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Unveiling in-gap states and Majorana zero modes in superconductor-topological insulator bilayer model

Umesh Kumar1,*, Rafał Rechciński2,3, Tatiana de Picoli4, Jukka Vayrynen4, and Satoshi Okamoto1

  • *Contact author: kumaru@ornl.gov
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Phys. Rev. Research 8, 023061 – Published 20 April, 2026

DOI: https://doi.org/10.1103/vgqt-49lx

Abstract

Interfaces between topological insulators and superconductors (SCs) are promising platforms for realizing Majorana zero modes (MZMs) via the superconducting proximity effect. We introduce a bilayer model consisting of the surface states of a three-dimensional topological insulator (3DTI) coupled to an s-wave superconductor and systematically study the role of interlayer tunneling strength (t⊥) motivated by the recent growth of the Fe(Te,Se)/Bi2Te3 heterostructure. We find that increasing t⊥ shifts the proximity-induced (PrI) gap minimum away from the Γ point, giving rise to momentum-selective interference patterns that manifest as spatial oscillations in the in-gap states. We introduce an antidot with a magnetic vortex in the model and investigate the resulting in-gap states, including MZMs and Caroli–de Gennes–Matricon (CdGM) modes. With increasing hybridization strength, the energy separation between MZMs and CdGM states increases, enhancing the isolation of MZMs. Importantly, in the strong hybridization limit, the leading CdGM separation remains large in spite of the decrease in the PrI gap. Spin- and spatially resolved wavefunction analysis reveals angular momentum asymmetries absent in conventional s-wave systems. A direct comparison with a standalone s-wave superconductor confirms the emergence of distinct p-wave-like features in the bilayer geometry. Our results provide experimentally relevant predictions for tuning the stability of MZMs and their differentiation from the CdGM modes in SC-3DTI heterostructures and offer a theoretical framework for probing unconventional superconductivity in engineered topological systems.

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Phys. Rev. Research 8, 023061– Published 20 April, 2026
  • Received 4 August 2025
  • Accepted 24 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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