Transmission spectrum of electrons through a Thue-Morse graphene superlattice

Abstract

The energy spectra of a Thue-Morse superlattice based on monolayer graphene containing a band gap are studied. The lattice consists of rectangular barriers located along the x axis. It is proposed that aperiodic Thue-Morse modulation be produced by a difference in the gap width in different elements of the superlattice. It is shown that effective splitting of the allowed bands (and, thereby, the formation of a series of gaps) under the influence of the aperiodic factor can be observed with both oblique and normal incidence of an electron wave on the superlattice. The spectra have periodicity that depends on the potential barrier height. In some segments of the spectrum, band splitting follows the Fibonacci inflation rule in each new generation. As in periodic graphene-based superlattices, a gap associated with a superlattice Dirac point is formed in all Thue-Morse generations. Its width depends substantially on the parameters of the problem; at the same time the position of this band on the energy axis depends weakly on the mass term in the hamiltonian and is independent of the superlattice period. The spectra have little dependence on the angle of incidence of the electron wave.