Disorder engineering and conductivity dome in ReS2 with electrolyte gating

Atomically thin rhenium disulphide (ReS2) is a member of the transition metal dichalcogenide family of materials. This two-dimensional semiconductor is characterized by weak interlayer coupling and a distorted 1T structure, which leads to anisotropy in electrical and optical properties. Here we report on the electrical transport study of mono- and multilayer ReS2 with polymer electrolyte gating. We find that the conductivity of monolayer ReS2 is completely suppressed at high carrier densities, an unusual feature unique to monolayers, making ReS2 the first example of such a material. Using dual-gated devices, we can distinguish the gate-induced doping from the electrostatic disorder induced by the polymer electrolyte itself. Theoretical calculations and a transport model indicate that the observed conductivity suppression can be explained by a combination of a narrow conduction band and Anderson localization due to electrolyte-induced disorder.

1. Is the sheet conductivity plotted in Figure 2(a) 2-point or 4-point? That should be explicitly specified. Figure 3(b), the authors show an insulator-metal-insulator (I-M-I) transition in a 10 nm thick ReS2 flake, but, in order to further analyze the second transition (metal-insulator transition occurring after the conductivity dome), the authors perform Hall effect measurements on a 2.2 nm thick ReS2 flake instead. Although the authors state earlier that among multilayer ReS2 (> 2L) flakes, the curves are essentially indistinguishable in terms of variation in doping and hysteresis, it would be better and more consistent if the authors can show the plot for insulator-metal-insulator transition occurring in a 2.2 nm flake instead of the thicker 10 nm flake in Figure 3(b). Or conversely, the authors should show the Hall effect mobility measurements on a 10 nm thick flake instead of a trilayer flake in Figure 3(c).

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The values of Vpe at which the I-M and M-I transitions occur will obviously be different for the 10 nm thick flake as compared to the 2.2 nm thick trilayer flake. Therefore, it is not straightforward to simply analyze the M-I transition occurring in a multilayer 10 nm thick flake (at Vpe ~ 2.3 V) by performing Hall measurements on a multilayer 2.2 nm thick flakes. It will be a lot easier to correlate the data and conduction regimes presented in Figure 3(b) to the mobilities shown in Figure 3(c) if they are extracted from the same flake with the same thickness. Figure 3(c), the Hall mobility values for n2D = 1.55e13 and Vpe = 0.9 V are not presented beyond 90 K (it is not there even in supplement figure S8). What is the reason for this? 3. In SI section 8, in lines 5-6 of the first paragraph, the authors state that they 'performed measurements in two-terminal "directional" monolayer structures (see previous section in SI)'. Where is this "previous" section the authors are pointing to? Or are they referring to the plot presented in section 12 figure S10(a)?

Reviewer #3 (Remarks to the Author):
In this manuscript, authors find disorder induced Anderson localisation which induces metalinsulaor transition at high doping level as increasing the polymer electrolyte voltage. Such Anderson localisation even completely suppresses the conductivity at high doping level in monolayer ReS2. Overall the findings are original and interesting. I would recommend to publish it after revision considering following comments: (1) Since authors ascribe the observed completely suppression of conductivity in monolayer ReS2 to disorder induced Anderson localisation, the signature of phase transition from insulator to metal as increasing temperature is expected.
(2) The effects of inter-layer interaction may play important roles, although such interaction is weak in ReS2.
(3) Is the sheet conductivity of 10 nm thick ReS2 at 300K presented in Fig. 3a and 3b not same?
(4) How large is the V_bg in Figure 1?
(5) The observed sheet conductivity in the ON state of multilayer devices is 4-8 times larger than that of monolayer devices. However, the difference of sheet conductivity among multilayer devices is rather small. What is the reason responsible for such large difference?
We thank the reviewers for careful reading of the manuscript, positive response and useful comments. Below, the questions are addressed point by point.

Reviewer #1 (Remarks to the Author):
In this manuscript, the authors report that the conductivity of the monolayer ReS2 is completely suppressed at high carrier density and conductivity dome with insulator-metal-insulator sequence in multilayer flakes. The conductivity suppress in monolayer can be explained as the combination of narrow conduction band and Anderson localization caused by electrolyte-induced disorder. The results are interesting. Therefore, the paper could be published in Nature Communications. However, the authors need to address the following points and the comments mentioned above.
(1) The authors claimed that the polymer electrolytes are the source of the disorder which caused the conductivity suppression at high carrier densities ReS2. As we know, liquid ions gate often react with the samples which is the origin of the defects. This process is irreversible. However, the current Is don't showing much degradation after 10 cycles of sweeping VPE.

Did authors find any degradation of Is or the damage of the samples after more cycles of sweeping VPE
Thank you for the questions. None of our devices showed degradation over time within months of measurements and multiple sweeps. They definitely survive more than 10 cycles and we did not find the point where degradation happens. Leakage currents were monitored to make sure nothing unusual is happening, as shown in Supplementary Figure S1. We write in the Supplementary Information, Section 2: "On Supplementary Figure S1 and what's the temperature during sweeping VPE？ These measurements have been performed at T = 300K, we now write in the section 4 of SI: "To rule out degradation during cycling or detrimental influence of ions on our device performance we performed cycling of V PE 10 times at elevated sweep speed (50 mV/s) in the monolayer ReS 2 EDLT, the measurements were performed at 300K." (2) The authors reported that the other monolayer TMDCs don't showing the completely suppressing of conductivity at high carrier densities. What's the main reason of the difference? Did the crystal structures of those other monolayer TMDCs are the same with the ReS2?
ReS 2 stands out from other semiconducting TMDs, which normally have 2H (more rarely 3R) crystal structure (Mo(W)Se(S) materials). ReS 2 has stable 1T' structure, which in turn leads to the unusual band structure. We write in the text: "We stress that the narrowness of the conduction band is crucial to revealing the wavefunction localization, as the key quantity in Anderson localization is the adimensional disorder strength W/D 36,38 . In our opinion, this phenomenon is responsible for such a peculiar behavior of monolayer ReS 2 among other 2D TMDCs."

(3) The theory calculation result of the narrow low-energy conduction band of ReS2 stand apart from other TMDCs is crucial to conductivity modulation in ReS2. Dose the conductivity can completely suppressed in monolayer ReS2 without the localization at disorder free or reduce the disorder strength by born nitride protecting the interface heterostructure?
Thank you for the question. The localization occurs because of band structure of ReS 2 and electrostatic disorder (effect of electrostatic disorder is more strong in this material due to exotic band structure with narrow low energy CB). Protecting monolayer ReS 2 with monolayer BN will have two effects: (i) decrease of effective capacitance due to increase of distance between conductive channel and ion gel; (ii) smoothing of electrostatic disorder coming from electrolyte due to an increased distance between the conductive channel and the interface with the ionic liquid. In fact, we can compare it to the having a bilayer ReS 2 instead of monolayer, as soon as the bottom layer of the bilayer will be already screened from disorder by the topmost layer. Protection of monolayer ReS 2 by h-BN would be an interesting subject for future study, but this is beyond the scope of the presented work.

Reviewer #2 (Remarks to the Author):
The authors have done a thorough experimental and theoretical work to demonstrate, and understand, the suppression of conductivity arising in ReS2 at high carrier densities due to electrolyte-induced disorder. This is a novel work and will be of interest to the scientific community working in the field of 2D materials. The overall data analyses and conclusions are sound and the manuscript can be published in Nature Communications, however, there are a few questions which the authors must address:

Is the sheet conductivity plotted in Figure 2(a) 2-point or 4-point? That should be explicitly specified.
This is sheet conductivity extracted from four-contact measurements. We now clarify it in the text: "The back-gate voltage V bg dependence of the sheet conductivity G extracted from four-probe measurements for different temperatures is shown on Figure 2(a)." Figure 2 (a) has also been modified accordingly. Figure 3(

b), the authors show an insulator-metal-insulator (I-M-I) transition in a 10 nm thick
ReS2 flake, but, in order to further analyze the second transition (metal-insulator transition occurring after the conductivity dome), the authors perform Hall effect measurements on a 2.2 nm thick ReS2 flake instead. Although the authors state earlier that among multilayer ReS2 (> 2L) flakes, the curves are essentially indistinguishable in terms of variation in doping and hysteresis, it would be better and more consistent if the authors can show the plot for insulator-metal-insulator transition occurring in a 2.2 nm flake instead of the thicker 10 nm flake in Figure 3(b). Or conversely, the authors should show the Hall effect mobility measurements on a 10 nm thick flake instead of a trilayer flake in Figure 3(c).
The values of Vpe at which the I-M and M-I transitions occur will obviously be different for the 10 nm thick flake as compared to the 2.2 nm thick trilayer flake. Therefore, it is not straightforward to simply analyze the M-I transition occurring in a multilayer 10 nm thick flake (at Vpe ~ 2.3 V) by performing Hall measurements on a multilayer 2.2 nm thick flakes. It will be a lot easier to correlate the data and conduction regimes presented in Figure 3(b) to the mobilities shown in Figure 3(c) if they are extracted from the same flake with the same thickness.
Thank you for the comment. With figure 3b, we are simply aiming to show that for multilayers the usual I-M transition is followed by an M-I transition at higher charge densities and in contrast with behavior shown on figure 2a where the deposition of the polymer electrolyte immediately suppresses the first M-I transition. The motivation for Hall measurements shown on Figure 3c is not to identify the charge densities where the transition occurs but to show that for a certain value of a doping level, the mobility is lower for higher values of Vpe, i.e. higher concentrations of ions on the surface of ReS2. - Figure 3(b) shows an overview of the I -M -I sequence for a typical multilayer flake. In other multilayers, the situation (within measured range of thicknesses with sample to sample variation caused by such factors as small V th variation) will be the same. The insulating state will appear at high V PE in multilayers of ReS 2 in the accessible range of gate voltages with the electrolyte we use. We are certain about this fact, because of (i) highly consistent room-temperature operation with the domelike shape and decrease of conductivity at high V PE ; (ii) consistent insulating state, measured at high V PE in at least two more samples (apart from the one discussed in the main text).
We can furthermore address this comment by comparing carrier density values. Both samples (10 nm and 2.2 nm flakes) are unavailable at the moment, but we can comment on the data we have. We can estimate the carrier density for the 10 nm thick sample at V PE = 0.25V from back-gating curves below the freezing point of the ionic liquid. V th = -28V ÷ -40V (depending on the extraction method) and 270 nm SiO 2 dielectric results in This fits very well into the Hall effect data from 2.2 nm thick flake (Supplementary Figure  S8(a)). In addition, no significant capacitance variation of the ion gel capacitance with flake thickness (among multilayers) is expected. All these considerations strongly point towards a universal behavior of n 2D vs V PE with a small device-to-device variation due a shift in V th .
As mentioned before, Figure 3(c) serves a different purpose. It shows how we deplete mobility in the metallic state with controllable introduction of disorder with electrolyte. Furthermore, disorder gradually pushes the material into the insulating state. We stress that this M-I transition is not a sharp event with respect to V PE . The interplay and competition between increasing disorder and movement of Fermi-level further into conduction band, after which disorder eventually "wins", leads to the progression of the material into the insulating state and further strong localization effects. We corrected the main text to be more clear on this point: "We first examine evolution of conductivity in the metallic state around the conductivity dome. We have performed Hall effect measurements in another multilayer ... " Figure 3(c), the Hall mobility values for n2D = 1.55e13 and Vpe = 0.9 V are not presented beyond 90 K (it is not there even in supplement figure S8). What is the reason for this?

Moreover, in
Unfortunately we do not have this data due to the fact that this device failed. However, we do not expect unusual behavior of mobility in the region from 90K to 180K. Our data in the metallic state at moderate carrier densities and low V PE (red filled markers on Figure 3(c)) is in full agreement with measurements from a device with a solid gate done by Pradhan et al. (Nano Lett., 2015, 15 (12), pp 8377-8384), where a typical decrease of mobility with increasing temperature in the metallic state is observed due to electron-phonon scattering. Moreover, the values of the mobility are in good agreement with those of Pradhan et al. We believe that the absence of these measurements does not influence any of the major conclusions of the manuscript.
3. In SI section 8, in lines 5-6 of the first paragraph, the authors state that they 'performed measurements in two-terminal "directional" monolayer structures (see previous section in SI)'. Where is this "previous" section the authors are pointing to? Or are they referring to the plot presented in section 12 figure S10(a)?
Thank you, it has been corrected: "We have performed measurements in two-terminal "directional" monolayer structures (see Section 12 of SI and Supplementary Figure S10)."

In this manuscript, authors find disorder induced Anderson localisation which induces metalinsulaor transition at high doping level as increasing the polymer electrolyte voltage. Such
Anderson localisation even completely suppresses the conductivity at high doping level in monolayer ReS2. Overall the findings are original and interesting. I would recommend to publish it after revision considering following comments: (1) Since authors ascribe the observed completely suppression of conductivity in monolayer ReS2 to disorder induced Anderson localisation, the signature of phase transition from insulator to metal as increasing temperature is expected.
Thank you for the question. That's exactly what happens in case of monolayer ReS 2 and is shown on Figure 2(a). Without PE deposition we observe insulator to metal transition. While with PE deposition the metallic state disappears. We write in the main text: "Without the electrolyte, we observe a metal-insulator transition around V bg = 5.6 V and fieldeffect mobilities of µ FE ~ 3 cm 2 /Vs, consistent with other studies of ReS 2 . 7,11,14,15 As soon as the electrolyte is deposited and V PE = 0V is applied (second panel), the overall conductivity decreases and the sample displays a purely insulating behavior. Increasing the V PE further results in a gradual decrease of conductivity (Figure 2(a), from left to right)." (2) The effects of inter-layer interaction may play important roles, although such interaction is weak in ReS2.
Thank you for the question. In experiments of Tongay et al (Nat Commun 2014, 5) photoluminescence measurements show weak interlayer interactions. We mention this in the main text: "Recent Raman spectroscopy 3,8 and photoluminescence measurements 3 indicate that atomic layers in 1T' ReS 2 , unlike those of MoS 2 , are decoupled from each other, 3 which gives rise to direct band gap preservation from monolayers to bulk crystals." Layer coupling (as well as atoms presented in the lattice, crystal structure, major defects and other factors) in fact determine the band structure and specifically narrow conduction band, which is the key feature for extreme sensitivity of this material to electrostatic disorder.
(3) Is the sheet conductivity of 10 nm thick ReS2 at 300K presented in Fig. 3a and 3b not same?
The curves of Figures 3(a) and 3(b) at 300K do not perfectly reproduce each other due to different V PE sweep rates. The difference is the following -for Figure 3(a) the sweep rate was set to 0.25 mV/s. For Figure 3(b), the sweep rate between the points was the same, at each point the current was set to stabilize, furthermore, cooldown and heatup were performed for each point. After heatup, the current was again set to stabilize. In this way, the effective sweep rate is much lower for Figure 3(b). We are however sure that with this measurement schedule, we get a homogeneous doping across the sample and drift-free conductivity. We also do not exclude a small V th drift due to the slow nature of such measurements. However, qualitatively, the curves look similar with a pronounced dome-like shape, despite the peak conductivity variation from 51 µS to 36 µS.
(4) How large is the V_bg in Figure 1?
Thank you for the question. We have two types of samples, discussed in the manuscript -on local back gates and on SiO 2 substrates with a global back gate. We disconnect the back gate for the devices fabricated on 270 nm SiO 2 with global back gate and leave it floating until the electrolyte is frozen due to the way we prepare substrates. Please, find the detailed explanation below: The e-beam alignment markers and fiducial markers for localizing the flakes on the sample are embedded into the SiO 2 substrate (in order to resist adhesive-tape exfoliation) with reactive ion etching and are thus connected to the back gate. We design our devices in a way that the electrodes/flakes do not touch the markers to avoid leakage. The polymer electrolyte is spin coated over the entire surface of the chip. Because of this, if we applied 0V to the global back gate we would effectively apply 0V to the polymer electrolyte over the large area through multiple markers. If we now also applied voltage to the polymer electrolyte (PE) electrode, there would be a competition between the two voltages, which would decrease the effectiveness of gating and would prevent us from carefully monitoring the leakage current from PE electrode (since a potential difference between the PE electrode and the markers would result in an additional leakage current). The sample on Figure 1(b) therefore has a disconnected back gate.
We note however, that we do not use room temperature measurements with PE to extract mobility values, which could be influenced by a small capacitive coupling with the back gate.
All the mobility values in the manuscript are extracted with electrolyte frozen. To prove that the back-gate capacitance does not change below freezing point of the ionic liquid, we extract the value of the geometric capacitance of 270 nm SiO 2 from the Hall effect data (please refer to Supplementary Figure S8(b)). We mention this in the Supplementary Information, section 8: "The extracted back gate capacitance for each cooldown corresponds very well to the geometric capacitance, showing that our measurements are correct." For the devices, fabricated on local gates and thin high-k oxide substrates, where the markers do not penetrate through the oxide and thus no shunt between the local gate and electrolyte occurs (the device discussed in Figure 2) floating or grounding the bottom gate does not make any difference.
(5) The observed sheet conductivity in the ON state of multilayer devices is 4-8 times larger than that of monolayer devices. However, the difference of sheet conductivity among multilayer devices is rather small. What is the reason responsible for such large difference?
We consider the following simple model. In the bilayer the top layer is still exposed to disorder, while the bottom layer is protected from disorder, has higher mobility and provides (from parallel conduction considerations) a significant increase of conductivity, having also high carrier density (for sake of simplicity, we neglect carrier hopping between the layers). By adding more layers, we increase the number of conductive channels. At the same time, the high doping is maintained in the 1-2 topmost layers, as shown in Yuan et al., Nat Phys 2013, 9 (9), 563-569. Thus the channels lying further away from the gate have negligible contribution to the overall conductivity. Consequently, there is a step-like change of conductivity from monolayer to anything thicker (within the thicknesses range which we address in current work).