Detection of electron velocity in graphene by Doppler effect

Electron velocity in a two-dimensional electron gas can be measured by Doppler shift. Thus, we construct the Doppler shift of light and apply it to the motion of electrons in a graphene sheet to estimate the electron velocity. Here, a laser beam with initial frequency is incident on the graphene sheet in a parallel direction, and then the frequency of the emitted light can be measured by spectroscopy after detecting the electron velocity. Then, the ratio of frequency shift from the Doppler effect is described in terms of the electron velocity, as well as the incident and the detection angle of laser beam. The thermal broadening of detected frequency as a function of velocity is also shown for different temperatures.