Tungsten-Halogen light source (Thorlabs) was used as the white light source. The spot size on the sample is estimated at 200 $\mu$m. The reflected spectrum was analyzed with a fiber-coupled spectrometer and CCD (Andor). For polarized PL measurements, emission was collected with a lens along the normal direction using the same spectrometer. A tunable CW dye laser (Matisse 2DR) with linewidth less than 20 MHz was used to pump the sample from 600 to 645 nm with intensity 9.5 W/cm2 over a spot size of $\sim 200$ $\mu$m. The samples were loaded inside an optical cryostat (Advanced Research Systems) capable of reaching 6 K. For all the data shown, the MC is pumped with $\sigma_{+}$ circularly polarized light and the $\sigma_{+}$ and $\sigma_{-}$ polarizations are resolved in collection. The same conclusions are achieved by pumping with $\sigma_{-}$ light. Reported best-fit parameters are obtained from weighted least-squares fitting with parameter uncertainties estimated using resampling. For polarized PL measurements on the bare MoS2, pumping and collection were performed using an objective (spot size $\sim 1\mu$m) to minimize the inhomogeneous broadening over the CVD monolayer to obtain the intrinsic polarization of the material.

Acknowledgments

This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0012130 (cavity spectroscopy), by the National Science Foundation MRSEC program under Grant No. DMR-1121262 (transfer and device assembly), and by the National Science Foundation under Grant No. DMR-1507810 (CVD growth). This work made use of the EPIC and KECK-II facilities of the NUANCE Center at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF NNCI-1542205); the MRSEC program (NSF DMR-1121262) at the Materials Research Center; the International Institute for Nanotechnology (IIN); the Keck Foundation; and the State of Illinois, through the IIN. This work utilized Northwestern University Micro/Nano Fabrication Facility (NUFAB), which is partially supported by Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF NNCI-1542205), the Materials Research Science and Engineering Center (NSF DMR-1121262), the State of Illinois, and Northwestern University. J.D.C. is supported by the Department of Defense through the National Defense Science and Engineering Fellowship (NDSEG) Program. J.D.C also gratefully acknowledges support from the Ryan Fellowship and the IIN. N.P.S. acknowledges support as an Alfred P. Sloan Research Fellow.

Author contributions

N.P.S. and Y.J.C. conceived the experiments. Y.J.C. fabricated the MC. J.D.C. and V.P.D. synthesized the monolayers. T.K.S. and Y.J.C. performed material characterization and transfer. Y.J.C. performed measurements and modeling. Y.J.C. and N.P.S co-wrote the paper. All authors discussed the results and commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.