Inter-layer charge transport controlled by exciton-trion coherent coupling

The possibility of electrical manipulation and detection of charged exciton (trion) before its radiative recombination makes it promising for excitonic devices. Using a few-layer graphene/monolayer WS$_{2}$/monolayer graphene vertical heterojunction, we report inter-layer charge transport from top few-layer graphene to bottom monolayer graphene, mediated by coherently formed trion state. This is achieved by using a resonant excitation and varying the sample temperature, the resulting change in the WS$_{2}$ bandgap allows us to scan the excitation around the exciton-trion spectral overlap with high spectral resolution. By correlating the vertical photocurrent and in situ photoluminescence features at the heterojunction as a function of the spectral position of the excitation, we show that (1) trions are anomalously stable at the junction even up to 463 K due to enhanced doping, and (2) the photocurrent results from the ultra-fast formation of trion through exciton-trion coherent coupling, followed by its fast inter-layer transport. The demonstration of coherent formation, high stabilization, vertical transportation and electrical detection of trions marks a step towards room temperature trionics.


Introduction:
Excitons are bound pairs of an electron and a hole, and play a crucial role in a variety of optoelectronic devices. The large optical absorption, large carrier effective mass, small dielectric constant, and strong out of plane confinement in monolayer transition metal dichalcogenides (TMDCs, for example, MX 2 where M = Mo, W; X = S, Se) lead to the observation of a variety of excitonic quasiparticles (namely, exciton, charged exciton or trion, biexciton) that remain stable even up to room temperature [1,2,3,4,5]. This makes these monolayers and their vertical heterostructures an ideal platform for exploring the physics of excitons and their manipulation [6].
A trion is a charged exciton constituting of two electrons and one hole (X − ) or two holes and one electron (X + ), which exhibits a binding energy on the order of 30 meV [3,7] in monolayer TMDCs -a number that is about an order of magnitude higher than that is observed in III-V semiconductor quantum wells [8,9,10]. Since the binding energy is higher than k B T at 300 K, trions in monolayer TMDCs are stable at room temperature. This makes trions particularly interesting for room temperature optoelectronic applications for two primary reasons.
First, trions carry a net charge, allowing us to manipulate and detect trions through electrical probing. Second, the radiative lifetime of trion has been reported in a broad range from few ps to tens of ps [11,12,13,14], but nonetheless, longer than that of exciton [11,15,16,17], providing us time for electrical manipulation before it radiatively recombines in a spontaneous manner. However, many of the perceived applications of trions have not yet been demonstrated experimentally. This is because trion being a heavy particle, exhibits poor in-plane mobility, resulting in relatively large transit time under electric field. This leads to radiative recombination of trion before collection at the electrodes, leaving little hope for efficient manipulation and detection in lithography limited planar structures.
Vertical layered heterostructures, where monolayer TMDC is encapsulated by a bottom electrode and an optically transparent top electrode provide an ideal solution to this problem.
The generated trion in the ultra-thin TMDC sandwiched layer can be swiftly transferred and collected at the vertical electrodes before radiative recombination, and thus can generate a 2 detectable electrical current. However, two important issues must be addressed for successful implementation of this scheme. First, interlayer carrier transfer is an extremely fast process (sub-picosecond timescale [18,19,20,21]). Any incoherent trion formation process (for example, through phonon scattering following non-resonant excitation) will be inefficient at the heterojunction, as photo-carriers will be transferred to the electrodes before formation of trion.
This calls for the need of an ultra-fast trion formation process, for example, through coherent exciton-trion coupling [12,22,23,24,25] following a resonant excitation. Second, due to strong screening by the adjacent vertical electrodes, the binding energy of the trion is likely to be suppressed [26], which can adversely affect its stability at room temperature.
In this work, exploiting efficient coherent coupling between exciton and trion driven by resonant excitation, we demonstrate strong photocurrent in a few-layer graphene (FLG)/monolayer WS 2 /monolayer graphene (MLG) vertical junction. The photocurrent results from electron hopping from top FLG to bottom MLG mediated through the coherently formed trion state in the WS 2 sandwiched layer. This is achieved by scanning the spectral overlap between the exciton and the trion using a fixed wavelength excitation at varying temperature. We further demonstrate an anomalous stabilization of trion at the heterojunction at elevated temperatures (up to 463 K) arising due to enhanced doping in the WS 2 sandwiched layer.  Figure 1d shows the Raman spectra obtained using a 532 nm laser at 296 K, both on the isolated WS 2 portion and on the junction. Compared to the isolated WS 2 , the Raman signal is slightly suppressed at the junction. Also, the A 1g peak at the junction is hardened by about 1 cm -1 with respect to the isolated portion (see inset of Figure 1d). This 3 suggests a change in doping in the monolayer WS 2 at the junction due to depletion of carriers to graphene resulting from band offset.

Results and Discussions:
The fabricated device is mounted on a thermal chuck and the device terminals are connected to Keithley 2636B SMUs through micromanipulators for electrical measurement. At every temperature step, the device is illuminated by a laser beam of photon energy 2.33 eV and 1.9591 eV through a 50X objective, and the photocurrent is measured while acquiring in situ photoluminescence (PL) spectra. The incident laser power is kept below 8.5 µW to avoid any undesirable effect due to laser induced heating. The horizontal axis is the detected photon energy and the vertical axis is the sample temperature varying from 296 K to 463 K. The individual spectra at different temperatures are shown in Supplementary Information S1. The sharp red shift of the A 1s exciton (X) peak with an increase in temperature is a result of the reduction in quasiparticle bandgap. On the junction, the PL intensity of both the X and the trion (X − ) peaks is significantly quenched (about 10 times) irrespective of the temperature, as illustrated in Supplementary Information S2. This quenching with 2.33 eV excitation can be attributed to two effects. First, since 2.33 eV excitation is off-resonant to X, the formation of the exciton has to happen through the relaxation of energy, by inelastic phonon scattering, which requires a timescale of few picoseconds. Second, once an exciton is formed, on an average it takes on the order of a picosecond for radiative recombination. During these processes, a large fraction of the excitons is transferred to graphene through ultra-fast processes including exciton transfer and non-radiative energy transfer [27,28], quenching the overall PL intensity.
The individual PL spectra acquired from the isolated WS 2 and the junction are shown in Figure 2c-d at 296 K and 463 K. The obtained PL peaks can be fitted with voigt function to extract the X and X − peaks. Note that, at elevated temperature, the X − spectral strength is almost negligible on isolated WS 2 , while it is surprisingly strong at the junction. This anoma-4 lous trion-stabilization at the junction at higher temperature in spite of screening effect is also supported by the enhanced separation between X and X − peaks in the bottom panel of Figure   2d. The position of the fitted X and X − peaks is systematically plotted as a function of temperature in Figure 3a. The corresponding separation between the two peaks (∆E = E X −E X − ) is shown in Figure 3b. We also show the k B T line indicating the thermal stability region. ∆E increases with temperature for both isolated WS 2 and at the junction. The rate of increment of ∆E with temperature is faster (slower) than the k B T line at the junction (isolated WS 2 ) portion. This is in agreement with the vanishingly small trion intensity at 463 K at the isolated WS 2 portion in Figure 2c (bottom panel), while at the junction, we observe a strong trion peak in Figure 2d (bottom panel). This anomalous behaviour at the junction can be attributed to an increasing doping with temperature in the junction. ∆E is given by [3,29,30] where E bT is the trion binding energy and δE n is the additional energy required for trion 'ionization' to knock an electron to an empty state in the conduction band. By noting that the A 1g Raman peak position of WS 2 is strongly modulated by electron-phonon coupling [31], it can be used to monitor the doping effect at the junction. In Figure 3c, we plot the shift of the WS 2 A 1g Raman peak in the junction with temperature, showing a softening of 2.5 cm -1 . Note that the increase in temperature would only soften the A 1g peak by 1.5-1.7 cm -1 [32,33,34], suggesting the additional softening due to electron-phonon coupling arising from increased n-type doping [35]. The origin of the enhanced n-type doping with temperature at the junction stems from the bandgap defect states in WS 2 . Such defect states are well studied in TMDC materials, and are known to produce sub-bandgap luminescence peaks at low temperature [4,36,37,38].
A representative PL spectrum of monolayer WS 2 taken at 3.7 K is shown in Supplementary Information S3. With an increase in temperature, due to a change in the Fermi-Dirac probability, the trap states get more activated. Upon illumination, the photogenerated carriers in the top FLG film populate these trap states, changing the doping in the WS 2 film, and in turn moving the Fermi level closer to the conduction band edge (see Figure 3d). The combined effect of stronger Fermi tail and enhanced doping results in higher probability of filled states at the conduction band edge and statistically it becomes increasingly difficult to ionize the trion by promoting one electron to the conduction band [3,29,30]. This in turn results in the anomalous stabilization of the trion at the junction at elevated temperature.
We note from Figure 2a that by changing the sample temperature, the X peak can be shifted from 2.016 eV at 296 K to 1.945 eV at 463 K (∆E = 71 meV). Thus, using a 1.9591 eV excitation at different sample temperatures, we can effectively scan the entire spectral range around X − and X, as shown by the red arrows in Figure  The photocurrent is found to be negligible when the laser spot is away from the junction. To confirm that there is no heating induced degradation in the device, we repeat the measurement cycle three times, and the variation in photocurrent from one cycle to the other is negligible.
I ph increases monotonically with T for off-resonant (2.33 eV) excitation, while it is strongly non-monotonic for resonant (1.9591 eV) excitation, suggesting fundamentally different photocurrent mechanisms at play in these two cases. For 2.33 eV excitation, the photocurrent results from both absorption in WS 2 as well as in graphene. With encapsulation by graphene from top and bottom, the exciton binding energy reduces in WS 2 , as well as there is a reduction in the continuum level due to bandgap renormalization [40]. Photons with an energy of 2.33 eV is then likely in the WS 2 continuum level, creating electron-hole pair, followed by separation by the built-in field. However, the sharp band offset at the WS 2 /graphene interface on both sides of WS 2 can significantly nullify any net photocurrent out of this process [41], as illustrated in the left panel in Figure 5d. This suggests that light absorbed by graphene is likely the primary contributor to the photocurrent. The hot carriers generated in the top FLG relax in ultra-fast (∼ picosecond) time scale [42,43]. However, since inter-layer transfer can also happen in a similar time scale [18,19,20,21], a fraction of the photoelectrons in FLG is injected through On the other hand, when 1.9591 eV excitation is used, we observe enhanced I ph coupled with a strong non-monotonic behaviour. To get insights, we re-plot I ph (normalized as While plotting, H is normalized by the overlap area between X and X − . Note that, the peak I ph occurs when the excitation energy is resonant (at 373 K) with the strongest overlap region between the exciton and the trion.
Such a strong tunability of the photocurrent by scanning the exciton-trion spectral overlap region suggests the crucial role of ultra-fast trion formation in the observed photocurrent.
Trion, unlike neutral excitons, being a quasiparticle with a net charge, can play an active role in the generation of the photocurrent. However, in order to contribute to the photocurrent in the present vertical heterostructure, trion must be formed at a timescale that is shorter than the ultra-fast inter-layer transport of excitons. It has been shown in the past that trion can be formed through both coherent and incoherent coupling with excitons [12,22,23,24,25]. The incoherent coupling takes few picoseconds through phonon emission [23,24], which is larger than the inter-layer transfer time [18,20,19,21], and is unlikely to play a significant role in the 8 present device. This suggests coherent formation of trion through coulomb interaction between excitons and electrons plays the primary role in the photocurrent generation. On the junction, these electrons can be efficiently supplied by the top FLG. When the incident photons are resonant with the spectral overlap region of the exciton and the trion, such coherent coupling is strongly enhanced. At low temperature, the lower energy side of the exciton peak is often attributed to defect bound excitons [24]. However, in our case, the deconvolution of the fitted In summary, we demonstrated a technique by which using an excitation with fixed photon energy and variable sample temperature, we obtain a high resolution spectral scan of the sam-9 ple. By exploiting this technique, we perform a spectral scan around the exciton-trion overlap region in an asymmetric vertical few-layer graphene/monolayer WS 2 /monolayer graphene heterojunction to demonstrate a unique inter-layer charge transport mechanism mediated by a coherently formed many-body (trion) state. The efficiency of this transport mechanism can be effectively tuned by scanning the excitation across the exciton-trion spectral overlap. This provides us a knob to control the vertical charge transport by tuning the degree of exciton-trion coupling. This marks a direct probing of coherent coupling between exciton and trion by the electrical detection of trion and would be useful for fast optoelectronic applications. In general, trion being a heavy particle, is not ideally suited for in-plane charge transport due to poor mobility. However, the present work demonstrates the possibility of ultra-fast trion transport through vertical inter-layer transfer. Such ultra-fast inter-layer trion transport can occur before valley and spin depolarization and thus opens up pathways for electrical probing of valley and spin dynamics. Further, the demonstration of enhanced stability of trion at elevated temperatures and its electrical detection is appealing for trion based optoelectronics without the need for any cooling apparatus.

Methods
Device fabrication: We prepare a stack of MLG/monolayer WS 2 /FLG by using dry transfer technique on a highly doped Si substrate coated with 285 nm thick thermally grown oxide. This stack is heated on a hot plate at 80 • C for 2 minutes for improved adhesion between layers.
Devices are fabricated using standard nanofabrication methods. The substrate is spin coated with PMMA 950C3 and baked on a hot plate at 180 • C for 2 minutes. This is followed by

SUPPLEMENTARY INFORMATION
Supplementary Information is available on (1) temperature dependent PL spectra with 532 nm excitation, (2) temperature dependent exciton and trion PL quenching on junction, (3) low temperature WS 2 PL spectrum, (4) temperature photoluminescence spectra with 633 nm excitation, and (5) temperature dependent homogeneous and inhomogeneous exciton broadening.