Design of electron wave filters in monolayer graphene with velocity modulations

We compare the transport properties of electrons in monolayer graphene by modulating the Fermi velocity inside the barrier. A critical transmission angle is found only when the Fermi velocity in the barriers is larger than the one outside the barriers. It is shown that the transmission exhibits periodicity with the incident angle below the critical transmission angle, and attenuates exponentially in the opposite situation. For both situations, peak splitting occurs in the transmission as the number of the velocity barriers increases, and the characteristics of the transmission suggest an interesting application of an excellent band-pass filter. The dependence of the conductance on the Fermi energy through an identical velocity- modulation structure differs wildly with different Fermi velocities of the barrier. The counterpart of the peak splitting is the sharp oscillations in the conductance profile. Furthermore, some oscillations for the multiple barriers are so sharp that the structure may be used as an excellent sensor.