On the origin of transversal current in double-layer heterostructures

Abstract

It is shown that usually used theoretical model for double-layer heterostructures as a pseudospin ferromagnet does not explain the observed two-dimensional spectrum. Its existence is possible when neglecting Coulomb interaction destroying two-dimensional structures and can be realized only in a strong magnetic field. That is connected also with the plain vortex lattices forming in strong magnetic fields due to thermodynamic instability. This model gives reasonable explanations of various observed effects depending on the filling of the corresponding bands. In particular in this work we show that in double-layer heterostructures a large interlayer conductance really observed can exist. Keywords: double-layer heterostructures, two-dimensional spectrum, magnetic fields.The experiments with double-layer heterostructures have a long history beginning from the late eighties of the previous century. The main number of theoretical works [1,2] used the layer index as an additional quasi-spin index. However the experimental work [3] showed that the theoretical results based on this assumption contradict to the performed experiment and require some other description close to the used for one-layer systems [4].We take the coordinate z perpendicular to the plain of the layers and the coordinates = ( , )x y r describe a twodimensional space with a constant electron potential energy ( ) = ( ) U z U z − (see Fig. 1). We assume the existence of a constant magnetic field B directed along z large enough to make the energy of electron Coulomb interaction proportional to B small compared to the magnetic energy proportional to B . That is very important because Coulomb interaction tends to destroy two-dimensional effects. Further we shall neglect Coulomb electron interaction assuming large enough magnetic field.It was shown in the theoretical work [5] for this case the situation is unstable and the creation of plain vortex lattices gives the thermodynamic gain. That is the case of the separate action of the variables z and r, therefore electron wave functions are the products of two functions ( ) ( ).Z z Φ r Various types of the vortex lattices are possible. The electron filling of the proper bands defines the physical properties. The separation of the variables gives two Shrödinger equationswhere ( ) U z is the two-well potential (see Fig. 1). The functions ( ) Φ r are defined by two-dimensional equationHere the effective vector potential eff A includes not only the vector potential of the external magnetic field (1 / 2)[ ] Br but also the contribution of vortices (with the Fig. 1. Interwell potential.