The role of vector potential coupling in hot electron cooling power in bilayer graphene at low temperature

We have studied, in bilayer graphene (BLG), the hot electron cooling power FVP (T, ns) due to acoustic phonons via vector potential (VP) coupling. It is calculated as a function of electron concentration ns and temperature T and compared with FDP (T, ns) that due to deformation potential coupling. For the ns around 1x10 12 cm, FVP (T, ns) is much smaller than FDP (T, ns). With increase of ns, FDP (T, ns) decreases faster than FVP (T, ns) does. A cross over is predicted and dominant contribution of FVP (T, ns) can be observed at large ns. In the BlochGrüneisen (BG) regime FVP (T, ns)~ ns -1/2 and FDP (T, ns)~ ns . Both FVP (T, ns) and FDP (T, ns) have the same T dependence with T 4 power law in BG regime. Behaviour of FDP (T, ns)~ ns -3/2 and T 4 is in agreement with the experimental results at moderate ns. Besides, in BG regime, we have predicted, for both the VP and DP coupling, a relation between F(T,ns) and the acoustic phonon limited mobility μp, opening a new door to determine μp from the measurements of F(T,ns)