Abstract
Spin–orbit coupling (SOC) is the key to realizing timereversalinvariant topological phases of matter^{1,2}. SOC was predicted by Kane and Mele^{3} to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene^{4,5,6,7} has precluded experimental observation in this material. Here we exploit a layerselective proximity effect—achieved via a van der Waals contact with a semiconducting transitionmetal dichalcogenide^{8,9,10,11,12,13,14,15,16,17,18,19,20,21}—to engineer Kane–Mele SOC in ultra clean bilayer graphene. Using highresolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct, incompressible, gapped phase at charge neutrality. The experimental data agree quantitatively with a simple theoretical model in which the new phase results from SOCdriven band inversion. In contrast to Kane–Mele SOC in monolayer graphene, the inverted phase is not expected to be a timereversalinvariant topological insulator, despite being separated from conventional band insulators by electricfieldtuned phase transitions where crystal symmetry mandates that the bulk gap must close^{22}. Our electrical transport measurements reveal that the inverted phase has a conductivity of approximately e^{2}/h (where e is the electron charge and h Planck’s constant), which is suppressed by exceptionally small inplane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inverted phase that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin–orbit regime in graphene heterostructures.
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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
Experimental work at UCSB was supported by the ARO under award MURI W911NF1610361. D.R. and J.C.H. acknowledge support by the US Department of Energy, DESC0016703, for synthesis of WSe_{2} crystals. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, and the CREST (JPMJCR15F3), JST. M.P.Z. was supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the US Department of Energy under contract no. DEAC0205CH11231 (van der Waals heterostructures programme, KCWF16). A.F.Y. acknowledges the support of the David and Lucile Packard Foundation and the Alfred. P. Sloan Foundation. J.O.I. acknowledges the support of the Netherlands Organization for Scientific Research (NWO) through the Rubicon grant, project number 680501525/2474. C.L. and L.S.L. acknowledge support of the STC Center for Integrated Quantum Materials under NSF grant no. DMR1231319. J.Y.K. acknowledges support by the National Science Scholarship from the Agency for Science, Technology and Research (A*STAR). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement no. DMR1644779 and the State of Florida. Measurements made use of a dilution refrigerator funded through the Major Research Instrumentation Program of the US National Science Foundation under award no. DMR1531389, and the MRL Shared Experimental Facilities, which are supported by the MRSEC Program of the US National Science Foundation under award no. DMR1720256.
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Nature thanks Saroj Prasad Dash and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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Contributions
J.O.I., X.C. and H.Z. fabricated the devices. J.O.I., X.C., E.M.S. and A.F.Y. performed the measurements. J.Y.K., C.L. and M.P.Z. performed the theoretical simulations, with J.Y.K. and C.L. advised by L.S.L. J.O.I., X.C., J.Y.K., C.L., L.S.L., M.P.Z. and A.F.Y. analysed the data. D.R. and J.C.H. grew the WSe_{2} crystals used in devices A1, S1 and A2/S2. T.T. and K.W. grew the hBN crystals used in all devices. J.O.I. and A.F.Y. wrote the paper in consultation with X.C., J.Y.K., C.L., L.S.L. and M.P.Z.
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Extended data figures and tables
Extended Data Fig. 1 Optical images and corresponding models for all the devices studied.
For each device, the optical image is shown at the top and the corresponding model shown under. a, Control device C1. b, Asymmetric device A1. c, Symmetric device S1. d, Another symmetric device with a singlesided region. Details about this device are presented in Extended Data Fig. 9. e, Another asymmetric device, A3. This device showed additional features in the magnetocapacitance measurements that are associated with a moiré superlattice potential due to alignment of the BLG with the top hBN, see Extended Data Fig. 7.
Extended Data Fig. 2 Electrical schematic showing the details of the penetration field capacitance measurements.
The components enclosed in the red dashed box are inside the cryostat, held at base temperature. Voltages are applied to V_{top} and V_{samp} (at a fixed V_{gate}) in order to adjust charge density n = c_{t}v_{t} + c_{b}v_{b} and displacement field D = (c_{t}v_{t} − c_{b}v_{b})/(2ϵ_{0}). See Methods for details.
Extended Data Fig. 3 Comparison between experimental and simulated penetration field capacitance for the three device configurations studied.
a, Penetration field capacitance, C_{P}, as a function of charge density n and displacement field D measured at B = 0 and T ≈ 50 mK in the control device, C1. b, Schematic of device C1, a BLG flake encapsulated with hBN. c, Simulated C_{P} as a function of interlayer bias, u, and charge density, n, from a lowenergy continuum model for device C1. d, Lowenergy bands for C1 near the K point of the Brillouin zone with k_{y} = 0. Line colour represents the expectation value of the outofplane projection of the electron spin, 〈S_{z}〉. Panels correspond to u = −10 meV (top), u = 0 meV (middle) and u = 10 meV (bottom). e, C_{P} for device A1. Arrows indicate weak features in C_{P}. f, Schematic of device A1, in which the BLG is asymmetrically encapsulated between WSe_{2} and hBN crystals. g, Simulated C_{P} for the asymmetric geometry with λ_{I} = 1.7 meV Ising SOC on the bottom layer. Arrows denote bandedge singularityassociated features arising from spinsplit valence (conduction) bands for electron (hole) doping, visible in h, the lowenergy band structure. h, Lowenergy bands for A1 near the K point of the Brillouin zone with k_{y} = 0. Line colour represents the expectation value of the outofplane projection of the electron spin, 〈S_{z}〉. Panels correspond to u = −10 meV (top), u = 0 meV (middle), and u = 10 meV (bottom). i, C_{P} measured for device S1. Note the incompressible phase centred at D = 0, n = 0, absent in either control or symmetric devices. j, Schematic of device S1, in which the BLG is symmetrically encapsulated between two fewlayer WSe_{2} crystals. k, Simulated C_{P} for the symmetric geometry, with an Ising SOC of equal magnitude (λ_{I} = 2.6 meV) but opposite signs on opposite layers. l, Lowenergy bands for S1 in the symmetric geometry near the K point of the Brillouin zone with k_{y} = 0. Line colour represents the expectation value of the outofplane projection of the electron spin, 〈S_{z}〉. Panels correspond to u = −10 meV (top), u = 0 meV (middle), and u = 10 meV (bottom).
Extended Data Fig. 4 Comparison between experimental data and numerical simulations including λ_{I} and λ_{R}.
a, Measured C_{P} of device A1 as a function of n and D. b–d, Simulated C_{P} from a lowenergy continuum model with SOC as follows: b, a onesided Ising SOC of λ_{I} = 1.7 meV; c, a onesided Rashba SOC of λ_{R} = 15 meV; and d, a onesided Ising SOC of λ_{I} = 1.7 meV and a Rashba SOC of λ_{R} = 15 meV. e, Linecut taken at the location of the dashed white line (D = 0.1 V nm^{−1}) in a. The symbols mark dips in C_{P} indicated with the same symbols in a. f, Linecut of the simulated data in b taken at u = −11.8 meV, equivalent to a displacement field of 0.1 V nm^{−1} for device A1. The symbols mark dips in C_{P} indicated with the same symbols in b. g, Linecut of the calculated density of states (DOS) in h for device A1 taken at u = −11.8 meV, equivalent to a displacement field of 0.1 V nm^{−1} for device A1. The symbols mark peaks in DOS which correspond to dips in C_{P} indicated with the same symbols in a, b, e, f and g. h, Calculated DOS for device A1. i, Lowenergy bands (specifically bands 3–6) near the K point of the Brillouin zone with k_{y} = 0, u = −10 meV and λ_{I} = 1.7 meV. A clear band splitting is observed in the conduction band associated with the addition of an Ising SOC. j–l, Fermi contours at E = −10 meV and u = −10 meV (j), E = 5 meV and u = −10 meV (k), and E = 6 meV and u = −10 meV (l). m, Lowenergy bands near the K point of the Brillouin zone with k_{y} = 0, u = −10 meV and λ_{R} = 15 meV. n–p, Fermi contours at E = −10 meV and u = −10 meV (n), E = 5 meV and u = −10 meV (o) and E = 6 meV and u = −10 meV (p).
Extended Data Fig. 5 Comparison between the ν = ±3 phase transitions in the control device C1 and the asymmetric device A1.
a, Energy level diagram of the zeroenergy LL in the absence of SOC. The ν = ±3 transitions are occurring between ground states with identical spin polarization. Note that offsets from u* = 0 are possible due to differing onsite energies within the BLG unit cell, which can arise from coupling to the hBN substrate, but that these offsets do not influence the spin degree of freedom. The solid and dashed lines differentiate spin orientation. b, Measured \({D}_{\nu =\pm 3}^{\ast }\) as a function of the total magnetic field (B_{T}) for fixed B_{⊥} = 4 T in control device C1. No Zeeman dependence is observed, consistent with expectations from an SOCfree model. The red dashed line is the average value of \({D}_{\nu =\pm 3}^{\ast }\). c, Energy level diagram of the zeroenergy LL with a layerselective Ising SOC of λ_{I} = 5 meV, with sign chosen so that the effect of the SOC opposes the external field (reproduced from Fig. 2f of the main text). Note that the ν = ±3 transitions now occur between ground states with opposite spin polarization. d, Measured \({D}_{\nu =\pm 3}^{\ast }\) as a function of B_{T} for fixed B_{⊥} = 4 T in device A1, reproduced from the main text. The red dashed line is a twoparameter fit with λ_{I} = 1.7 meV and ϵ_{BLG} = 2.8, with the latter needed for the conversion between experimentally measured D and theoretically calculated u. e, Schematic of the effect of B_{T} in an asymmetric device. The red curve plots the dot product of the spin orientation on the top layer and the magnetic field, and the blue curve plots the product of the spin orientation on the bottom layer and the magnetic field. Whereas the LL in the unaffected layer always aligns its spin polarization with the external magnetic field (see the red arrows in the dashed boxes for total external magnetic fields of 5, 10 and 20 T, respectively), the spin polarization of LLs in the SOCproximitized bottom layer result from a competition between SOCinduced Zeeman field (out of plane) and the changing direction of the physical Zeeman field (see the blue arrows in the dashed boxes). The affected spin cants only slightly for \({E}_{{\rm{Z}}}\ll {\lambda }_{{\rm{I}}}\), but eventually the Zeeman energy overwhelms the SOC and the two spins align as E_{Z}/λ_{I} → ∞.
Extended Data Fig. 6 Measured penetration field capacitance for devices A1, C1 and S1 at 18 T.
a–c, C_{P} measured as a function of D and n at B = 18 T for devices C1 (a), A1 (b) and S1 (c). The red dashed line in c shows the location of the linecut plotted in Extended Data Fig. 7a.
Extended Data Fig. 7 Fractional quantum Hall and Chern insulator states at high magnetic field.
a, Fractional quantum Hall states (black labels) observed at 18 T in device S1. C_{P}/C_{ref} taken at D = 1.5 V nm^{−1} in Extended Data Fig. 6c (red dashed line), corresponding to a range of −4 < ν < −2. In the N = 0 orbital, fractional quantum Hall states up to sevenths are clearly observed. In the N = 1 orbital, an incompressible state is observed at halffilling. b, Fractional Chern insulator states in asymmetric device A3 at high magnetic fields with the BLG and hBN perfectly aligned. C_{P} (normalized by C_{ref}) is shown as a function of nominal electron density n_{0}/c (where c is the geometric capacitance) and applied perpendicular magnetic field B, at a fixed polarizing electric field p_{0} \(\left(\frac{{p}_{0}}{c}=\frac{2{\epsilon }_{0}}{c}D=6{\rm{V}}\right)\). c, Schematic of the observed insulating states in units normalized to the moiré unit cell area (A_{moiré}): these are the number of flux quanta per moiré unit cell n_{Φ} (= B/A_{moiré}Φ_{0}) and the number of electrons per moiré unit cell n_{e} = n/A_{moiré}, where Φ_{0} = h/e is a flux quantum and n is the electron density. The insulating states are characterized by their inverse slope and intercept in these units, t and s, respectively. We observe a topological Chern band with δt = C = 1 and δs = 1, which originates at n_{Φ} = 1 between insulating states (t, s) = (1, 1) and (2, 0) (black lines). We observe fractional Chern insulating states at 1/3, 2/5, 3/5, 2/3 filling of the band (blue lines) with quantum numbers t, s = (4/3, 2/3), (7/5, 3/5), (8/5, 2/5), (5/3, 1/3), labelled respectively.
Extended Data Fig. 8 Phase transitions as a function of magnetic field for the rest of the zeroth LL and the N = 2, 3 excited states.
Following the analysis for \({D}_{\nu =\pm 3}^{\ast }\) in Fig. 2h, we plot the dips in C_{P} at corresponding polarizations (p_{0}/c ∝ D) as a function of perpendicular magnetic field (B) in device A1 for ν = 0 (a), ν = ±1 (b), ν = ±2 (c), ν = ±5 (d), ν = ±6 (e), ν = ±7 (f), ν = ±9 (g), ν = ±10 (h) and ν = ±11 (i). The labels (−, +) indicate the different phase transitions for each integer gap.
Extended Data Fig. 9 Summary of data from device A2/S2.
a, Optical image of device A2/S2. b, R_{xx} as a function of D and n at B = 0 T for the S2 portion of the device. The inverted phase is evident at charge neutrality and zero displacement field. c, R_{xx} as a function of B_{∥} and D for the S2 portion. d, C_{P} as a function of n and D at B = 4 T for device A2/S2. Two sets of ν = ±3 transitions are evident, indicated by the white arrows. e, ν = ±3 transitions for device A2/S2. The crossing between ν = −3 and ν = +3 coming from the onesided portion of the device (A2) is consistent with the crossing found in the asymmetric device A1. No crossing is evident in the symmetric portion which is consistent with transitions in S1.
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Island, J.O., Cui, X., Lewandowski, C. et al. Spin–orbitdriven band inversion in bilayer graphene by the van der Waals proximity effect. Nature 571, 85–89 (2019). https://doi.org/10.1038/s4158601913042
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