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Spectral properties of graphene with periodic array of defects in a magnetic field. (English) Zbl 1406.82029
The fractal structure of the spectrum is an intriguing property of periodic nanosystems in a magnetic field. This type of spectrum was observed for periodic arrays of quantum dots as it was announced in numerous publications. The graphene can be used for a detailed investigation of the properties above. To calculate the spectrum for various magnetic fields, the tight-binding approximation or the zero-range potential model can be applied. Because Hamiltonians are used, one obtains the spectral equation in an explicit form. Here, the variation of the Hofstadter butterfly-type structure of the spectrum for a periodic array of defects in graphene is analyzed. The three types of defects are investigated: vacancy, nanopore and the Stone-Wale defect. A comparison of results of computations shows that the periodic defect significantly influences the spectrum, particularly, the bands and gaps. In the periodic vacancy case, the gap appears even in the case when there is no magnetic field. The nanopore, naturally, has a greater influence on the spectrum than the other mentioned defects.
##### MSC:
 82D80 Statistical mechanical studies of nanostructures and nanoparticles 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 78A35 Motion of charged particles
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