Letter | Published:

Experimental realization and characterization of an electronic Lieb lattice

Nature Physics volume 13, pages 672676 (2017) | Download Citation

Abstract

Geometry, whether on the atomic or nanoscale, is a key factor for the electronic band structure of materials. Some specific geometries give rise to novel and potentially useful electronic bands. For example, a honeycomb lattice leads to Dirac-type bands where the charge carriers behave as massless particles1. Theoretical predictions are triggering the exploration of novel two-dimensional (2D) geometries2,3,4,5,6,7,8,9,10, such as graphynes and the kagomé and Lieb lattices. The Lieb lattice is the 2D analogue of the 3D lattice exhibited by perovskites2; it is a square-depleted lattice, which is characterized by a band structure featuring Dirac cones intersected by a flat band. Whereas photonic and cold-atom Lieb lattices have been demonstrated11,12,13,14,15,16,17, an electronic equivalent in 2D is difficult to realize in an existing material. Here, we report an electronic Lieb lattice formed by the surface state electrons of Cu(111) confined by an array of carbon monoxide molecules positioned with a scanning tunnelling microscope. Using scanning tunnelling microscopy, spectroscopy and wavefunction mapping, we confirm the predicted characteristic electronic structure of the Lieb lattice. The experimental findings are corroborated by muffin-tin and tight-binding calculations. At higher energies, second-order electronic patterns are observed, which are equivalent to a super-Lieb lattice.

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Acknowledgements

Financial support from the Foundation for Fundamental Research on Matter (FOM, grants 16PR3245 and DDC13), which is part of the Netherlands Organisation for Scientific Research (NWO), as well as the European Research Council (‘FIRSTSTEP’,692691) is gratefully acknowledged. We thank J. van der Lit and N. van der Heijden for fruitful discussions.

Author information

Affiliations

  1. Debye Institute for Nanomaterials Science, Utrecht University, PO Box 80 000, 3508 TA Utrecht, the Netherlands

    • Marlou R. Slot
    • , Thomas S. Gardenier
    • , Peter H. Jacobse
    • , Stephan J. M. Zevenhuizen
    • , Daniel Vanmaekelbergh
    •  & Ingmar Swart
  2. Institute for Theoretical Physics, Utrecht University, PO Box 80 089, 3508 TB Utrecht, the Netherlands

    • Guido C. P. van Miert
    • , Sander N. Kempkes
    •  & Cristiane Morais Smith

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Contributions

M.R.S., T.S.G., P.H.J. and I.S. planned the experiment, including the proposal of the design of the CO lattice. M.R.S. and T.S.G. performed the experiments and analysed the data. P.H.J. carried out the tight-binding calculations and G.C.P.v.M. performed the muffin-tin model calculations. S.J.M.Z. developed a program that partially automates the lattice assembly. All authors contributed to the discussions and the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Ingmar Swart.

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DOI

https://doi.org/10.1038/nphys4105

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