Finite-difference method applied for eight-band kp model for Hg1−xCdxTe/HgTe quantum well

Abstract

In this work the finite-difference method (FDM) is presented for the undoped Hg[Formula: see text]CdxTe/HgTe quantum well (QW) which allows to calculate the band structures based on Kane’s 8 × 8 kp model including all second-order terms representing the remote-band contributions. In particular the common central-difference form is employed in the discretization procedure. The FDM is applied in the envelope function approach (EFA) for the [001]-oriented system for two cases: without a magnetic field ([Formula: see text] = 0) and with a magnetic field perpendicular to the layer ([Formula: see text]). A proposed presented method can solve all the states simultaneously and can be used for a wide range of temperatures and widths of QW for different values of [Formula: see text] for Hg[Formula: see text]CdxTe/HgTe QW as well as for more complex structures, e.g., asymmetric QW, double quantum wells (DQWs), multiple quantum wells (MQWs) and for the so-called 3D topological insulator with a strained HgTe layer. The results obtained by this method are in a complete agreement with the previous ones. Based on that it is shown that the different [Formula: see text]–Cd compounds in the barrier as well as in the QW make the critical width different than 6.4 nm for HgTe QW. What is also very interesting from the application point of view of the strained mixed HgCdTe QW is that for a different width and a different mismatch lattice it is possible to observe the influence of the upper and lower parts of the Dirac cone in, e.g., a magneto-transport experiment.