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| XXXIX Workshop on Geometric Methods in Physics | 19.06–25.06.2022 |
| XI School on Geometry and Physics | 27.06–1.07.2022 |
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Jiří HrivnákElectron in triangular graphene dotsTwo types of honeycomb lattice Fourier--Weyl transforms associated to the irreducible crystallographic root system $A_2$ are utilized to study electronic properties of triangular graphene quantum dots. The triangular dots with armchair and zigzag edges are represented by two fundamentally different geometric configurations of the honeycomb lattice inside the fundamental domain of the $A_2$ affine Weyl group. The Schr\"{o}dinger equations produced by tight-binding models of electron propagation with the nearest and next-to-nearest couplings are exactly solved through armchair and zigzag honeycomb Fourier--Weyl transforms. The inclusion of boundary conditions in the tight-binding Hamiltonians provides four types of electronic stationary states expressed via the honeycomb Weyl orbit functions. The contrasting behavior of the armchair and zigzag electronic probability densities is demonstrated. This is a joint work with Lenka Motlochov\'{a}. |
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| University of Bialystok |
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