Atomic manipulation of in-gap states in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>Bi</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mi>Pd</mml:mi></mml:math>superconductor

Mier, Cristina; Hwang, Jiyoon; Kim, Jin‐Kyung; Bae, Yujeong; Nabeshima, Fuyuki; Imai, Yoshio; Maeda, Akiko; Lorente, Nicolás; Heinrich, Andreas; Choi, Deung-Jang

doi:10.1103/physrevb.104.045406

Cited by 19 publications

(32 citation statements)

References 52 publications

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“…[45], the study of the evolution of the in-gap-band structure with the changing parameter together with the spin polarization is an excellent probe to unravel topological phases. Comparison of the Green's function obtained LDOS with experiments indeed show that Cr spin chains on β-Bi 2 Pd wide-band superconductor can undergo a topological phase transition when the number of atoms increase 27 . There, it is also shown that the staggered magnetic moment gives valuable information as predicted in Ref.…”

Section: Introductionmentioning

confidence: 68%

“…The characterization of molecular-like in-gap states has been made possible by the scanning tunneling microscope (STM) [22][23][24][25] . As more impurities are added, delocalized states form in ferromagnetic structures such that their lowest eigenergies can cross the chemical potential level of the superconductor as has been found experimentally 26,27 . Thus, the spin chain can lead to closing of the superconducting gap and to a phase transition.…”

Section: Introductionmentioning

confidence: 75%

“…Figure 1 shows the comparison of the density of states −Im G BCS ( k, ω + i0 + )/π computed using both schemes. The shown case is for k F = 0.15 a −1 0 and a = 3.36 Å that we have used to describe the β-Bi 2 Pd superconductor 23,27 The calculation of the density of states −Im G BCS ( k, ω + i0 + )/π also reveals a cutoff for k > k F when k F is smaller than the Brillouin zone value π/a. This reflects the fact that small values of r are not well-taken care of by the real-space Green's function.…”

Section: Wide-band Electronic Green's Function For Superconductorsmentioning

confidence: 95%

“…In particular, it has the advantage of a simple and efficient numerical implementation where the main operations are matrix inversions. Previous works have shown that this technique permits us to rationalize the experimental findings in wide-band superconductors with large impurity exchange coupling 23,27 . The imaginary part of the real-space Green's function is the local density of states (LDOS), then using Tersoff-Hamman's theory 43 , we can evaluate the quantities obtained in STM experiments by real-space Green's functions.…”

Section: Introductionmentioning

confidence: 94%

“…Recent experiments show that ferromagnetic spin chains can be assembled on s-wave superconductors that have a substantial Rashba spin-orbit coupling [8][9][10][11]26,27,36 . These structures can create topological phases that should show MBS at the edges of the structures even in the presence of substantial disorder 37 .…”

Section: Introductionmentioning

confidence: 99%

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Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors

Mier,

Choi,

Lorente

2021

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Magnetic impurities create in-gap states on superconductors. Recent experiments explore the topological properties of one-dimensional arrays of magnetic impurities on superconductors, because in certain regimes p-wave pairing can be locally induced leading to new topological phases. A by-product of the new accessible phases is the appearance of zero-energy edge states that have non-Abelian exchange properties and can be used for topological quantum computation. Despite the large amount of theory devoted to these systems, most treatments use approximations that render their applicability limited when comparing with usual experiments of 1-D impurity arrays on wide-band superconductors. These approximations either involve tight-binding-like approximations where the impurity energy scales match the minute energy scale of the superconducting gap and are many times unrealistic, or they assume strongly-bound in-gap states. Here, we present a theory for s-wave superconductors based on a wide-band normal metal, with any possible energy scale for the magnetic impurities. The theory is based on free-electron Green's functions. We include Rashba coupling and compare with recent experimental results, permitting us to analyze the topological phases and the experimental edge states. The infinite-chain properties can be analytically obtained, giving us a way to compare with finite-chain calculations. We show that it is possible to converge to the infinite limit by doing finite numerical calculation, paving the way for numerical calculations not based on analytical Green's functions.

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Section: Introductionmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 75%

Section: Wide-band Electronic Green's Function For Superconductorsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors

Mier,

Choi,

Lorente

2021

Preprint

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Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor

et al. 2022

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Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe2. The adatoms couple entirely via the substrate, retaining their quantum spin nature. In dimers, we observe that the deepest YSR state undergoes a quantum phase transition due to Ruderman-Kittel-Kasuya-Yosida interactions, a distinct signature of quantum spins. Chains exhibit coherent hybridization and band formation of the YSR excitations, indicating ferromagnetic coupling. Longer chains develop separate domains due to coexisting charge-density-wave order of NbSe2. Despite the spin-orbit-coupled substrate, we find no signatures of Majoranas, possibly because quantum spins reduce the parameter range for topological superconductivity. We suggest that adatom chains are versatile systems for investigating correlated-electron physics and its interplay with topological superconductivity.

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Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors

et al. 2023

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Spin chains proximitized by s-wave superconductors are predicted to enter a mini-gapped phase with topologically protected Majorana modes (MMs) localized at their ends. However, the presence of non-topological end states mimicking MM properties can hinder their unambiguous observation. Here, we report on a direct method to exclude the non-local nature of end states via scanning tunneling spectroscopy by introducing a locally perturbing defect on one of the chain’s ends. We apply this method to particular end states observed in antiferromagnetic spin chains within a large minigap, thereby proving their topologically trivial character. A minimal model shows that, while wide trivial minigaps hosting end states are easily achieved in antiferromagnetic spin chains, unrealistically large spin-orbit coupling is required to drive the system into a topologically gapped phase with MMs. The methodology of perturbing candidate topological edge modes in future experiments is a powerful tool to probe their stability against local disorder.

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Atomic manipulation of in-gap states in theβ−Bi2Pdsuperconductor

Cited by 19 publications

References 52 publications

Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors

Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors

Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor

Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors

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