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    Spin-orbit control of Dirac points and topological end states in inverted gap nanowires under a transverse electric field

    Andrea Vezzosi1,2,3,*, Andrea Bertoni2,†, Marco Gibertini1,2,‡, and Guido Goldoni1,§

    • 1Dipartimento di Fisica, Informatica e Matematica, Università di Modena e Reggio Emilia, Via Campi 213/a, 41125 Modena, Italy
    • 2Istituto Nanoscienze CNR-NANO, Via Campi 213/a, 41125 Modena, Italy
    • 3Laboratory of Computational Chemistry and Biochemistry, Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland

    • *Contact author: andrea.vezzosi@unimore.it
    • †Contact author: andrea.bertoni@nano.cnr.it
    • ‡Contact author: marco.gibertini@unimore.it
    • §Contact author: guido.goldoni@unimore.it

    Phys. Rev. B 112, 085425 – Published 27 August, 2025

    DOI: https://doi.org/10.1103/1pwr-lzz5

    Abstract

    We predict that broken-gap InAs/GaSb core/shell nanowires, when operating in the topological insulating regime, undergo a collapse of the hybridization gap under the application of a transverse electric field. We perform predictive, self-consistent k·p calculations for realistic nanostructures and show that a gap closure occurs at two Kramers-related, massless Dirac points at a critical value of the field in the V/μ range. An analysis based on the Bernevig-Hughes-Zhang model shows that the newly predicted semimetal phase stems from the cancellation between the kinetic electron-hole hybridization and the spin-orbit interaction, which is controlled by the external field. Remarkably, the so-called end states—midgap states localized at the terminations of a finite-length nanowire in the inverted regime, analogously to spin Hall edge states—are supported only below the critical field, and suddenly disappear as the system is driven through the semimetal phase, eventually evolving into trivial surface states. This abrupt disappearance exposes a nontrivial transition in one dimension driven by spin-orbit coupling.

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