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Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

Nature Nanotechnology volume 13, pages 392–397 (2018)Cite this article

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Abstract

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from −5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

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Fig. 1: Edge-free quantum dot.
Fig. 2: Addition energy maps from dI/dV spectra.
Fig. 3: Addition energy maps for spin and valley gaps.
Fig. 4: Valley crossing.

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References

  1. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  Google Scholar 

  2. Pioro-Ladriere, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776–779 (2008).

    Article  Google Scholar 

  3. Wu, X. et al. Two-axis control of a singlet-triplet qubit with an integrated micromagnet. Proc. Natl Acad. Sci. USA 111, 11938–11942 (2014).

    Article  Google Scholar 

  4. Abanin, D. A. et al. Giant nonlocality near the Dirac point in graphene. Science 332, 328–330 (2011).

    Article  Google Scholar 

  5. Shimazaki, Y. et al. Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene. Nat. Phys. 11, 1032–1036 (2015).

    Article  Google Scholar 

  6. Sui, M. et al. Gate-tunable topological valley transport in bilayer graphene. Nat. Phys. 11, 1027–1031 (2015).

    Article  Google Scholar 

  7. Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).

    Article  Google Scholar 

  8. Wallbank, J. R. et al. Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures. Science 353, 575–579 (2016).

    Article  Google Scholar 

  9. Rahman, R. et al. Engineered valley-orbit splittings in quantum-confined nanostructures in silicon. Phys. Rev. B 83, 195323 (2011).

    Article  Google Scholar 

  10. Yang, C. H. et al Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting. Nat. Commun. 4, 2069 (2013).

    Google Scholar 

  11. Gokmen, T. et al. Parallel magnetic-field tuning of valley splitting in AlAs two-dimensional electrons. Phys. Rev. B 78, 233306 (2008).

    Article  Google Scholar 

  12. Kobayashi, T. et al. Resonant tunneling spectroscopy of valley eigenstates on a donor-quantum dot coupled system. Appl. Phys. Lett. 108, 152102 (2016).

    Article  Google Scholar 

  13. Gamble, J. K. et al. Valley splitting of single-electron Si MOS quantum dots. Appl. Phys. Lett. 109, 253101 (2016).

    Article  Google Scholar 

  14. Scarlino, P. et al. Dressed photon-orbital states in a quantum dot: Intervalley spin resonance. Phys. Rev. B 95, 165429 (2017).

    Article  Google Scholar 

  15. Mi, X., Péterfalvi, C. G., Burkard, G. & Petta, J. High-resolution valley spectroscopy of Si quantum dots. Phys. Rev. Lett. 119, 176803 (2017).

    Article  Google Scholar 

  16. Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: Magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).

    Article  Google Scholar 

  17. Pesin, D. & MacDonald, A. H. Spintronics and pseudospintronics in graphene and topological insulators. Nat. Mater. 11, 409–416 (2012).

    Article  Google Scholar 

  18. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

    Article  Google Scholar 

  19. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  Google Scholar 

  20. Woods, C. R. et al. Commensurate-incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).

    Article  Google Scholar 

  21. Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 353, 461–470 (2016).

    Article  Google Scholar 

  22. Freitag, N. M. et al. Electrostatically confined monolayer graphene quantum dots with orbital and valley splittings. Nano Lett. 16, 5798–5805 (2016).

    Article  Google Scholar 

  23. Bischoff, D. et al. Localized charge carriers in graphene nanodevices. Appl. Phys. Rev. 2, 031301 (2015).

    Article  Google Scholar 

  24. Allen, M. T., Martin, J. & Yacoby, A. Gate-defined quantum confinement in suspended bilayer graphene. Nat. Commun. 3, 934 (2012).

    Article  Google Scholar 

  25. Goossens, A. M. et al. Gate-defined confinement in bilayer graphene-hexagonal boron nitride hybrid devices. Nano Lett. 12, 4656–4660 (2012).

    Article  Google Scholar 

  26. Müller, A. et al. Bilayer graphene quantum dot defined by topgates. J. Appl. Phys. 115, 233710 (2014).

    Article  Google Scholar 

  27. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).

    Article  Google Scholar 

  28. Kretinin, A. V. et al. Electronic properties of graphene encapsulated with different two-dimensional atomic crystals. Nano Lett. 14, 3270–3276 (2014).

    Article  Google Scholar 

  29. Sachs, B., Wehling, T. O., Katsnelson, M. I. & Lichtenstein, A. I. Adhesion and electronic structure of graphene on hexagonal boron nitride substrates. Phys. Rev. B 84, 195414 (2011).

    Article  Google Scholar 

  30. van Wijk, M. M., Schuring, A., Katsnelson, M. I. & Fasolino, A. Moiré patterns as a probe of interplanar interactions for graphene on h-BN. Phys. Rev. Lett. 113, 135504 (2014).

    Article  Google Scholar 

  31. Chizhova, L. A., Libisch, F. & Burgdörfer, J. Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly. Phys. Rev. B 90, 165404 (2014).

    Article  Google Scholar 

  32. San-Jose, P., Gutiérrez-Rubio, A., Sturla, M. & Guinea, F. Spontaneous strains and gap in graphene on boron nitride. Phys. Rev. B 90, 075428 (2014).

    Article  Google Scholar 

  33. Slotman, G. J. et al. Effect of structural relaxation on the electronic structure of graphene on hexagonal boron nitride. Phys. Rev. Lett. 115, 186801 (2015).

    Article  Google Scholar 

  34. Jung, J. et al. Moiré band model and band gaps of graphene on hexagonal boron nitride. Phys. Rev. B 96, 085442 (2017).

    Article  Google Scholar 

  35. Ambrosetti, A., Ferri, N., DiStasio, R. A. Jr. & Tkatchenko, A. Wavelike charge density fluctuations and van der Waals interactions at the nanoscale. Science 351, 1171–1176 (2016).

    Article  Google Scholar 

  36. Morgenstern, M. et al. Origin of Landau oscillations observed in scanning tunneling spectroscopy on n-InAs(110). Phys. Rev. B 62, 7257–7263 (2000).

    Article  Google Scholar 

  37. Dombrowski, R., Steinebach, C., Wittneven, C., Morgenstern, M. & Wiesendanger, R. Tip-induced band bending by scanning tunneling spectroscopy of the states of the tip-induced quantum dot on inas(110). Phys. Rev. B 59, 8043–8048 (1999).

    Article  Google Scholar 

  38. Xue, J. M. et al. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat. Mater. 10, 282–285 (2011).

    Article  Google Scholar 

  39. Decker, R. et al. Local electronic properties of graphene on a BN substrate via scanning tunneling microscopy. Nano Lett. 11, 2291–2295 (2011).

    Article  Google Scholar 

  40. Mashoff, T. et al. Bistability and oscillatory motion of natural nanomembranes appearing within monolayer graphene on silicon dioxide. Nano Lett. 10, 461–465 (2010).

    Article  Google Scholar 

  41. Georgi, A. et al. Tuning the pseudospin polarization of graphene by a pseudomagnetic field. Nano Lett. 17, 2240–2245 (2017).

    Article  Google Scholar 

  42. Libisch, F., Rotter, S., Güttinger, J., Stampfer, C. & Burgdörfer, J. Transition to Landau levels in graphene quantum dots. Phys. Rev. B 81, 245411 (2010).

    Article  Google Scholar 

  43. Haigh, S. J. et al. Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices. Nat. Mater. 11, 764–767 (2012).

    Article  Google Scholar 

  44. Wong, D. et al. Characterization and manipulation of individual defects in insulating hexagonal boron nitride using scanning tunnelling microscopy. Nat. Nanotech. 10, 949–953 (2015).

    Article  Google Scholar 

  45. Morgenstern, M., Freitag, N., Nent, A., Nemes-Incze, P. & Liebmann, M. Graphene quantum dots probed by scanning tunneling microscopy. Ann. Phys. 529, 1700018 (2017).

    Article  Google Scholar 

  46. Petta, J. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).

    Article  Google Scholar 

  47. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004).

    Article  Google Scholar 

  48. Trauzettel, B., Bulaev, D. V., Loss, D. & Burkard, G. Spin qubits in graphene quantum dots. Nat. Phys. 3, 192–196 (2007).

    Article  Google Scholar 

  49. Wang, Z. et al. Origin and magnitude of ‘designer’ spin-orbit interaction in graphene on semiconducting transition metal dichalcogenides. Phys. Rev. X 6, 041020 (2016).

    Google Scholar 

  50. Jiang, Y. et al. Visualizing strain-induced pseudomagnetic fields in graphene through an hBN magnifying glass. Nano Lett. 17, 2839–2843 (2017).

    Article  Google Scholar 

  51. Mashoff, T., Pratzer, M. & Morgenstern, M. A low-temperature high resolution scanning tunneling microscope with a three-dimensional magnetic vector field operating in ultrahigh vacuum. Rev. Sci. Instr. 80, 053702 (2009).

    Article  Google Scholar 

  52. Voigtländer, B., Cherepanov, V., Elsaesser, C. & Linke, U. Metal bead crystals for easy heating by direct current. Rev. Sci. Instr. 79, 033911 (2008).

    Article  Google Scholar 

  53. Feenstra, R. Tunneling spectroscopy of the (110)-surface of direct-gap III-V semiconductors. Phys. Rev. B 50, 4561–4570 (1994).

    Article  Google Scholar 

Download references

Acknowledgements

The authors appreciate helpful discussions with C. Stampfer, H. Bluhm, R. Bindel, M. Liebmann and K. Flöhr as well assistance during the measurements by A. Georgi. N.M.F., P.N.-I. and M.M. acknowledge support from the European Union Seventh Framework Programme under Grant Agreement no. 696656 (Graphene Flagship) and the German Science foundation (Li 1050-2/2 through SPP-1459), L.A.C., J.B. and F.L. from the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF) through the SFB 041-ViCom and doctoral college Solids4Fun (W1243). TB calculations were performed on the Vienna Scientific Cluster. R.V.G., A.K.G. and K.S.N. also acknowledge support from the EPSRC (Towards Engineering Grand Challenges and Fellowship programs), the Royal Society, the US Army Research Office, the US Navy Research Office and the US Airforce Research Office. K.S.N. is also grateful to the ERC for support via Synergy grant Hetero2D. A.K.G. was supported by Lloyd's Register Foundation. P.N.-I. acknowledges support from the Hungarian Academy of Sciences Lendület under grant no. LP2017-9/2017.

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Authors and Affiliations

  1. II. Institute of Physics B, JARA-FIT, RWTH Aachen University, Aachen, Germany

    Nils M. Freitag, Péter Nemes-Incze, Christian Holl & Markus Morgenstern

  2. Institute for Theoretical Physics, TU Wien, Vienna, Austria

    Tobias Reisch, Larisa A. Chizhova, Joachim Burgdörfer & Florian Libisch

  3. Centre for Energy Research, Institute of Technical Physics and Materials Science, Budapest, Hungary

    Péter Nemes-Incze

  4. School of Physics & Astronomy, University of Manchester, Manchester, UK

    Colin R. Woods, Roman V. Gorbachev, Yang Cao, Andre K. Geim & Kostya S. Novoselov

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Contributions

N.M.F. carried out the STM measurements with assistance of P.N.-I. and C.H. and evaluated the experimental data under supervision of P.N.-I. and M.M. P.N.-I. performed the strain calculations, while T.R., F.L., and L.A.C. contributed DFT and TB calculations. C.R.W., Y.C., R.V.G., A.K.G. and K.S.N. provided the sample. M.M. conceived and coordinated the project together with N.M.F., P.N.-I. and F.L. The comparison between theory and experiment was conducted by N.M.F., M.M., F.L. and P.N.-I. M.M., N.M.F., P.N.-I. and F.L. wrote the manuscript with contributions from all authors.

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Correspondence to Markus Morgenstern.

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Supplementary Information

Supplementary Figures 1–8, Supplementary Text, Supplementary References.

Supplementary Video 1

Evolution of the wavefunctions of the valley states when moving the quantum dot through the graphene–boron-nitride structure

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Freitag, N.M., Reisch, T., Chizhova, L.A. et al. Large tunable valley splitting in edge-free graphene quantum dots on boron nitride. Nature Nanotech 13, 392–397 (2018). https://doi.org/10.1038/s41565-018-0080-8

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