Transmission spectra of electrons through the Thue-Morse graphene superlattice

The transmission spectra of the Thue-Morse superlattice (SL) based on a monolayer gapped graphene are investigated. The SL consists of rectangular barriers located along the Ox axis. The Thue-Morse aperiodic modulation is proposed to be realized due to the difference in values of the gap width in different SL elements. It is shown that the effective splitting of the allowed bands (and thereby the arising of a series of gaps) is observed under the influence of the aperiodic factor in the case of normal incidence of the electron wave on the SL as well as in the case of oblique incidence. The spectra are periodical with potential barrier height. In some regions of the spectra, the splitting of bands is subjected to the Fibonacci inflation rule in every new Thue-Morse generation. As in the periodical graphene-based SL, in every Thue-Morse sequence a superlattice Dirac point is created. The width of the gap associated with this point depends on SL parameters substantially; at the same time the energy location of this gap depends weakly on mass term in the Hamiltonian and it does not depend on SL period. The spectra dependence on the angle of electron wave incidence is not substantial