This week I made holiday from computational finance. Some of the regular readers might remember my blog post entry about
artificial grapheme. We did a lot of calculations, analysed the data and found surprisingly good agreements with the experiment (a group in Stanford). Our collaborator from the university of Tampere visited us last week and we finalised the paper.
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| Examples of model potentials for flakes of artificial graphene. Electrons are confined in the red (dark gray) regions between circular scattering centers represented by Fermi functions. (a-c) show the three smallest flakes (L1, L2, L3, see text) and (d) corresponds to the largest flake (L9). Note that the figures are not in scale: the size of the scatterers and their mutual distance are constants. |
Although the artificial grapheme flake is a finite size system it shows properties of its periodic counterpart (graphene) when increasing its size, namely the formation of a Hofstadter butterfly and the formation of a Dirac point and according to the experiment a splitting of the point when applying a magnetic field.
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| Density of states (integration over eigenstates) in the largest flake of artificial graphene (L9) as a function of the magnetic flux. A clear Hofstadter butterfly -type pattern can be seen. |
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| Density of states for different flakes at various magnetic fields. At zero flux the increasing flake size shows the formation of the Dirac point at E ≈ 16 a.u. The magnetic field splits the point in accordance with experimental data [K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, Nature 483, 306 (2012)] |
