Model of tunnelling through double quantum layer in a magnetic field

Several explicitly solvable models are constructed for electron tunneling in a system of double two-dimensional periodic arrays of quantum dots with two laterally coupled leads in a homogeneous magnetic field are constructed. The theory of self-adjoint extensions of symmetric operators is used for modelling of electron transport. Dependencies of the transmission coefficient on the magnetic field, the energy of electron and the distance between layers are investigated. The results are compared with those of tunnelling through the corresponding single-layer periodic arrays.