A modified transfer matrix approach to include Zeeman spin splitting in dispersion relations for coupled quantum wells

In our work, we calculate the dispersion relations for InGaAs – InAlAs based double quantum wells (narrow gap structures). We have developed an improved 4 × 4 version of the Transfer Matrix Approach, considering contributions from external fields when tunneling through central barrier exists. The transverse electric field is necessary to reach the resonance of electronic levels in asymmetric structures. The in-plane magnetic field induces the Zeeman effect and the spin splitting of the resonant levels. We have also included abrupt barrier effects due to the nature of the interfaces between the above materials.