Control of excitons in multi-layer van der Waals heterostructures

Van der Waals heterostructures composed of ultrathin layers of transition metal dichalcogenides (TMD), such as MoS₂, WSe₂, etc., offer an opportunity to realize artificial materials with designable properties, forming a new platform for studying basic phenomena and developing optoelectronic devices.¹ In the TMD structures, excitons have high binding energies and are prominent in the optical response. The energy, intensity, and polarization of exciton emission give information about the electronic, spin, and valley properties of TMD materials.^2–23 

The exciton phenomena are expected to become even richer in structures that contain two 2D layers. The energy-band diagram of such a coupled quantum well (CQW) structure is shown schematically in Figure 1(b). Previous studies of GaAs,²⁴ AlAs,²⁵ and InGaAs²⁶ CQWs showed that excitons in these structures can be effectively controlled by voltage and light. Two types of excitons are possible in a CQW structure. The spatially direct excitons (DXs) are composed of electrons and holes in the same layer, while the indirect excitons (IXs) are bound states of electrons and holes in the different layers separated by a distance d (Figure 1(b)). IXs can form quantum degenerate Bose gases.^27,28 The realization and control of quantum IX gases was demonstrated^29,30 in GaAs CQW structures at temperatures T below a few degrees Kelvin. In a recent theoretical work,³¹ it was predicted that the large exciton binding energies in TMD CQW structures may bring the domain of these phenomena to high temperatures. On the other hand, DXs in TMD CQW structures have high oscillator strength, making these structures good emitters.^2–23 The CQW structures allow the control of the exciton emission by voltage. These properties make the CQW structures an interesting new system for studying exciton phenomena in the TMD materials.

The DX binding energy $EDX$ is larger³¹ than $EIX$ of the IXs, and so, in the absence of an external field, the DXs are lower in energy. The electric field F normal to the layers induces the energy shift $eFd$ of IXs. The transition between the direct regime where DXs are lower in energy to the indirect regime where IXs are lower in energy occurs when $eFd>EDX−EIX$⁠.²⁶ Both the direct and indirect regimes show interesting exciton phenomena. The indirect regime was considered in earlier studies of GaAs,²⁴ AlAs,²⁵ InGaAs,²⁶ and TMD^18,21 CQW structures. The direct regime in the TMD CQW structures is considered in this work. Exploring the direct regime is essential for understanding both the universal properties of complex exciton systems in the CQW structures and the specific properties of direct excitons in the TMD layers. We found that the exciton spectra in the direct regime have three exciton emission lines. The ability to control the CQW structure by voltage provides an important tool for understanding the complex exciton emission in the TMD structures. The measured dependence of exciton spectra on the voltage, temperature, and excitation indicated that the lines correspond to the emission to neutral and charged excitons.

The structure studied here was assembled by stacking mechanically exfoliated layers on a Si/SiO₂ substrate, which acts as a global backgate (Figure 1(a)). The top view of the device showing the contours of different layers is presented in Figure 1(c). The CQW is formed where the two MoS₂ monolayers, separated by a hexagonal boron nitride (hBN) bilayer, overlap. The upper 20–30 nm thick hBN served as a dielectric cladding layer for a top graphene electrode. The voltage V_g applied between the top graphene layer and a backgate was used to create the bias across the CQW structure.

The excitons were generated by continuous wave (cw) semiconductor lasers with excitation energies $Eex=3.1$⁠, 2.3, or 1.96 eV focused to a spot of diameter $∼5 μm$ (the circle in Figure 1(c)). The photoluminescence (PL) spectra were measured using a spectrometer with a resolution of 0.2 meV and a CCD. In the time-resolved PL measurements, the excitons were generated by a pulsed semiconductor laser with $Eex=3.1 eV$⁠, and the emitted light was diffracted by the spectrometer and detected by a photomultiplier tube and time correlated photon counting system. The measurements were performed in a ⁴He cryostat.

Figure 2 shows the PL spectra at different temperatures T. At the lowest T, the spectrum consists of two high-energy emission lines with the linewidth of $∼20 meV$ and a broader low-energy line. Additional data and analysis presented below suggest that the high-energy lines correspond to the emission of neutral DXs while the low-energy line to the emission of charged DXs also known as trions.

The energy splitting of 25 meV between the high-energy emission lines constitutes only 5% of the MoS₂ exciton binding energy^{7,8,12–16,20,22} of about 0.5 eV. It is also much smaller than 0.2 eV energy difference of the A and B excitons³ caused by the spin-orbit splitting of the valence band (see Figure 4(c)). These data indicate that the high-energy lines represent different species of A excitons. They can be A excitons with different electron spin states. The calculated 10% difference³² in the masses, 0.44 vs. $0.49m0$⁠, of the conduction band spin states results in a 5% difference in the reduced electron-hole masses and, in turn, exciton binding energies. This leads to the energy splitting $∼25 meV$ consistent with the experiment.

It is worth noting that the two MoS₂ layers in the structure have inequivalent dielectric environment (Figure 1). This may lead to the difference in the binding energy of excitons in these layers in the effective mass approximation.³³ However, experimental and theoretical studies show that the TMD excitonic states with large binding energy are robust to environmental perturbations,¹⁵ meaning the exciton energy is the same for the two MoS₂ layers in the structure. Although dielectric environment changes the exciton binding energy,³³ it also changes the self-energies of the electron and the hole. For the excitons in GaAs-based³⁴ systems, these two contributions to the total exciton energy partially cancel one another. A similar cancellation presumably occurs in van der Waals heterostructures.

The lower-energy emission line is shifted by about 50 meV from the first two (Figure 2). This shift is in the range, 20–50 meV, of trion binding energies reported^5,10–12 for monolayer MoS₂. The relative intensity of the high-energy exciton lines increases with T (Figure 2), which is consistent with the thermal dissociation of trions. The observed red shift of the lines with increasing temperature originates from the band gap reduction, which is typical in semiconductors,³⁵ the TMDs included.^11,20,36,37

Figure 3 shows the dependence of the exciton PL on the excitation power $Pex$⁠. The relative intensity of the trion line increases with $Pex$ (Figure 3). This effect may be due to an enhanced probability of trion formation at larger carrier density. A similar increase in the trion PL intensity relative to the exciton was observed in earlier studies of GaAs CQW structures.³⁸ 

Figure 4 shows that the polarization of exciton emission can be controlled by the helicity of optical excitation. For a circularly polarized excitation nearly resonant with the exciton line, a high degree of circular polarization $∼30%$ of exciton PL is observed (Figures 4(a) and 4(b)), which is consistent with studies of monolayer TMD.^4–6,9,17 This observation indicates that the spin relaxation time is long compared to the exciton recombination and energy relaxation times.³⁹ The conventional explanation for the slow spin relaxation of excitons invokes spin-orbit coupling (SOC) and spin-valley coupling effects. As illustrated in Figure 4(c), the SOC splits valence band of the MoS₂ monolayers, leading to the appearance of the aforementioned A and B exciton states. The B excitons are $∼0.2 eV$ higher in energy, and their contribution to the PL is negligible. The A excitons can come from either K or $K′$ valley. It is important however that the spin and valley indices are coupled, so that exciton spin relaxation requires inter-valley scattering (Figure 4(c)). If this scattering is weak, the spin relaxation can be long. Virtually, no circular polarization is observed for the nonresonant optical excitation (Figure 4(b)), indicating that the high-energy photoexcited carriers loose their spin polarization during energy relaxation. Our time-resolved PL measurements revealed that the exciton and trion lifetimes are short, shorter than the 0.25 ns resolution of the photon counting system. Such small lifetimes facilitate the realization of the regime where the spin relaxation time is long compared to the exciton recombination time, and therefore, the polarization of exciton emission remains high.

Figure 5 shows the gate-voltage dependence of the exciton PL. The small exciton lifetime $<0.25 ns$ indicates the direct regime in the studied range of voltage because the IX lifetimes are expected to be in the ns range.^18,21,23,31The positions of the exciton lines remain essentially unchanged while the trion line exhibits a red shift with the slope $≲0.3 meV$ per 1 V of V_g. The smallness of the shifts of the lines corroborates the conclusion that the CQW is in the direct regime. Indeed, if we assume that the electric field in the device is uniform, the IX energy shift with voltage should be $δEIX/Vg=eFd/Vg∼10 meV/V$⁠. The main effect of the gate voltage in the direct regime is the control of the exciton and trion PL intensities: the high-energy exciton emission increased at the negative V_g, while the low-energy trion emission increased at the positive V_g (Figure 5). This behavior is attributed by the voltage-dependent electron concentration n_e in the MoS₂ layers. The initial electron concentration n₀ at V _g = 0 arises from unintentional dopants typically present in MoS₂ materials. The change $Δne=ne(Vg)−n0$ of n_e as a function of V_g can be estimated from simple electrostatics. Treating the CQW as a single unit and neglecting a minor contribution from quantum capacitance, we find

where $Ca,b, Ra,b$ are the geometric capacitances and leakage resistances of the dielectrics above (below) this double layer. (Incidentally, the leakage current across the device did not exceed a few $μA$ until an eventual breakdown of the device at $Vg∼70 V$⁠.) Since generally $CaRa≠CbRb$⁠, the applied voltage changes n_e and, as a result, modifies the concentration of trions relative to the neutral excitons.

In summary, we presented optical studies of excitons in a MoS₂ coupled quantum well van der Waals heterostructure. We observed three emission lines. The dependence of these lines on experimental parameters indicates that the two high energy lines correspond to the emission of neutral excitons and the lowest energy line to the emission of charged excitons (trions). We demonstrated control of the exciton emission by the gate voltage, temperature, and also by the helicity and power of optical excitation.

This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences under award DE-FG02-07ER46449. M.M.F. was supported by the Office of the Naval Research. Work at the University of Manchester was supported by the European Research Council and the Royal Society. We thank S. Dai for help with Figure 1(a).