Interaction-driven capacitance in graphene electron-hole double layer in strong magnetic fields

Abstract

Fabrication of devices made by isolated graphene layers has opened up possibility of examining highly correlated states of electron systems in parts of their phase diagram that is impossible to access in their counterpart devices such as semiconductor heterostructures. An example of such states are graphene double monolayer electron-hole systems under strong magnetic fields where the separation between layers can be adjusted to be as small as one magnetic length with interlayer tunneling still suppressed. In those separations, it is known that correlations between electrons and holes are of crucial importance and must be included in determination of observable quantities. Here we report the results of our full numerical Hartree-Fock study of coherent and crystalline ground states of the interacting balanced electron-hole graphene systems in small and intermediate separations with each layer occupying up to four lowest lying Landau levels. We show that in the Hartree-Fock approximation the electrons and holes pair to form a homogeneous Bose-condensed (excitonic) state, while crystalline states of such exciton systems remain incoherent at intermediate layer separations. Our results of calculation of capacitance of such states as a function of interlayer separation and filling factor provides quantitative and qualitative signatures that can be examined in real experiments. We show that the capacitance of some crystallized states as well as uniform coherent states are significantly enhanced compared to geometrical values solely due to Coulomb interactions and quantum corrections.