Transport properties of superconducting hybrid structures based on quantum wells with normal and inverted band ordering

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In our project, we will study theoretically the transport properties of hybrid structures based on HgTe and InAs/GaSb quantum wells (QWs) in the insulating or semiconducting state with the normal and inverted band ordering. QWs proximity-coupled to an s-wave superconductor will be considered, whereby special attention will be given to the influence of the Rashba and Dresselhaus spin-orbit interactions on the transport properties. Further, the transport properties of the QW coupled to a normal and a superconducting contact in the presence of the Zeeman field will be analyzed. Interesting properties of the hybrid structures predicted recently in the band structure calculations, which are caused by the spin-orbit interaction, will be studied here analyzing transport. The first one is a reversion of the chirality of Majorana edge states in a topological superconductor induced in a QW by changing the relative strength of the Rashba and Dresselhaus spin-orbit terms, an effect that goes along with a change of the bulk topological invariant. The second feature is the high tunability of the Rashba spin-orbit energies and the effective g-factors with a moderate variation of potential drop across the QW width. These features could have a significant effect on the transport properties of the hybrid structures and offer additional methods of transport tuning.Moreover, we will study transport properties of a QW in the inverted regime with a magnetically gapped region connected to the superconducting contacts. Two cases will be considered: when magnetic and superconducting regions are induced at one edge of the QW, and when they extend over the whole width of the structure, i.e. over the helical edge states at the opposite boundaries of the QW. In the second case four Majorana fermions (predicted earlier to appear at the interface between superconducting and magnetically gapped regions in the QW) build a processable fermionic qubit with logical basis states of the same parity. We expect, that the qubit can be tuned externally changing the phase difference between the Josephson junctions as well as an overlap of the helical edge states at the two boundaries by gate voltage, which might be interesting for quantum computation processing with non-abelian anyons.We will analyze the influence of disorder on the transport properties of hybrid structures. In the case of the inverted regime of the QW both bulk and edge state contributions to the transport in the structures will be considered simultaneously. This will provide more realistic estimations of the transport properties in the analyzed systems and will be important for the interpretation of future experiments.