On the role of two-dimensional phonons in the possibility of the observation of the quantum hall effect in graphene at room temperature

An explanation of the possibility of the observation of the quantum Hall effect in graphene at room temperature with allowance for the two-dimensional nature of the electron and phonon excitations has been proposed. It has been shown that the two-dimensional character of the electron-phonon interaction under conditions of a strong magnetic field establishes the threshold for the energy of the emitted or absorbed phonon, thus reducing the fraction of the electronic states involved in the percolation process. The number of mixed states is proportional to the root of the magnetic field rather than to the temperature. Therefore, the percolation threshold in a rather strong magnetic field no longer depends on the temperature and the limitation on the maximum observation temperature with allowance for exclusively two-dimensional phonons arises owing to the temperature smearing of the Fermi distribution function. The contribution of three-dimensional phonons, as well as the quantitative agreement with the experiment, has also been discussed.