Thue-Morse Graphene Superlattice Research Articles

Low-dimensional thermoelectricity in aperiodic gated graphene superlattices

We investigate numerically the thermoelectric properties of aperiodic graphene superlattices generated by applying an external electric field following the Fibonacci and Thue–Morse sequences. We find that aperiodicity reduces and fragments the transmission bands natural in periodic superlattices as well as redistributes the density of states of the system. We also find an overall reduction of the conductance in aperiodic graphene superlattices with respect to periodic ones. Furthermore, as the generation of the aperiodic structure increases, the conductance decreases and a series of peaks arise on it. This behavior is more pronounced in Thue–Morse superlattices than in Fibonacci ones. In the case of the thermoelectric properties, we obtain that Fibonacci graphene superlattices present similar values for the Seebeck coefficient and the power factor as in periodic superlattices, while Thue–Morse graphene superlattices show an enhancement of the thermoelectric properties, in particular the power factor is two times larger than the corresponding one to periodic and Fibonacci graphene superlattices. So, according to our findings, aperiodicity can be used as a tuning parameter to improve the thermoelectric properties of graphene superlattices.

Bandgap engineering in aperiodic Thue-Morse graphene superlattices

The lack of bandgap in graphene is the main factor that prevents that this outstanding material be implemented in optoelectronics. In this work, we show that by nanostructuring graphene aperiodically it is possible to have an efficient transmission bandgap engineering. In particular, we are considering aperiodic graphene superlattices in which electrostatic barriers are arranged following the basic construction rules of the Thue-Morse sequence. We find that the transmission bandgap can be modulated readily by changing the angle of incidence as well as by appropriately choosing the generation of the Thue-Morse superlattice. Even, this angle-dependent bandgap engineering is more effective than the corresponding one for periodic graphene superlattices.

Spin transport and tunnel magnetoresistance in ferromagnetic graphene/Thue–Morse graphene superlattice double junction

Abstract We have theoretically investigated the spin transport properties and tunnel magnetoresistance of the double junction, which consists of the fifth-stage Thue–Morse graphene superlattice (TMGSL) or periodic graphene superlattice (PGSL) and three ferromagnetic graphene (FG) electrodes. The results indicate that the middle ferromagnetic graphene stripe can lead to obvious defect effect on the conductance. Meanwhile, the FG/TMGSL double junction possesses more marked defect effect when compared to the FG/PGSL double junction, along with larger and more irregular oscillation conductance and tunnel magnetoresistance.

Transmission spectrum of electrons through a Thue-Morse graphene superlattice

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.

Spin transport and magnetoresistance in Thue-Morse graphene superlattice with two ferromagnetic graphene electrodes

We investigate theoretically the spin-dependent transport and tunnel magnetoresistance in a system consisting of two ferromagnetic graphene (FG) electrodes separated by the Thue-Morse graphene superlattice (TMGSL) or periodic graphene superlattice (PGSL). Using transfer matrix methods, the spin-dependent conductance, tunnel magnetoresistance, and spin polarization of current of the FG/TMGSL/FG junctions are numerically calculated and compared with those of the FG/PGSL/FG junctions. The results indicate that all the physical quantities considered here show typical quasiperiodic oscillations as the electrostatic barrier height increases. Furthermore, the conductances, spin polarization of the current for the parallel configuration of magnetization, and tunnel magnetoresistance monotonically increase or decrease with increasing exchange splitting energy. Interestingly, compared to the FG/PGSL/FG junctions, all the physical quantities, considered here, of the FG/TMGSL/FG junctions can exhibit a more marked growth stage effect, along with stronger and more irregular oscillations with increasing electrostatic barrier height.

Exotic electronic properties in Thue–Morse graphene superlattices

To show the specific behavior of Dirac fermions in a quasi-periodic structure, we investigate the electronic properties in a deterministic Thue–Morse graphene superlattice. Our main findings include the following. (i) Unlike conventional Schrödinger electrons, quasi-periodic features such as the striking self-similarity and trifurcation in the transmission spectrum can be manifested only at oblique incidence. (ii) In the vicinity of the usual Dirac point, extra Dirac points emerge; their locations are dependent merely on the second generation of the Thue–Morse structure and the number is double that in the periodic graphene superlattice. (iii) A classification is given about the wavefunctions in the Thue–Morse structure which are transformed from the critical states into extended ones at the Dirac points. (iv) The electrons can transmit perfectly at the extra Dirac points, and such a collimation supplies a convenient way to experimentally detect the numbers and the locations of the extra Dirac points. These exotic electronic properties in the aperiodic graphene superlattices may facilitate some applications in graphene-based electronics.