External mechanisms for valley polarisation and its effect on the magnetisation of graphene: strain and electric field

Abstract In order to control and manipulate a new degree of freedom of the charge carries, the scientific community has been focused the attention on the valley polarization and its consequences, since this effect opens doors for a plenty of new technological devices. The aim of the present work is to describe how external mechanisms on graphene flakes, like mechanical stress combined with crossed real electric and magnetic fields, lead to the emergence of a significant valley polarisation with inversion symmetry broken. We show, numerically and analytically, that the valley characteristics written on the beating pattern of the de Haas-van Alphen oscillations can be directly measured. We also verified that the period of these beats is related to the valley asymmetry.