Room-temperature quantum Hall effect in graphene: the role of the two-dimensional nature of phonons

We consider two-dimensional nature of the electron-phonon coupling in graphene as a source for the room-temperature quantum Hall effect discovered in 2007. It is shown that magnetic field introduces strong cut-off for coupling with the two-dimensional acoustic phonons, viz. the processes with energy tranfer exceeding ℏsl_B⁻¹ are exponentially suppressed, while for three-dimensional phonons the cut-off is set by a temperature T (here s is the sound velocity and l_B ∼ B^−1/2 is the magnetic length). Consequently, at sufficiently high temperatures and magnetic fields only a small part (∼ ℏsl_B⁻¹/T) of the electron states is involved in coupling with a given electron state in comparison with the case of three-dimensional phonons. Hence, the percolation threshold is postponed, and the quantum Hall effect survives up to T = 300 K