The modulation of the de Haas-van Alphen effect in graphene by electric field.

This paper explores the de Haas-van Alphen effect (dHvA) of graphene in the presence of an in-plane uniform electric field. Three major findings are yielded. First of all, the electric field is found to modulate the de Haas-van Alphen magnetization and magnetic susceptibility through the dimensionless parameter (β = E/(v(F)B). As the parameter β increases, the values of magnetization and magnetic susceptibility increase to positive infinity or decrease to negative infinity at the exotic point β(c) = 1. Furthermore, the dHvA oscillation amplitude rises abruptly to infinity for zero temperature at β(c) = 1, but eventually collapses at a finite temperature, thereby leading to the de Haas-van Alphen effect vanishing. In addition, the magnetic susceptibility depends on the electric and magnetic fields, suggesting that graphene should be a non-linear magnetic medium in the presence of an external field. These results, which are different from those obtained in the standard non-relativistic 2D electron gas, are attributed to the anomalous Landau level spectrum of graphene.