Landau level spectrum of Bloch electrons in a honeycomb lattice

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Abstract
The energy spectrum of a tight-binding honeycomb lattice in the presence of a uniform magnetic field is analysed. The graph of the spectrum over a wide range of rational reduced flux Φ/Φ0 through elementary hexagonal cells is plotted. The energy spectrum is found to have recursive properties similar to those discussed previously on the square and triangular lattices. New features of the spectrum are also obtained. Specific properties (gaps, subbands, etc.) are shown to be a direct consequence of frustration and are compared with the spectrum of Bravais lattices. Our results are shown to be relevant for the recent measurements of the upper critical field of a superconducting honeycomb network. A comparison of the structure of the edge of the spectrum on square, triangular and honeycomb lattices is also outlined