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

Abstract

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), the contribution from the deformation potential (DP) coupling. For the ns around 1 × 1012cm−2, 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 Bloch- Grüneisen (BG) regime FVP (T, ns) ~ ns−1/2 and FDP (T, ns) ~ ns−3/2. Both FVP (T, ns) and FDP (T, ns) have the same T dependence with T4 power law in the BG regime. Behaviour of FDP (T, ns) ~ ns−3/2 and T4 is in agreement with the experimental results at moderate ns. Besides, in the 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)