Low Temperature Physics: 44, 803 (2018); https://doi.org/10.1063/1.5049162
Fizika Nizkikh Temperatur: Volume 44, Number 8 (August 2018), p. 1025-1032    ( to contents , go back )

The energy spectra of the graphene-based quasi-periodic superlattice

A.M. Korol1,2, A.I. Sokolenko2, and I.V. Sokolenko3

1Laboratory on Quantum Theory in Linkoping, ISIR, P.O. Box 8017, S-580, Linkoping, Sweden

2National University for Food Technologies, 68, Volodymyrska str., Kyiv 01601, Ukraine
E-mail: korolam@ukr.net

3Кrypton Ocean Group, 37/97, Zhylians’ka str., Kyiv 01033, Ukraine

Received January 1, 2018, revised March 15, 2018


The spectra of the Dirac quasi-electrons transmission through the Fibonacci quasi-periodical superlattice (SL) are calculated and analyzed in the continuum model with the help of the transfer matrix method. The one-dimensional SL based on a monolayer graphene modulated by the Fermi velocity barriers is studied. A new quasi-periodical factor is proposed to be considered. We show that the Fibonacci quasi-periodic modulation in graphene superlattices with the velocity barriers can be effectively realized by virtue of a difference in the velocity barrier values (no additional factor is needed and we keep in mind that not each factor can provide the quasi-periodicity). This fact is true for a case of normal incidence of quasi-electrons on a lattice. In contrast to the case of other types of the graphene SL spectra studied reveal the remarkable property, namely the periodic character over all the energy scale and the transmission coefficient doesn’t tend asymptotically to unity at rather large energies. Both the conductance (using the known Landauer–Buttiker formula) and the Fano factor for the structure considered are also calculated and analyzed. The dependence of spectra on the Fermi velocity magnitude and on the external electrostatic potential as well as on the SL geometrical parameters (width of barriers and quantum wells) is analyzed. Using the quasi-periodical SL one can control the transport properties of the graphene structures in a wide range. The obtained results can be used for applications in the graphene-based electronics.

PACS: 73.21.Cd Superlattices;
PACS: 73.63.–b Electron transport in nanomaterials and structures.

Key words: graphene, Fibonacci superlattice, velocity barriers, transmission spectra.

Published online: June 27, 2018

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