Possibility of multiple tunnelling current peaks in a coupled quantum well system

In this work, we have numerically integrated in space and time the effective-mass nonlinear Schrödinger equation for an electron wave packet in a bilayer electron system. Considering both Hartree and exchange-correlation potentials, we have calculated the tunnelling rates between the two quantum wells when an external bias is applied in the double quantum well system. Due to the nonlinear effective-mass equation, it is found that the charge dynamically trapped in both wells produces a reaction field which modifies the system resonant condition. At different electronic sheet densities, we have shown the possibility of having multiple resonant tunnelling peaks in a bilayer electron system.