Keywords :
Bound-states; Edge state; Finite size; Insulator-superconductor; Majorana; One-dimensional; Superconductor heterostructures; Topological insulators; Topological properties; Two-dimensional; Electronic, Optical and Magnetic Materials; Condensed Matter Physics; Physics - Mesoscopic Systems and Quantum Hall Effect
Abstract :
[en] Heterostructures of magnetic topological insulators (MTIs) and superconductors (SCs) in two-dimensional (2D) slab and one-dimensional (1D) nanoribbon geometries have been predicted to host, respectively, chiral Majorana edge states (CMESs) and Majorana bound states (MBSs). We study the topological properties of such MTI/SC heterostructures upon variation of the geometry from wide slabs to quasi-1D nanoribbon systems and as a function of the chemical potential, the magnetic doping, and the induced superconducting pairing potential. To do so, we construct effective symmetry-constrained low-energy Hamiltonians accounting for the real-space confinement. For a nanoribbon geometry with finite width and length, we observe different phases characterized by CMESs, MBSs, as well as coexisting CMESs and MBSs, as the chemical potential, the magnetic doping, and/or the width are varied.
Funding text :
This project is financially supported by the QuantERA grant MAGMA, by the National Research Fund Luxembourg under Grant No. INTER/QUANTERA21/16447820/MAGMA, by the German Research Foundation under Grant No. 491798118, by MCIN/AEI/10.13039/501100011033 under Project No. PCI2022-132927, and by the European Union NextGenerationEU/PRTR. L.S. acknowledges support from Grants No. PID2020-117347GB-I00 funded by MCIN/AEI/10.13039/501100011033 and No. PDR2020-12 funded by GOIB. K.M. acknowledges financial support by the Bavarian Ministry of Economic Affairs, Regional Development, and Energy under Grant No. 07 02/686 58/1/21 1/22 2/23 and by the German Federal Ministry of Education and Research (BMBF) via the Quantum Future project MajoranaChips (Grant No. 13N15264) within the funding program Photonic Research Germany.This project is financially supported by the QuantERA grant MAGMA, by the National Research Fund Luxembourg under Grant No. INTER/QUANTERA21/16447820/MAGMA, by the German Research Foundation under Grant No. 491798118, by MCIN/AEI/10.13039/501100011033 under Project No. PCI2022-132927, and by the European Union NextGenerationEU/PRTR. L.S. acknowledges support from Grants No. PID2020-117347GB-I00 funded by MCIN/AEI/10.13039/501100011033 and No. PDR2020-12 funded by GOIB. K.M. acknowledges financial support by the Bavarian Ministry of Economic Affairs, Regional Development, and Energy under Grant No. 07 02/686 58/1/21 1/22 2/23 and by the German Federal Ministry of Education and Research (BMBF) via the Quantum Future project \u201CMajoranaChips\u201D (Grant No. 13N15264) within the funding program Photonic Research Germany.
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