Guido van Miert

Experimental realization and characterization of an electronic Lieb lattice

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 particles [1]. Theoretical predictions are triggering the exploration of novel 2D geometries [2–10], such as graphynes, Kagomé and the Lieb lattice. The latter is the 2D analogue of the 3D lattice exhibited by perovskites [2]; it is a square-depleted lattice, which is characterised by a band structure featuring Dirac cones intersected by a flat band. Whereas photonic and cold-atom Lieb lattices have been demonstrated [11–17], 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 CO molecules positioned with a scanning tunneling microscope (STM). Using scanning tunneling microscopy, spectroscopy and wave-function 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.

Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals

Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal (

Excess charges as a probe of one-dimensional topological crystalline insulating phases

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High-Chern-number bands and tunable Dirac cones in beta-graphyne

) and inversion (

Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers

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Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension.

) symmetry. This allows us to link the presence of edge states in

Higher-order topological insulators protected by inversion and rotoinversion symmetries

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Lattice models with exactly solvable topological hinge and corner states

and

Dislocation charges reveal two-dimensional topological crystalline invariants

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Higher-order topological insulators protected by (roto)inversion symmetries

symmetric 2D insulators, which are topologically trivial according to the Altland-Zirnbauer table, to a