Abstract
Electron superlattices allow the engineering of correlated and topological quantum phenomena. The recent emergence of moiré superlattices in two-dimensional heterostructures has led to exciting discoveries related to quantum phenomena. However, the requirement for the moiré pattern poses stringent limitations, and its potential cannot be switched on and off. Here, we demonstrate remote engineering and on/off switching of correlated states in bilayer graphene. Employing a remote Coulomb superlattice realized by localized electrons in twisted bilayer WS2, we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS2. When the remote superlattice is turned off, the two-dimensional electron gas in the bilayer graphene is described by a Fermi liquid. When it is turned on, correlated insulating states at both integer and fractional filling factors emerge. This approach enables in situ control of correlated quantum phenomena in two-dimensional materials hosting a two-dimensional electron gas.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the findings of this study are available at https://doi.org/10.5061/dryad.w3r2280xx.
References
Esaki, L. & Tsu, R. Superlattice and negative differential conductivity in semiconductors. IBM J. Res. Dev. 14, 61–65 (1970).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).
Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).
Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).
Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).
Huang, D., Choi, J., Shih, C.-K. & Li, X. Excitons in semiconductor moiré superlattices. Nat. Nanotechnol. 17, 227–238 (2022).
Regan, E. C. et al. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat. Rev. Mater. 7, 778–795 (2022).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).
Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021).
Zhang, Z. et al. Correlated interlayer exciton insulator in heterostructures of monolayer WSe2 and moiré WS2/WSe2. Nat. Phys. 18, 1214–1220 (2022).
Gu, J. et al. Dipolar excitonic insulator in a moiré lattice. Nat. Phys. 18, 395–400 (2022).
Chen, D. et al. Excitonic insulator in a heterojunction moiré superlattice. Nat. Phys. 18, 1171–1176 (2022).
Forsythe, C. et al. Band structure engineering of 2D materials using patterned dielectric superlattices. Nat. Nanotechnol. 13, 566–571 (2018).
Li, Y. et al. Anisotropic band flattening in graphene with one-dimensional superlattices. Nat. Nanotechnol. 16, 525–530 (2021).
Dubey, S. et al. Tunable superlattice in graphene to control the number of Dirac points. Nano Lett. 13, 3990–3995 (2013).
Naik, M. H. & Jain, M. Ultraflat bands and shear solitons in moiré patterns of twisted bilayer transition metal dichalcogenides. Phys. Rev. Lett. 121, 266401 (2018).
Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene. Nat. Phys. 2, 177–180 (2006).
Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).
Zheng, Z. et al. Unconventional ferroelectricity in moiré heterostructures. Nature 588, 71–76 (2020).
Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774–778 (2022).
de la Barrera, S. C. et al. Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field. Nat. Phys. 18, 771–775 (2022).
Seiler, A. M. et al. Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 608, 298–302 (2022).
Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).
Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).
Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).
Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).
Shabani, S. et al. Deep moiré potentials in twisted transition metal dichalcogenide bilayers. Nat. Phys. 17, 720–725 (2021).
Liu, Y., Stradins, P. & Wei, S.-H. Van der Waals metal–semiconductor junction: weak Fermi level pinning enables effective tuning of Schottky barrier. Sci. Adv. 2, e1600069 (2016).
Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Compressibility of the two-dimensional electron gas: measurements of the zero-field exchange energy and fractional quantum Hall gap. Phys. Rev. B 50, 1760–1778 (1994).
Kim, S. et al. Direct measurement of the Fermi energy in graphene using a double-layer heterostructure. Phys. Rev. Lett. 108, 116404 (2012).
Lee, K. et al. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 58–61 (2014).
Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene. Nature 592, 43–48 (2021).
Yang, F. et al. Experimental determination of the energy per particle in partially filled Landau levels. Phys. Rev. Lett. 126, 156802 (2021).
Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934).
Slagle, K. & Fu, L. Charge transfer excitations, pair density waves, and superconductivity in moiré materials. Phys. Rev. B 102, 235423 (2020).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Acknowledgements
The dilution fridge measurements were supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. The device fabrication was supported by Army Research Office award W911NF2110176. The optical characterization was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division (DE-AC02-05-CH11231), within the van der Waals Heterostructure Program (KCWF16). K.W. and T.T. acknowledge support from JSPS KAKENHI (grant nos. 19H05790, 20H00354 and 21H05233).
Author information
Authors and Affiliations
Contributions
F.W. conceived the research. Z.Z. and J.X. fabricated the devices and performed most of the experimental measurements together. W.Z., R.Q., S.K., M.C. and A.Z. contributed to the fabrication of the van der Waals heterostructures. C.S. and S.W. helped with transport measurements. Z.Z., J.X. and F.W. performed data analysis. K.W. and T.T. grew the hBN crystals. All the authors discussed the results and wrote the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data
Extended Data Fig. 1 Determination of chemical potential jump height at \(v_{{\rm{WS}}_2}=1\) in device I.
The data is collected at zero magnetic field and at the temperature T = 18 K. The blue curve is the chemical potential of twisted bilayer WS2 extracted from the charge neutral points of bilayer graphene. The black dashed lines are the linear fit to the left and right of the jump. 70 data points are used for these two linear fit. The deviation from the two linear fits in the chemical potential defines the jump width, which represents the error bar in the estimation of carrier density. The center of the jump width defines the jump position. The jump height, indicated by the double arrow line, is calculated by the vertical separation of the linear fitted lines at the jump position. The error bar for jump height is estimated from the standard deviation of the slope of the two fitted lines.
Extended Data Fig. 2 Insulating states in the twisted bilayer WS2 lead to jumps in the chemical potential sensed by the bilayer graphene.
a, 2D color plot of four-terminal resistance (Rxx) as a function of Vt and Vbias with the bottom gate voltage fixed at Vb = −16 V. The data is collected at zero magnetic field and at the temperature T = 18 K. On the left (right) of the yellow dashed line, the twisted bilayer WS2 is intrinsic (electron-doped). In the right region, the charge neutral line of bilayer graphene, characterized by a large resistance, can be clearly identified. Along this bilayer graphene charge neutral line, the chemical potential (\(\mu_{\mathrm{WS}_2}\)) and electron densities (\(n_{\mathrm{WS}_2}\)) of the twisted bilayer WS2 can be directly calculated. The values of \(\mu_{\mathrm{WS}_2}\) and \(n_{\mathrm{WS}_2}\) are indicated on the right and top axis, respectively. The chemical potential shows several discrete jumps at specific electron densities (denoted by the yellow and white arrows), corresponding to the insulating states formed at the different filling \(v_{\mathrm{WS}_2}\) in the twisted bilayer WS2 moiré superlattice. Two prominent jumps, denoted by two yellow arrows, correspond to the insulating states formed at the integer filling factor \(v_{\mathrm{WS}_2}\) = 1 and 2 in the twisted bilayer WS2 moiré superlattice. The electron density separation between the two jumps is around 0.23 × 1012 cm-2. The twist angle of the twisted bilayer WS2 is approximately 59.2 degrees. The moiré superlattice period of device I is estimated to be 22 nm. b, The magnitude of chemical potential jumps, their corresponding electron densities, and our tentative assignments of filling factors of the twisted bilayer WS2. The deviation from the two linear fits in the chemical potential defines the jump width, which represents the error bar in the electron density. An example is shown in Extended Data Fig. 1. The center of the jump width defines the jump position. The jump height is estimated by the vertical separation of the linear fitted lines at the jump position. The error bar for jump height is estimated from the standard deviation of the slope of the two fitted lines. The chemical potential jumps at the \(v_{\mathrm{WS}_2}=1\) and 2 are the strongest, which allows us to determine the moiré period of the twisted bilayer WS2.
Extended Data Fig. 3 Remote Coulomb superlattice behavior in device III with a superlattice period of 13 nm.
a, The 2D color plot of Rxx as a function of top gate voltage Vt and bottom gate voltage Vb at Vbias = −0.8 V. The data is collected at zero magnetic field and at the nominal temperature T = 10 mK. The phase diagram has four regions depending on the electron doping in the twisted bilayer WS2 (intrinsic or electron-doped) and bilayer graphene (hole- or electron-doped). When the remote Coulomb superlattice is turned on, the hole-doped bilayer graphene shows a correlated insulator state at νbigr = 1. b, Vertical electric field dependence of the insulating state at νbigr = 1. The top gate voltage is at Vt = 6 V. The data is collected at zero magnetic fields and at the nominal temperature T = 10 mK. The correlated insulator states become more pronounced at the higher vertical electric field. c, Landau fan diagram when the remote Coulomb superlattice is turned off. (The twisted bilayer WS2 is intrinsic at Vt = 0 V and Vbias = 0 V.) The data is collected at the nominal temperature T = 10 mK. νLL is Landau level filling factor. Here the VCNP is around Vb = −13.3 V. d, Magnetic field dependence of the correlated insulator states when the remote Coulomb superlattice is turned on. The bias gate voltage is at Vbias = −0.3 V, and the top gate voltage is at Vt = 6 V. The data is collected at the nominal temperature T = 10 mK. A resistance peak at νbigr = 1 is always present at all magnetic fields, demonstrating the strong electron correlation when the remote Coulomb superlattice is turned on. Two resistance peaks appear at high magnetic fields. We tentatively assigned them to the generalized Wigner crystal states at νbigr = 1/3 and 2/3. Here the VCNP is around Vb = − 17.5 V.
Extended Data Fig. 4 Three-dimensional phase diagram at two representative temperatures of device I.
a and b, Three-dimensional (3D) color plots of Rxx as a function of the bottom gate voltage Vb, bias gate voltage Vbias, and top gate voltage Vt at T = 10 mK (a) and 18 K (b). The data is collected at zero magnetic field. Here the Rxx is plotted in a log scale to better visualize the resistance peaks at higher hole doping densities in bilayer graphene. The charge-neutral line of bilayer graphene forms a closed loop across the three surfaces. Inside the charge neutral loop, the bilayer graphene is hole-doped, and twisted bilayer WS2 is electron-doped. This charge neutral loop bends down (lower top gate voltage) at higher temperatures, which is possibly due to the improved contact resistance at the twisted bilayer WS2.
Extended Data Fig. 5 Estimation of thermal activation gap for the νbigr = 1 correlated insulator state of bilayer graphene.
Arrhenius plot of the peak resistance at Vt = 3.5 V. The linear fit at high temperatures yields the thermal excitation gap of (59 ± 2) K. The error bar is from the linear fit. The data is collected at zero magnetic field.
Extended Data Fig. 6 Vb-dependent resistance of device II at different temperatures.
The top gate voltage is at Vt = 6 V, and the bias gate voltage is at Vbias = −0.4 V. The data is collected at zero magnetic field. We assign νbigr = 1 and 0 to the two resistance maximums. The resistance at νbigr = 1 and 0 decreases with increasing temperatures, confirming the insulting behavior. Between the νbigr = 1 and 0 state, the resistance increases with increasing temperature, reflecting the metallic behavior. We note that the Rxx peak positions at νbigr = 1 and 0 show a slight shift with increasing temperature for fixed gate voltages (Similar effect is observed in device I, Extended Data Fig. 4). We have shifted the Vb for the curves above 10 mK so that the resistance peaks at νbigr = 1 and 0 matches.
Extended Data Fig. 7 Quantized Hall resistance when the Coulomb superlattice is turned off.
a and b, The Hall resistance shows plateaus at quantized resistance of 1/νLL (h/e2) when the magnetoresistance minimum is observed in device I (a) and device II (b). Here νLL is the Landau level filling factor, h is the Planck constant, and e is the electron charge. The data is collected at the nominal temperature T = 10 mK.
Extended Data Fig. 8 Characterization of remote Coulomb superlattice in device II.
a, 2D color plot of four-terminal resistance (Rxx) as a function of Vt and Vbias with the bottom gate voltage fixed at Vb = −60 V. In the right region, the charge neutral line of bilayer graphene is identified by a large resistance. Along the charge neutral line, the chemical potential (\(\mu_{{\rm{WS}}_2}\)) and electron densities (\(n_{\mathrm{WS}_2}\)) of the twisted bilayer WS2 are calculated according to Eqs. (1) and (2) in the Methods. The values of \(\mu_{\mathrm{WS}_2}\) and \(n_{\mathrm{WS}_2}\) are indicated on the right and top axis, respectively. Two prominent jumps, denoted by two yellow arrows, correspond to the insulating states formed at the integer filling factor \(v_{{\rm{WS}}_2}\) =1 and 2 in the twisted bilayer WS2 moiré superlattice. The electron density separation between the two jumps is around 0.61 × 1012cm-2. The twist angle of the twisted bilayer WS2 is approximately 58.7 degrees. The moiré superlattice period of device II is estimated to be 14 nm. The temperature of this plot is at T = 19.5 K. The data is collected at zero magnetic field. b, The magnitude of chemical potential jumps, their corresponding electron densities, and our tentative assignments of filling factors of the twisted bilayer WS2. The deviation from the two linear fits in the chemical potential defines the jump width, which represents the error bar in the electron density. An example is shown in Extended Data Fig. 1. The center of the jump width defines the jump position. The jump height is estimated by the vertical separation of the linear fitted lines at the jump position. The error bar for jump height is estimated from the standard deviation of the slope of the two fitted lines. The chemical potential jumps at the \(v_{{\rm{WS}}_2}\) = 1 and 2 are the strongest, which allows us to determine the moiré period of the twisted bilayer WS2. The other chemical potential jumps occur at either integer filling or n/3 fillings of the moiré superlattice. The insulating states at n/3 fillings correspond to generalized Wigner crystal states.
Extended Data Fig. 9 Vertical electric field and magnetic field dependence of insulating states of bilayer graphene in device II when the remote Coulomb superlattice is turned on.
a, Vertical electric field dependence of the insulating state at νbigr = 1 and 2. The data is collected at zero magnetic field and at the nominal temperature T = 10 mK. The top gate voltage is at Vt = 6 V. The correlated insulator states become more pronounced at the higher vertical electric field. b, Magnetic field (B) dependence of the insulating states at the dashed line in a. The bottom gate voltage is at Vb = −25 V, and the top gate voltage is at Vt = 6 V. The resistance peak at νbigr = 1 is nearly insensitive to the magnetic field, demonstrating the strong electron correlation when the remote Coulomb superlattice is turned on. The resistance peaks at tentatively assigned νbigr = 2/3 and 1/3 indicate the possible magnetic field stabilized generalized Wigner crystal states in bilayer graphene. The data is collected at the nominal temperature T = 10 mK.
Extended Data Fig. 10 Characterization of remote Coulomb superlattice in device III.
a, 2D color plot of four-terminal resistance (Rxx) as a function of Vt and Vbias with the bottom gate voltage fixed at Vb = −20 V. In the right region, the charge neutral line of bilayer graphene is identified by a large resistance. Along the charge neutral line, the chemical potential (μWS2) and electron densities (nWS2) of the twisted bilayer WS2 are calculated according to Eqs. (1) and (2) in the Methods. The values of \(\mu_{\mathrm{WS}_2}\) and \({n}_{\mathrm{WS}_2}\) are indicated on the right and top axis, respectively. Four jumps, denoted by four yellow arrows, correspond to the insulating states formed at the different integer filling factor \(v_{\mathrm{WS}_2}\) in the twisted bilayer WS2 moiré superlattice. The vertical dashed lines correspond to the chemical potential jumps at four integer filling factors. The average electron density separation between the three jumps is around 0.64 × 1012/cm2. The twist angle of the twisted bilayer WS2 is approximately 58.6 degrees. The moiré superlattice period of device III is estimated to be 13 nm. The temperature is at T = 18 K. The data is collected at zero magnetic field. b, The magnitude of chemical potential jumps, their corresponding electron densities, and our tentative assignments of filling factors of the twisted bilayer WS2. The deviation from the two linear fits in the chemical potential defines the jump width, which represents the error bar in the electron density. An example is shown in Extended Data Fig. 1. The center of the jump width defines the jump position. The jump height is estimated by the vertical separation of the linear fitted lines at the jump position. The error bar for jump height is estimated from the standard deviation of the slope of the two fitted lines. The chemical potential jumps at the \(v_{\mathrm{WS}_2}=1\) and 2 are the strongest, which allows us to determine the moiré period of the twisted bilayer WS2. The other chemical potential jumps occur at either integer filling or n/3 fillings of the moiré superlattice. The insulating states at n/3 fillings correspond to generalized Wigner crystal states.
Supplementary information
Supplementary Information
Supplementary Figs. 1–6.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, Z., Xie, J., Zhao, W. et al. Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice. Nat. Mater. 23, 189–195 (2024). https://doi.org/10.1038/s41563-023-01754-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41563-023-01754-3
This article is cited by
-
A moiré proximity effect
Nature Materials (2024)
