Electric field-induced valley degeneracy lifting in uniaxial strained graphene: Evidence from magnetophonon resonance

Abstract

A double peak structure in the magnetophonon resonance (MPR) spectrum of uniaxial strained graphene, under crossed electric and magnetic fields, is predicted. We focus on the $\ensuremath{\Gamma}$ point optical phonon modes coupled to the inter-Landau level transitions $0\ensuremath{\leftrightarrows}\ifmmode\pm\else\textpm\fi{}1$ where MPR is expected to be more pronounced at high magnetic field. We derive the frequency shifts and the broadenings of the longitudinal and transverse optical phonon modes taking into account the effect of the strain modified electronic spectrum on the electron-phonon coupling. We show that the MPR line for a given phonon mode acquires a double peak structure originating from the twofold valley degeneracy lifting. The latter is due to the different Landau level spacings in the two Dirac valleys resulting from the simultaneous action of the inplane electric field and the strain-induced Dirac cone tilt. We discuss the role of some key parameters such as disorder, strain, doping, and electric field amplitude on the emergence of the double peak structure.