Quasi-periodic Graphene Superlattice Research Articles

Magnetoconductivity in quasiperiodic graphene superlattices

The magnetoconductivity in Fibonacci graphene superlattices is investigated in a perpendicular magnetic field B. It was shown that the B-dependence of the diffusive conductivity exhibits a complicated oscillatory behavior whose characteristics cannot be associated with Weiss oscillations, but rather with Shubnikov-de Haas ones. The absense of Weiss oscillations is attributed to the existence of two incommensurate periods in Fibonacci superlattices. It was also found that the quasiperiodicity of the structure leads to a renormalization of the Fermi velocity v_{F} of graphene. Our calculations revealed that, for weak B, the dc Hall conductivity sigma _{yx} exhibits well defined and robust plateaux, where it takes the unexpected values pm 4e^{2}/hslash left( 2N+1right) , indicating that the half-integer quantum Hall effect does not occur in the considered structure. It was finally shown that sigma _{yx} displays self-similarity for magnetic fields related by tau ^{2} and tau ^{4}, where tau is the golden mean.

Quasiperiodic graphene superlattices: Self-similarity of the Landau level spectra

We have numerically calculated the magnetic subbands of a quasiperiodic Fibonacci graphene superlattice subject to a perpendicular magnetic field. It is shown that, when all energies and lengths are written in units of the cyclotron energy and cyclotron radius, respectively, these subbands exhibit a self-similar behavior at two magnetic fields related by τ4. To see explicitly that behavior, the energy spectrum corresponding to one of the fields must be rigidly shifted upwards in energy and in the lateral direction. It was also found that to obtain a good coincidence between both spectra, one of them must be properly rescaled in energy.

Tuning the Fano factor of graphene via Fermi velocity modulation

In this work we investigate the influence of a Fermi velocity modulation on the Fano factor of periodic and quasi-periodic graphene superlattices. We consider the continuum model and use the transfer matrix method to solve the Dirac-like equation for graphene where the electrostatic potential, energy gap and Fermi velocity are piecewise constant functions of the position x. We found that in the presence of an energy gap, it is possible to tune the energy of the Fano factor peak and consequently the location of the Dirac point, by a modulation in the Fermi velocity. Hence, the peak of the Fano factor can be used experimentally to identify the Dirac point. We show that for higher values of the Fermi velocity the Fano factor goes below 1/3 at the Dirac point. Furthermore, we show that in periodic superlattices the location of Fano factor peaks is symmetric when the Fermi velocity vA and vB is exchanged, however by introducing quasi-periodicity the symmetry is lost. The Fano factor usually holds a universal value for a specific transport regime, which reveals that the possibility of controlling it in graphene is a notable result.

Periodic to quasi-periodic graphene superlattice transition by Fermi velocity modulation

Graphene superlattices have attracted great research interest in the last years, since it is possible to manipulate the electronic properties of graphene in these structures. They can be periodic, quasi-periodic or disordered, each one presenting different electronic properties. In this work we investigate the possibility of transforming a periodic and quasi-periodic graphene superlattice one into another by a Fermi velocity modulation. We analyzed finite and infinite superlattices. We considered an one-dimensional superlattice and show that the transformation can be perfectly done for charge carriers moving in the direction of the superlattice. However, for oblique moving, some features can not be transformed by the Fermi velocity. The results obtained here are relevant for the development of novel graphene-based electronic devices.

Transport and Conductance in Fibonacci Graphene Superlattices with Electric and Magnetic Potentials

We investigate the electron transport and conductance properties in Fibonacci quasi-periodic graphene superlattices with electrostatic barriers and magnetic vector potentials. It is found that a new Dirac point appears in the band structure of graphene superlattice and the position of the Dirac point is exactly located at the energy corresponding to the zero-averaged wave number. The magnetic and electric potentials modify the energy band structure and transmission spectrum in entirely diverse ways. In addition, the angular-dependent transmission is blocked by the potential barriers at certain incident angles due to the appearance of the evanescent states. The effects of lattice constants and different potentials on angular-averaged conductance are also discussed.

Double-periodic quasi-periodic graphene superlattice: non-Bragg band gap and electronic transport

Electronic band gap and transport in quasi-periodic graphene superlattice (GSL) of double-periodic sequence are investigated. It is found that such quasi-periodic structure can possess a zero-averaged wave-number (zero-) gap which is associated with an unusual Dirac point. Different from Bragg gap, the zero- gap is less sensitive to the incidence angle, and robust against the lattice constants. The locations of Dirac point and multi-Dirac-points in the GSLs of various sequences are also compared. The control of electron transport over the zero- band gap in GSLs may facilitate the development of many graphene-based electronics.

Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice

We investigate electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice. It is found that such structure can possess a zero-k¯ gap which exists in all Fibonacci sequences. Different from Bragg gap, zero-k¯ gap associated with Dirac point is less sensitive to the incidence angle and lattice constants. The defect mode appeared inside the zero-k¯ gap has a great effect on transmission, conductance, and shot noise, which can be applicable to control the electron transport.