Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices

Teixeira, Raphael L. R. C.; Kuzmanovski, Dushko; Black‐Schaffer, Annica M.; Silva, Luis G. G. V. Dias da

doi:10.1103/physrevb.99.035127

Cited by 6 publications

(13 citation statements)

References 38 publications

(54 reference statements)

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“…This, however, does not affect the existence of a topological phase, as we find that fixing a constant ∆ for all sites does not change the phase diagram, although general properties of the system do change. The superconducting order in the middle of the sample is compatible to the one found in the full bulk calculations, 25 i.e. not using a finite slab system, which ensures that the bulk properties are the same.…”

Section: Model and Methodsmentioning

confidence: 81%

“…As expected, these systems are nearly indistinguishable from the phase diagrams resulting from a full-bulk calculation. 25 As we move the chain closer to the edge, the topological phase diagram changes, significantly increasing the phase space area of the topological phase for µ 0.4t, see, e.g., Figs. 2(a) and 3(a).…”

Section: Topological Phase Diagramsmentioning

confidence: 99%

“…In a previous work, 25 we established that a combination of the QSHI+SC+FM and MAG+SC approaches can realize MBSs at the ends of a magnetic chain placed in the bulk of a QSHI with induced superconductivity. This arrangement allows for phase diagrams with "boundless" topological phases, where the topological phase is independent on certain parameters, but, notablyy, where the form of which depends crucially on the magnetic ordering in the chain.…”

Section: Introductionmentioning

confidence: 99%

“…22 Other studies have shown that graphene-like materials, such as silicene and stanene, even host induced superconductivity when doped. 11,[23][24][25] Together, these properties make 2D topological insulators with honeycomb geometry a promising candidate for realizing MBSs in the QSHI+SC+FM scheme.…”

Section: Introductionmentioning

confidence: 99%

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Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges

Teixeira,

Kuzmanovski,

Black-Schaffer

et al. 2020

Preprint

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The most promising mechanisms for the formation of Majorana bound states (MBSs) in condensed matter systems involve one-dimensional systems (such as semiconductor nanowires, magnetic chains, and quantum spin Hall insulator (QSHI) edges) proximitized to superconducting materials. The choice between each of these options involves trade-offs between several factors such as reproducibility of results, system tunability, and robustness of the resulting MBS. In this article, we propose that a combination of two of these systems, namely a magnetic chain deposited on a QSHI edge in contact with a superconducting surface, offers a better choice of tunability and MBS robustness compared to magnetic chain deposited on bulk. We study how the QSHI edge interacts with the magnetic chain, and see how the topological phase is affected by edge proximity. We show that MBSs near the edge can be realized with lower chemical potential and Zeeman field than the ones inside the bulk, independently of the chain's magnetic order (ferromagnetic or spiral order). Different magnetic orderings in the chain modify the overall phase diagram, even suppressing the boundless topological phase found in the bulk for chains located at the QSHI edge. Moreover, we quantify the "quality" of MBSs by calculating the Majorana Polarization (MP) for different configurations. For chains located at the edge, the MP is close to its maximum value already for short chains. For chains located away from the edge, longer chains are needed to attain the same quality as chains located at the edge. The MP also oscillates in phase with the in-gap states, which is relatively unexpected as peaks in the energy spectrum corresponds to stronger overlap of MBSs.

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Section: Model and Methodsmentioning

confidence: 81%

Section: Topological Phase Diagramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges

Teixeira,

Kuzmanovski,

Black-Schaffer

et al. 2020

Preprint

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“…In what follows we study the subgap states of a single impurity existing in the proximitized periodic honeycomb lattice, that have received a great deal of interest both in experimental [11][12][13][14][15] and theoretical studies [16][17][18] . In particular, more complex nanostructures embedded into such proximitized QSHI material could develop the Majorana-type quasiparticles 19 .…”

Section: Introductionmentioning

confidence: 99%

In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor

Głodzik¹,

Domański²

2020

J. Phys.: Condens. Matter

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We study the in-gap states of a single magnetic impurity embedded in a honeycomb monolayer proximitized to s-wave bulk superconductor, analyzing a role played by the intrinsic spin-orbit coupling (SOC) introduced by Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)]. This interaction induces the quantum spin Hall insulating (QSHI) phase with a gap around the Fermi energy. In this gap, spin-polarized states reside, which, via the superconducting proximity effect, evolve into the Shiba-like bound states. We explore their spatial profiles and analyze the quantum phase transition (QPT), where the Shiba-like quasiparticles cross each other leading to abrupt reversal of the local currents circulating around the magnetic impurity. The mutual interplay of the Kane-Mele spin orbit interaction with the proximity induced electron pairing could be important for designing the edge modes of more complex nanostructures, such as magnetic nanowires or islands, in topological superconducting phase.

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A self-consistent investigation of the topological state in the Ising superconductors

Jiang

Shang

2019

J. Phys.: Condens. Matter

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By self-consistently solving the Bogoliubov-de Gennes equations, we investigate the superconductivity, the magnetization and the local density-of-state (DOS) of the Ising superconductor. The calculations show that the Ising spin orbital coupling is responsible for the anisotropic behaviors of the Ising superconductor in response to the external magnetic field. In the absence of the magnetic impurities, only opposite spin triplet superconducting (SC) pairing correlations can be induced from the intrinsic on-site singlet SC pairing. The equal spin triplet SC correlations can be induced when a magnetic impurity chain with in-plane spin direction is deposited on the Ising superconductor. The chain could support a pair of Majorana Fermions, which are originated from the induced 1-dimensional equal spin triplet SC pairing correlations. The local DOS for the Majorana Fermion states exhibits an excellent agreement with the experimental observations. The low energy spectrum as a function of the exchange coupling strength forms two hourglass shapes. The waist of the hourglass may serves as a boundary to separate the zero energy crossings of the two lowest energy levels into topologically trivial and non-trivial quantum states. These results not only account for the experimental observations in a realistic way, but also clarify several important questions in the studies of the Ising superconductors.

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Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices

Cited by 6 publications

References 38 publications

Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges

Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges

In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor

A self-consistent investigation of the topological state in the Ising superconductors

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