Superconductivity and spin-orbit coupling in curved systems

A proper understanding of quantum physics on curved surfaces embedded in the ordinary three-dimensional space has become immediate due to the present drive in constructing low-dimensional nanostructures such as sheets and tubes that can be bent into curved, deformable objects such as tori and spirals. The main objective of this WP is to provide such a comprehensive understanding, in particular for the two driving mechanisms that can lead to the generation of non-Abelian Majorana fermions: spin-orbit interaction and the modifications of the pairing mechanisms both in intrinsic conventional superconductors and in semiconducting/superconducting heterostructures via the proximity effect.

In order to demonstrate the emergence of a curvature-induced spin-orbit interaction, we will adopt a thin-wall quantization procedure and perform a dimensional reduction procedure of the relativistic Pauli equation in confined curved three-dimensional manifolds. The non-commutativity between the generators of the Clifford algebra in curved geometries and the position operator yields an effective spin-orbital entanglement, which can be the fundamental source of curvature-induced spin-orbit effects.

A following objective is to exploit curvature-induced spin-orbit interactions in novel semiconducting/superconducting heterostructures where Majorana bound states can be generated. For this, we will study the proximity effect by explicitly taking into account the nanoscale variation of strain of bent nanodevices. Strain effects are expected to cause carrier localization in the regions under tensile strain and this can influence the mechanism of penetration of the Cooper pairs in the semiconducting regions. To analyze proximity effects in rolled-up superconducting semiconducting bilayers, microscopic tight-binding models will be developed and subsequently solved within the self-consistent approach.

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Matias Garcia



The project CNTQC acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the
Seventh Framework Programme for Research of the European Commission, under FET-Open grant number: 618083.