Diamagnetism and suppression of screening as hallmarks of electron-hole pairing in a double layer graphene system

We study how the electron-hole pairing reveals itself in the response of a double layer graphene system to the vector and scalar potentials. Electron-hole pairing results in a rigid (London) relation between the current and the difference of vector potentials in two adjacent layers. The diamagnetic effect can be observed in multiple connected systems in the magnetic field parallel to the graphene layers. Such an effect would be considered as a hallmark of the electron-hole pairing, but the value of the effect is extremely small. Electron-hole pairing significantly changes the response to the scalar potential, as well. It results in a complete (at zero temperature) or partial (at finite temperature) suppression of screening of the electric field of a test charge situated at some distance to the double layer system. A strong increase of the electric field induced by the test charge under decrease in temperature can be considered as a spectacular hallmark of the electron-hole pairing.