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 F VP ( T , n s ) due to acoustic phonons via vector potential (VP) coupling. It is calculated as a function of electron concentration n s and temperature T and compared with F DP ( T , n s ), the contribution from the deformation potential (DP) coupling. For the n s around 1 × 10 12  cm −2 , F VP ( T , n s ) is much smaller than F DP ( T , n s ). With increase of n s , F DP ( T , n s ) decreases faster than F VP ( T , n s ) does. A cross over is predicted and dominant contribution of F VP ( T , n s ) can be observed at large n s . In the Bloch- Gruneisen (BG) regime F VP ( T , n s ) ~ n s −1/2 and F DP ( T , n s ) ~ n s −3/2 . Both F VP ( T , n s ) and F DP ( T , n s ) have the same T dependence with T 4 power law in the BG regime. Behaviour of F DP ( T , n s ) ~ n s −3/2 and T 4 is in agreement with the experimental results at moderate n s . Besides, in the BG regime, we have predicted, for both the VP and DP coupling, a relation between F ( T , n s ) and the acoustic phonon limited mobility μ p , opening a new door to determine μ p from the measurements of F ( T , n s )