Observation of Dirac bands in artificial graphene in small-period nanopatterned GaAs quantum wells

Abstract

Charge carriers in graphene behave like massless Dirac fermions (MDFs) with linear energy-momentum dispersion1, 2, providing a condensed-matter platform for studying quasiparticles with relativistic-like features. Artificial graphene (AG)—a structure with an artificial honeycomb lattice—exhibits novel phenomena due to the tunable interplay between topology and quasiparticle interactions3,4,5,6. So far, the emergence of a Dirac band structure supporting MDFs has been observed in AG using molecular5, atomic6, 7 and photonic systems8,9,10, including those with semiconductor microcavities11. Here, we report the realization of an AG that has a band structure with vanishing density of states consistent with the presence of MDFs. This observation is enabled by a very small lattice constant (a = 50 nm) of the nanofabricated AG patterns superimposed on a two-dimensional electron gas hosted by a high-quality GaAs quantum well. Resonant inelastic light-scattering spectra reveal low-lying transitions that are not present in the unpatterned GaAs quantum well. These excitations reveal the energy dependence of the joint density of states for AG band transitions. Fermi level tuning through the Dirac point results in a collapse of the density of states at low transition energy, suggesting the emergence of the MDF linear dispersion in the AG.

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Fig. 1: Principle of the realization of AG in a modulation-doped Al1–x Ga x As/GaAs QW.
Fig. 2: Nanofabrication of AG pattern on a modulation-doped Al0.1Ga0.9As/GaAs QW sample.
Fig. 3: Spectra of inter-AG-band transitions in sample A.
Fig. 4: Dependence of RILS on incident photon energy in sample A.
Fig. 5: Spectra of inter-AG-band transitions in sample B with a smaller Fermi energy than that in sample A.

References

  1. 1.

    Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  Google Scholar 

  2. 2.

    Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Google Scholar 

  3. 3.

    Park, C. H. & Louie, S. G. Making massless Dirac fermions from a patterned two-dimensional electron gas. Nano Lett. 9, 1793–1797 (2009).

    Google Scholar 

  4. 4.

    Gibertini, M. et al. Engineering artificial graphene in a two-dimensional electron gas. Phys. Rev. B 79, 241406 (2009).

    Article  Google Scholar 

  5. 5.

    Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

    Article  Google Scholar 

  6. 6.

    Tarruell, L., Greif, D., Uehlinger, T., Jotzu, G. & Esslinger, T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 483, 302–305 (2012).

    Article  Google Scholar 

  7. 7.

    Graß, T., Chhajlany, R., Tarruell, L., Pellegrini, V. & Lewenstein, M. Proximity effects in cold atom artificial graphene. 2D Mater. 4, 015039 (2017).

    Article  Google Scholar 

  8. 8.

    Sepkhanov, R. A., Bazally, Ya. B. & Beenakker, C. W. Extremal transmission at the Dirac point of a photonic band structure. Phys. Rev. A 75, 063813 (2007).

    Article  Google Scholar 

  9. 9.

    Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).

    Article  Google Scholar 

  10. 10.

    Ling, L., Joannopoulos, J. D. & Soljacic, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).

    Article  Google Scholar 

  11. 11.

    Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).

    Article  Google Scholar 

  12. 12.

    Heitmann, D. & Kotthaus, J. The spectroscopy of quantum dot arrays. Phys. Today 46, 56–63 (1993).

    Article  Google Scholar 

  13. 13.

    Hirler, F. et al. Spatially direct and indirect optical transitions in shallow etched GaAs/AIGaAs wires, dots and antidots. Semicond. Sci. Technol. 8, 617–621 (1993).

    Article  Google Scholar 

  14. 14.

    Weiner, J. S. et al. Electron gas in semiconductor multiple quantum wires: spatially indirect optical transitions. Phvs. Rev. Lett. 63, 1641–1644 (1989).

    Article  Google Scholar 

  15. 15.

    Egeler, T. et al. Anisotropic plasmon dispersion in a lateral quantum-wire superlattice. Phys. Rev. Lett. 65, 1804–1807 (1990).

    Article  Google Scholar 

  16. 16.

    Singha, A. et al. Two-dimensional Mott–Hubbard electrons in an artificial honeycomb lattice. Science 332, 1176–1179 (2011).

    Article  Google Scholar 

  17. 17.

    Soibel, A., Meirav, U., Mahalu, D. & Shtrikman, H. Fabrication and transport measurements of honeycomb surface superlattices. Semicond. Sci. Technol. 11, 1756–1760 (1996).

    Article  Google Scholar 

  18. 18.

    Nadvornik, L. et al. From laterally modulated two-dimensional electron gas towards artificial graphene. New J. Phys. 14, 053002 (2012).

    Article  Google Scholar 

  19. 19.

    Wang, S. et al. Observation of electron states of small period artificial graphene in nano-patterned GaAs quantum wells. Appl. Phys. Lett. 109, 113101 (2016).

    Article  Google Scholar 

  20. 20.

    Polini, M., Guinea, F., Lewenstein, M., Manoharan, H. C. & Pellegrini, V. Artificial honeycomb lattices for electrons, atoms and photons. Nat. Nanotech. 8, 625–633 (2013).

    Article  Google Scholar 

  21. 21.

    Scarabelli, D. et al. Fabrication of artificial graphene in a GaAs quantum heterostructure. J. Vac. Sci. Technol. B 33, 06FG03 (2015).

    Article  Google Scholar 

  22. 22.

    Czaplewski, D. A., Holt, M. V. & Ocola, L. E. The range and intensity of backscattered electrons for use in the creation of high fidelity electron beam lithography patterns. Nanotechnology 24, 305302 (2013).

    Article  Google Scholar 

  23. 23.

    Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2010).

    Google Scholar 

  24. 24.

    Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  Google Scholar 

  25. 25.

    Sushkov, O. P. & Neto, A. H. C. Topological insulating states in laterally patterned ordinary semiconductors. Phys. Rev. Lett. 110, 186601 (2013).

    Article  Google Scholar 

  26. 26.

    Albrecht, C. et al. Evidence of Hofstadter’s fractal energy spectrum in the quantized Hall conductance. Phys. Rev. Lett. 86, 147–150 (2001).

    Article  Google Scholar 

  27. 27.

    Geisler, M. et al. Detection of a Landau band-coupling-induced rearrangement of the Hofstadter butterfly. Phys. Rev. Lett. 92, 256801 (2004).

    Article  Google Scholar 

  28. 28.

    Melinte, S. et al. Laterally modulated 2D electron system in the extreme quantum limit. Phys Rev Lett. 92, 036802 (2004).

    Article  Google Scholar 

  29. 29.

    Žutić, I., Fabian, J. & Sarma, S. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).

    Article  Google Scholar 

  30. 30.

    Han, W., Kawakami, R., Gmitra, M. & Fabian, J. Graphene spintronics. Nat. Nanotech. 9, 794–807 (2014).

    Article  Google Scholar 

Download references

Acknowledgements

The work at Columbia University was supported by grant DE-SC0010695 from the US Department of Energy Office of Science, Division of Materials Sciences and Engineering, and by the National Science Foundation, Division of Materials Research, under award DMR-1306976. The growth of GaAs/AlGaAs QWs at Purdue University was supported by grant DE-SC0006671 from the US Department of Energy Office of Science, Division of Materials Sciences and Engineering. The growth of GaAs/AlGaAs QWs at Princeton University was supported by the Gordon and Betty Moore Foundation under award GMBF-2719 and by the National Science Foundation, Division of Materials Research, under award DMR-0819860. V.P. acknowledges the European Graphene Flagship (contract no. CNECT-ICT-604391) for financial support and the Italian Ministry of Research (MIUR) through the program ‘Progetti Premiali 2012’ – Project ‘ABNANOTECH’. The authors thank G.P. Watson for technical assistance with the ICP-RIE etching and A. Levy and F. Qiao for discussions.

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S.W. performed ICP-RIE processing and optical experiments. S.W. and L.D. performed numerical calculations. S.W., L.D., Y.Y.K. and A.P. analysed the data. D.S. and S.W. fabricated the AG lattices. G.C.G., M.J.M., K.W. and L.N.P. fabricated the QW samples. S.W., D.S., L.D., Y.Y.K., S.J.W. and A.P. co-wrote the paper with input from other authors. V.P., S.J.W. and A.P. conceived the experiments and supervised the project.

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Correspondence to Lingjie Du.

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Wang, S., Scarabelli, D., Du, L. et al. Observation of Dirac bands in artificial graphene in small-period nanopatterned GaAs quantum wells. Nature Nanotech 13, 29–33 (2018). https://doi.org/10.1038/s41565-017-0006-x

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