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Eoin O'Farrell, Ahmet Avsar, Jun You Tan, Goki Eda, Nano Letters is published and Barbaros Özyilmaz by the American Chemical Society. 1155 Sixteenth

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Quantum transport detected by strong proximity interaction at a graphene-WS2 van der Waals interface ∗,† ¨ E.C.T. O’Farrell,∗,† A. Avsar,† J.Y. Tan,† G. Eda,† and B. Ozyilmaz

Centre for Advanced 2D Materials, National University of Singapore, Singapore 117546, Department of Physics, National University of Singapore, Singapore 117551, and NanoCore, National University of Singapore, Singapore 117576 E-mail: [email protected]; [email protected]

Abstract Magnetotransport measurements demonstrate that graphene in a van der Waals heterostructure is a sensitive probe of quantum transport in an adjacent WS2 layer via strong Coulomb interactions. We observe a large low-field magnetoresistance (≫ e2 /h) and a − ln T temperature dependence of the resistance. In-plane magnetic field resistance indicates the origin is orbital and non-classical. We demonstrate a strong electron-hole asymmetry in the mobility and coherence length of graphene demonstrating the presence of localized Coulomb interactions with ionized donors in the WS2 substrate, which ultimately leads to screening as the Fermi level of graphene is tuned toward the conduction band of WS2 . This leads us to conclude that graphene couples to quantum localization processes in WS2 via the Coulomb interaction ∗

To whom correspondence should be addressed Centre for Advanced 2D Materials, National University of Singapore, Singapore 117546 ‡ Department of Physics, National University of Singapore, Singapore 117551 ¶ NanoCore, National University of Singapore, Singapore 117576 †

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and results in the observed signatures of quantum transport. Our results show that theoretical descriptions of the van der Waals interface should not ignore localized strong correlations.

Keywords Graphene, WS2 , Heterostructure, Quantum transport, Proximity interaction The isolation of graphene and monolayers of other van der Waals (vdW) crystals has led to a resurgence of interest in vdW heteroepitaxy between different two dimensional crystals. 1–3 For graphene a major focus has been reducing scattering from charge traps, and surface roughness, by utilising highly insulating, crystalline substrates such as hexagonal Boron Nitride (h-BN). More recently strain between crystallographically aligned graphene and h-BN was found to break local sublattice symmetry of graphene opening a gap at the charge neutrality point. 4,5 More generally interfacial interactions in two dimensional electronic gases (2DEGs) give rise to novel states, for example superconducting interfaces between insulating polar oxides. 6 The intrinsically atomically sharp nature of the interface at a vdW interface is anticipated to lead to an enhancement of the Coulomb interaction that can be accessed in bilayer structures. 7,8 It is therefore of clear interest to investigate the effect of interactions at vdW heterointerfaces. In this letter we investigate the interface between semimetallic graphene and semiconducting WS2 and show that the Coulomb interaction enables graphene to probe quantum transport in WS2 . Key to this observation is the work function tunability of graphene that allows the substrate to be probed at a range of energies. This work demonstrates the importance of localized Coulomb interactions across the vdW interface and a route to local probing of Coulomb based quantum phenomena such as magnetism and excitonic correlations in a device configuration. WS2 is a semiconductor with a bandgap of ≈ 1.5 eV in bulk form, 9 a member of a series of transition metal dichalcogenides (TMDCs) that have drawn intense interest due to the remarkable evolution of electronic structure on reaching an isolated monolayer. For monolayer WS2 inversion symmetry is broken, leading to a direct band gap. The breaking of inversion symmetry allows


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the spin polarized valleys at K and −K to be individually addressed by electromagnetic fields thereby rendering these materials exceptionally promising for spin and opto-electronics. 10 WS2 is also known to show extremely strong excitonic effects 11 making the manipulation of the Coulomb interaction in this material of significant interest. In this article we show that graphene couples to quantum transport in WS2 defects in a grapheneWS2 (g-WS2 ) heterostructure. We observe a crossover of the low field magnetoresistance (MR) from negative to positive by tuning the graphene carrier density (ne ) from hole to electron-like. Consideration of both magnetic field (B) and temperature (T ) dependence as well as classical interfacial effects indicates that the origin is quantum and orbital in nature despite having magnitude ≫ e2 /h. We demonstrate the presence of strong and localized Coulomb interactions at the interface by considering the effect of carrier polarity of graphene on the mobility and coherence length. Localized Coulomb interactions transfer significant momentum between graphene and WS2 , therefore we show that the low field MR is consistent with quantum interference in the WS2 substrate which is detected by a drag-like interaction with graphene. g-WS2 vdW heterostructures were fabricated by micro-mechanically exfoliating WS2 (the preparation of WS2 is described by Zhao et al. 9 ) onto Si/SiO2 (300 nm) wafer that is used as a back-gate. Graphene is transferred onto WS2 , 12 and patterned into a Hall bar, and contacted electrically by Cr (2 nm)/Au (100 nm). Cr is used as a sticking layer because it makes a relatively poor electrical contact to the TMDCs (cf. Ti 13 ), thereby minimizing possible parallel transport through the WS2 substrate from outside the graphene region; a device schematic is shown in Fig. 1c inset. We present results from two devices, #26 and #27, which have WS2 thickness 8.8 and 16.5 nm, respectively. Both samples have graphene channel width 1 µm and quantities described per square are defined by the graphene geometry. Fig. 1a shows the square conductance (σ ) for #26 and #27 against back-gate bias at low temperature (#26 T = 0.05 K, #27 T = 5.0 K) and zero magnetic field (B). At negative gate bias both devices show typical behavior for graphene; the conductance decreases monotonically towards the neutrality point and the maximum in the mobility is µ#26 = 43, 000, µ#27 = 25, 000 cm2 /Vs. At


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hole-like densities we observe linear conductance suggesting the role of Coulomb scattering, fitting to a conductance model for graphene 14 with the dielectric value for bulk WS2 15 we obtain impurity concentrations 1.9 × 1011 cm−2 and 3.5 × 1011 cm−2 for samples #26 and #27, respectively. At positive gate bias we observe saturation in σ , this saturation has been reported for similar devices on WS2 16,17 and MoS2 18 substrates. Saturation of σ is due to saturation in ne (Fig. 1b), which we measure using Shubnikov de Haas (SdH) oscillations to isolate the contribution from graphene. The saturation in the carrier density of graphene at positive gate bias implies that carriers are induced in the WS2 substrate. The inferred carrier density in WS2 based on the relation Cg (Vg − VCNP ) = ng + nWS2 is shown by the dashed line. 18 These carriers are not expected to contribute significantly to the total conductance because WS2 has conductivity 3 orders of magnitude lower than graphene at comparable density (i.e. < 1012 cm−2 ). 19 In this region it has been shown that carriers in TMDCs are strongly localized and that conduction occurs via quantum hopping processes. 20 We additionally verify the quality of our device by the integer quantum Hall effect (IQHE) at high magnetic field at negative and positive density (see supplementary information). The deviation of ρ from B = 0 under a perpendicular magnetic field is shown in Fig. 1c at representative carrier densities for sample #26 including regions close to the onset, and deep inside the conductivity saturation region on the electron branch. In the region |B| < 1 T and negative (hole) density we find a B = 0 maximum in ρ . Biasing the back-gate to positive densoty tunes this to a B = 0 minimum, where a small antisymmetric linear in B term has been subtracted to remove any Hall admixture. The low field MR is large, ≈ −20% at negative density and 10% at positive density. We first consider the possibility of classical and interfacial effects on the MR. Classical MR for semiconductors can generally be described by the Köhler relation ∆ρ/ρ0 = F (µB), where F is an analytic function, and µ is the mobility which rescales the magnetic field i.e. a decrease in mobility leads to an increase in the magnetic field required to observe the same MR. Considering first the hole side, ne < 0 in Fig. 1c, we find that the MR is reduced closer to the charge neutrality point which follows the opposite trend from the mobility. Similarly on the electron-like side we observe a larger MR


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where the mobility is lower i.e. also in the opposite tendency expected from the Köhler relation. The Köhler rescaling of the MR measured at ne = −0.7 and +0.7 are denoted by the dashed black curves in Fig. 1c. The observed trend in our measurement is also opposite to MR in disordered graphene, 21 whereby the MR decreases away from neutrality and contrasts with observations of graphene on h-BN substrates where there is no qualitative difference between electron and hole doping. Finally in Fig. 1d we show the MR measured in parallel magnetic field. The parallel field MR in a two dimensional electron gas (2DEG) has several potential contributions from, for example, interfacial roughness 22 or rippling, 23 the influence of these properties can potentially be tuned by the gate bias and could therefore be related to observed crossover in the perpendicular MR. However, in contrast to the perpendicular MR the parallel MR is small and is not observed to vary significantly between positive and negative density. This observation shows that the crossover in the perpendicular MR is driven by the orbital MR. We now consider the temperature dependence for sample #27 (see supplementary material for MR of #27) measured over 3 orders of magnitude from 0.1 to 100 K, wherein qualitatively similar MR was observed as for sample #26 with the exception that the region of large MR did not extend deep into the saturation region, instead becoming flat (see supplementary information). Starting from hole-like density (Fig. 2a) we observe a moderate increase in the resistance in the region 10−100 K, below ≈ 10 K the resistance saturates and universal conductance fluctuations are visible 1 . A similar, but more pronounced, increase in ρ is observed on increasing toward positive gate bias (Fig. 2b-d). The increase in ρ on lowering T is approximately logarithmic, the dashed lines are fits to a ln(T ) + b where the fit is applied in the region where the largest temperature dependence was observed. In Fig. 2e at positive density far in the saturation regime we observe metallic behavior, this density corresponds to the region where the MR is small. Therefore, we directly correlate the large MR with a logarithmic correction to the T dependence of the resistance, the supplementary information presents the same data in terms of the conductance. 1

High temperature (5 − 100 K) data were taken by sweeping T at fixed gate in a 4 He cryostat, lower temperature data were taken by sweeping the gate at fixed T in a 3 He-4 He dilution cryostat


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The anomalous B and T dependence of transport in g-WS2 that occurs far from neutrality and that is absent from graphene on purely insulating substrates such as SiO2 or h-BN leads us to consider the role of WS2 . A number of previous studies of the graphene-semiconducting TMDC heterostructures have demonstrated anomalous electronic behavior in this structure: Avsar et al. 16 showed that graphene couples to defect levels in WS2 that possess strong spin orbit coupling; Larentis et al. 18 and Yankowitz et al. 25 considered the effect of a TMDC substrate on the electronic properties of graphene and showed that the back-gate geometry, that is also utilized in this letter, induces carrier occupation of the TMDC that will interact with graphene as well as unusual localized electronic states that are not yet fully understood. In g-WS2 graphene dominates conduction, but the effect of screening of the carrier density of graphene at high back-gate bias shows that carriers are also induced in WS2 . Furthermore it is known from studies of conventional bilayer quantum wells that the interaction with a second charge layer affects lateral transport in a single layer. 26,27 Therefore we consider if the WS2 substrate can induce the observed signatures of quantum transport into the MR of graphene. In the low temperature regime (< 1 K) we expect the phonon contribution to negligible, the temperature dependence is small below 10 K indicating that the phonon contribution remains small. At higher temperatures phonons are expected to influence the transport, but the suppression of the resistance upturn by a small magnetic field, as shown in Fig. 2f, demonstrates that phonons, which do not couple strongly to B, do not play a key role in this phenomenon so we discount them from the forthcoming discussion. Instead we consider the Coulomb interaction between graphene and charges in WS2 . The very small separation, d, between graphene and WS2 enables the interaction energy (e2 /4πǫǫ0 d) to be large (∼ 100 meV) for d = 1 nm. We demonstrate the role of the Coulomb interaction and Coulomb scattering from the WS2 substrate by extracting the mobility, using the density measured by SdH, as shown in Fig. 3. Sample #26 shows a sharp and large drop in the mobility by a factor of ≈ 2.5 when crossing from the hole to the electron side. Sample #27 shows a similar drop that is less pronounced across the neutrality point, significantly in this device the mobility also increases significantly in the screened regime at


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higher electron density where the large MR is absent. Furthermore as shown in the supplementary information we observe an asymmetry in the mean free path (mfp), the mfp is approximately a factor of two lower on the electron side and decreases at low magnetic fields where the large MR is present, both at electron and hole densities. The strong dependence on the polarity of the graphene carrier is understood as the effect of charged impurity scattering whereby attractive and repulsive interactions have significantly different scattering cross-sections, 28 this finding has two implications. First, the charged scattering sites are localized to a significant degree and in sample #26 largely unscreened, contrasting to the double layer graphene structure in which the mobility of a given layer is enhanced when the second layer is occupied as mobile carriers screen potential fluctuations and thereby enhance the mobility. 27 Second, the charged impurity scattering is predominantly due to positively charged impurities, this is inferred from the decrease in mobility on the electron side in graphene, it is known that attractive Coulomb scattering gives rise to larger decrease in the mobility. 28,29 This finding is consistent with the interaction between graphene and WS2 being dominated by ionized donors close to the conduction band of WS2 . 30 The increase in the mobility at higher electron density is due to the enhanced screening of scattering centers by carriers in graphene. Strong spin-orbit coupling of these ionized donors enables the mechanism whereby carriers in graphene can acquire spin-orbit coupling. 16 Having demonstrated that graphene in the gWS2 structure is strongly affected by Coulomb scattering we consider how this may give rise to the observed anomalous transport. In a Coulomb drag experiment the Coulomb interaction transfers momentum between the drive layer and the output layer. 31 In general the transresistance of the output layer is measured, but momentum transfer from the drive to the output layer implicitly affects the drive layer. This correction is enhanced when the active layer is clean, such that the scattering time is longer than the interlayer scattering time. Furthermore, in the case that the interaction is localized it must involve the transfer of large momenta by the uncertainty relation ∆r∆q ∼ ~. 32


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The orbital nature of the MR, the temperature dependence and the violation of Köhler’s law indicate that quantum transport may be the origin of the observed MR and therefore we consider quantum interference. Fig. 4a shows weak localization (WL) at low magnetic field both at positive and negative densities, where the conductance was averaged over several closely spaced gate biases within total interval of 1 V to average over conductance fluctuations. The field range of WL is typical of that observed for graphene and we fit the conductance to a quantum interference model specific to graphene to obtain the phase coherence length (lφ ), and the inter (li ) and intra-valley (l⋆ ) scattering lengths. The values that we obtain for lφ (Fig. 4b) are O(1 µm), similar to those typically obtained at low temperature for epitaxial graphene. 35

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symmetry breaking Bychkov-Rashba term in order to perform the fit. 36 Significantly there is not a qualitative difference between weak localization at hole and electron densities, which is in contrast to the sign change in the MR that is observed at higher B. Consistent with previous reports of WL in graphene we find that lφ decreases close to the CNP. Additionally, on the electron branch where we observed a significant decrease in mobility we find that lφ is ≈ 2 times lower which supports our conclusion of significant inelastic scattering due to the interaction between carriers in graphene and localized charge in the WS2 substrate. 37 As the large MR cannot be explained by only by transport in graphene we proceed to consider if the Coulomb interaction with the WS2 substrate may give rise to the MR observed in Fig. 1, specifically, as the MR was shown to originate from quantum transport we consider if the quantum transport of localized carriers in WS2 and the Coulomb interaction with graphene can lead to the observed MR. Recently Avsar et al. 16 showed that graphene couples to defect sites in the WS2 giving rise to spin orbit coupling in graphene, giant spin orbit splitting in the valence band of the closely related TMDC WSe2 has also been observed by weak anti localization measurements. 38 Typical values for lφ and lSO (spin-orbit coherence length) in the semiconducting TMDCs are ≤ 100 nm (WSe2 , 2

For graphene at low temperatures typically lφ ≫ li , l⋆ , therefore Bφ ≪ Bi , B⋆ , the MR that we report at B > 50 mT makes the extraction of li and l⋆ unreliable across the full range of density. Typical values are li = 0.5 µm, l⋆ = 0.3 µm.


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valence band 38 ) and (MoS2 , conduction band 39 ) which have similar electronic structure to WS2 . While bilayer quantum well structures have been extensively investigated the vdW heterostructure allows the combination of materials with significantly different electronic structure, in this case graphene and WS2 . There is an order of magnitude difference between lφ in these materials, this difference together with the strong Coulomb interaction leads us to suggest that the graphene drive layer with large lφ may coherently probe quantum transport with short lφ in the coupled WS2 layer and this localization length in WS2 may provide the additional length scale observed in the MR. We therefore fit the low field magnetoconductance (MC) to the Maekawa-Fukuyama expression for quantum interference in a 2DEG including spin-orbit coupling. 40 The amplitude of the MC is significantly larger than e2 /h therefore we include a rescaling factor A which physically describes the coupling between graphene and localized Coulomb scattering in WS2 . We allow A to vary between different back-gate biases reflecting the changing electronic properties of WS2 :

∆σ (H) = A × σM F (H, HSO , Hφ , γ).

(1)

σM F is the original Maekawa-Fukuyama (MF) expression for B perpendicular to the sheet with 2 parameters Hφ = ~/4elφ2 , HSO = ~/4elSO and γ = gµB H/4eDHSO . Where ~ is the reduced

Planck constant, e is the electron charge, g is the Landé g factor, µB is the Bohr magneton and D is the diffusion coefficient, which we estimate for WS2 3 . lφ(SO) are phase (spin-orbit) coherence lengths. Fits of Eqn. 1 in the range B = −0.85 − 0.85 T, i.e. below the onset of SdH oscillations together with the fitting parameters are shown in Fig. 4b and we infer that the rescaling parameter becomes negative for electron-like densities in graphene. Eqn. 1 fits the low field MC well, excluding deviations that we attribute to universal conductance fluctuations. Furthermore, the values obtained for the phase coherence length (50 nm) and spin orbit length (≈ 100 nm) in the g-WS2 heterostructure are comparable to those measured in 3

We choose a value of D corresponding to transport in the WS2 substrate. As we are unable to extract this directly from our measurement we use D = 0.01 cm2 /s, calculated using the Einstein relation and a representative mobility µ = 100 cm2 /Vs for the W dichalcogenides. We found the quality of the fit and the values of the fit parameters of Eqn. 1 are not significantly sensitive to this.


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bulk WSe2 38 (lφ = 50 nm, valence band) and MoS2 39 (lSO = 100 nm, conduction band) which have similar electronic structure to WS2 . The accurate fit to the MF quantum interference equation is consistent with a quantum transport origin for the anomalous MR. However the coefficient A shows a strong gate dependence and ultimately changes sign with changing gate bias. We therefore consider if the observations are consistent with momentum transfer between quantum transport in WS2 and lateral transport in graphene. In particular we consider two key observations: first, the sign change of the MR; second, the decrease in the amplitude of the MR on the electron branch. These two observations were reproduced in both samples #26 and #27 (see supplementary information for MR of sample #27). We now construct a qualitative description of these processes based on the interlayer drag resistance, a full quantitative description of the effect of the Coulomb interaction and therefore the calculation of A in the strongly interacting non-Fermi liquid regime is beyond existing theoretical descriptions. The drag resistance between two layers, L and R, can be evaluated to leading order as 41 ρLR

Z ∞ ImχR (q, ω)ImχR (q, ω) 1 X 2 2 dω q |Ue (q)| ∝ n L nR eβ~ω + e−β~ω − 2 0

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q~

where n is the density, ~q is momentum, U is the interaction potential, χ is the susceptibility and ω is the frequency. Momentum transfer from graphene to WS2 increases the resistance of the graphene layer, the degree of localization of the charges in WS2 will affect the graphene resistance in two ways. First, the degree of localization will affect the q dependence of momentum transfer. Second, the degree of localization influences the ability of charges in WS2 to screen the Coulomb interaction and thereby decrease the resistance. 27 We begin by describing the negative MR at large negative back-gate. In this case the density of charges in WS2 is lowest, we expect the charges to be isolated and for their localization to be strongest; therefore in this region we discount the effect of screening and we expect χ to be relatively q independent. Therefore the interlayer force is dominated by the q dependence of the interlayer interaction. The decrease in MR under the application of B is consistent with the 14 ACS Paragon Plus Environment

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stronger localization of charge at B = 0 leading to the momentum transfer at higher q and thereby enhances the resistance of graphene at B = 0. Within our explanation of the origin of the MR the decrease in magnitude can be understood as being due to the onset of screening as the carrier density accumulates in WS2 . Screening has the opposite tendency from the localized Coulomb interactions that we have described leading to a decrease in scattering. 27 The appearance of positive MR is more challenging we suggest the following explanation. Positive MR occurs close to the onset of screening and therefore intralayer correlations within the WS2 layer are significant. This leads to a shift of the maximum in χ(q, ω) to lower q, therefore we suggest interlayer force is maximized as the carriers are delocalized and larger momemtum transfer is possible. We now comment on the WS2 substrate thickness dependence of samples #26 (8.8 nm) and #27 (16.5 nm). Our measurements have revealed strong Coulomb interactions with localized charges the WS2 substrate, but as these charges become mobile they tend to screen the Coulomb interaction. In the thinner sample #26 we observed strong MR across the entire range of densities, whereas for sample #27 the large MR was confined only to more negative back-gate where WS2 is the most strongly localized. At negative back-gate bias the thinner sample #26 shows a larger MR −25% cf. −15% for sample #27. This is consistent with the enhancement of Coulomb interactions in the thinner substrate, the relatively modest thickness dependence has also been observed in the low density regime of GaAs-based bilayers. 26 In the thicker sample #27 the movement of the graphene Fermi-level toward the WS2 conduction and the onset of screening completely suppresses the MR, in contrast in the thinner sample these processes large MR and screening co-exist. Screening depends on the correlated response of multiple charges in the WS2 , we expect the length scale of the density-density correlation in WS2 to be comparable to the lφ , the thinner sample has thickness 8.8 nm ≈ 10 % of lφ we therefore suggest that even in the presence of screening effects the graphene layer probes significantly smaller length scale or equivalently is sensitive to phenomena at higher momentum.


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In summary we have demonstrated that at a vdW interface between graphene and WS2 the interaction is dominated by localized Coulomb scattering and thereby graphene is strongly sensitive to quantum interference processes in WS2 . This finding relies on ability of graphene to probe length scales in WS2 below the coherence length so that the Coulomb interaction is dominated by high q processes. While further theoretical efforts are required to fully understand this process the significance of this result is that vdW heterostructures may be used to probe and manipulate quantum processes. In the case of WS2 valleytronics has drawn significant attention, our results suggest that by controlling the valley population and therefore momentum distribution of WS2 using circularly polarized light it may be possible to controllably induce valley dependent scattering in graphene. Furthermore we have shown accurate theoretical models of the vdW interface should not ignore localized, high energy processes and strong correlations.

Supporting information

Additional information concerning: Temperature dependence of low

field magnetoresistance (I); Magnetoresistance of sample #27 (II); Temperature dependence of conductance (III); Integer quantum Hall effect at high magnetic field (IV); Dingle analysis of mean free path (IV).

Acknowledgement We acknowledge useful discussions with A.H. Castro-Neto, D.E. Khmelnitskii, and T. Taychatana¨ acknowledges support by the National Research Foundation, Prime Ministers Office, pat. B.O. Singapore under it’s Competitive Research Programme (CRP Award No. NRF-CRP9-2011-3), and the SMF-NUS Research Horizons Award 2009-Phase II. G.E. acknowledges support by National Research Foundation, Singapore under NRF Research Fellowship (NRF-NRFF2011-02).

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