The Quantum Transport Properties In Graphene With Fermi Velocity Modulations

Graphene has already given rise to a great amount of new physics and potentialapplications in nanoelectronic devices and electronic transport in graphene has become thesubject of enormous attention. The low-energy excitations of the nonrelativistic2D electronsystem in graphene are consistent with the massless limit of the two-dimensional Diracequation, namely, the Dirac-Weyl equation, for massless relativistic quasiparticles. The bandstructure of this single carbon atom layer has a linear dispersion relationship near the twoinequivalent Dirac points where the valence and conduction bands touch each other and formtwo conically shaped valleys. The Fermi velocity, which is independent of the momentum,can be controlled by the strength of the electron-electron interactions.Recently, much interest has been aroused by research on graphene-basedvelocity-modulation structures, where the Fermi velocity of the Dirac fermion depends on itsposition in space, e.g., a velocity well (barrier) defines the region in which the Fermi velocityis less than (greater than) that in the surrounding background. The quantum transportproperties in graphene-based velocity-modulation structures are quite different from those ingraphene-based structures controlled by magnetic and electric fields, e.g., the total internalreflection angle of a velocity barrier is independent of the energy of the incident electron, butdepends on the Fermi velocities of the different regions which play the role of the refractiveindex in optics. Therefore, the quantum transport in graphene-based velocity-modulationstructures provides a new avenue for manipulating electrons in graphene and opens upanother route for developing new nanoelectronic devices with desirable transport properties.In this paper, we concentrate on the transport properties in symmetric and asymmetricgraphene-based velocity-modulation structures. The major contents and important results aregiven as follows:Firstly, based on the transfer matrix method, transport properties in graphene-basedsymmetric double velocity-barrier and velocity-well structures under the influence ofmagnetic and electric fields have been investigated. It is found that velocity wells (barriers)have properties similar to those of electrostatic wells (barriers) according to the similar features of the transmission probability, conductance and Fano factor. The number of resonantpeaks increases when compared to the single velocity barrier or well case for angle dependenttransmission probabilities. The Fano factor for the combined velocity and electrostaticbarriers oscillates strongly in the region ofEF U0due to the velocity-modulation effectwhich greatly enlarges the resonant tunneling region of the double electrostatic barrierstructure. The conductance and the Fano factor for velocity wells are shown to oscillate morerapidly than for the case of velocity barriers. When a magnetic field is applied, the plateauwidth of the Fano factor with a Poissonian value shortens (broadens) in the velocity well(barrier) case due to the velocity-modulation effect. The conductances and the Fano factorsfor different values of the velocity ratio are identical at the point ofEF U0. Thesemiquantitative analysis results of the critical values c,E cFandE care consistent withthose of the numerical calculation.Secondly, we have studied transport properties in graphene-based asymmetric doublevelocity well and electric well structures using the transfer matrix method. It is found that theconductance shows periodic quantum oscillatory behavior with increasing Fermi energy insymmetric double wells. The results also show that quantum beats occur in the oscillation ofthe conductance for asymmetric double velocity wells. The node positions in the beatingpattern depend on the sizes of the asymmetric double velocity wells. The beat frequency forthe asymmetric double well is exactly equal to the frequency difference between theoscillations in two isolated single wells. The beating effect can be found in asymmetric doubleelectric wells, but only if the widths of the two wells are different. This implies that theoscillation frequency of the conductance is almost independent of the depth of the electricwell. We have proposed a qualitative interpretation based on the fact that the positions of theresonant levels depend upon the sizes of quantum wells. The beating behavior can provide anew way to identify the symmetry of double well structures.