Interaction-driven capacitance in Graphene electron-hole double layer in the quantum Hall regime

TL;DR

This paper investigates the quantum mechanical effects on capacitance in graphene electron-hole double layers under strong magnetic fields, revealing significant enhancements due to electron correlations.

Contribution

It provides a mean-field analysis of coherent and crystalline ground states in balanced graphene electron-hole systems across multiple Landau levels, including capacitance calculations.

Findings

Capacitance is significantly enhanced compared to geometric estimates.

Quantum corrections play a crucial role in the observed capacitance.

Correlations between electrons and holes are essential at small and intermediate layer separations.

Abstract

Fabrication of devices made by isolated Graphene or Graphene-like single layers (such as h-BN) 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 (or Graphene like) double layer electron-hole systems under strong magnetic fields where the separation between layers can be of the order of one magnetic length with interlayer tunneling still suppressed. In those separations correlations between electrons and holes are of crucial importance and must be included in determination of observable quantities. Here we report a thorough mean-field study of the 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 calculate the capacitance of such states as a function of layer separation and filling factor. Our calculations show significant enhancement of the capacitance compared to geometrical value due to quantum mechanical corrections.