Identification of topological superconductivity in magnetic impurity systems using bulk spin polarization

Mashkoori, Mahdi; Pradhan, Saurabh; Björnson, Kristofer; Fransson, Jonas; Black‐Schaffer, Annica M.

doi:10.1103/physrevb.102.104501

Cited by 24 publications

(17 citation statements)

References 51 publications

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“…The study of the spin state 27,45 of the chain while varying the magnetic coupling supports the occurrence of a topological phase transition at J ∼ 2.7 eV (with parameters U = 5.5 eV, k F = 0.4 a −1 0 and α = 3.0 eV-Å) and, hence, the presence of MBS in this case. This is also in agreement with the phase diagram from Fig.…”

Section: Finite-chain Spectral Dependence On the Number Of Atomssupporting

confidence: 57%

“…As shown in Ref. [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 .…”

Section: Introductionmentioning

confidence: 97%

“…One is to study the properties of the MBS. Previous works have shown that the spin-polarization of MBS are a crucial quantity to determine 10,[44][45][46] . As shown in Ref.…”

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

Preprint

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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: Finite-chain Spectral Dependence On the Number Of Atomssupporting

confidence: 57%

Section: Introductionmentioning

confidence: 97%

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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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“…Generally, these detection methods could be supplemented by additional signatures observable in the bulk such as, e.g., the closing of the topological bulk gap and the inversion of spin polarization in the energy bands. [223][224][225][226][227][228][229][230] For pedagogical reviews covering experimental Majorana signatures, we refer to Refs. 2, 3, 73, 74, and 76.…”

Section: Discussionmentioning

confidence: 99%

Majorana bound states in semiconducting nanostructures

Laubscher,

Klinovaja

2021

Preprint

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In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple 'minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional s-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students-both theorists and experimentalists-seeking to familiarize themselves with some of the basic concepts in the field.

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“…In this work, we propose a solution to the problem described above, based on an alternative probe of second-order TSCs (SOTSCs) with broken time-reversal symmetry, which can be implemented with the help of scanning tunneling microscopes (STMs) [69][70][71][72][73][74][75][76][77][78]. We consider a subclass of SOTSCs represented by two simple models: the first one supports two MCSs at a single pair of two opposite corners and the second one supports four MCSs-one at every corner of the setup.…”

mentioning

confidence: 99%

Quadrupole spin polarization as signature of second-order topological superconductors

et al. 2021

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We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.

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Identification of topological superconductivity in magnetic impurity systems using bulk spin polarization

Cited by 24 publications

References 51 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

Majorana bound states in semiconducting nanostructures

Quadrupole spin polarization as signature of second-order topological superconductors

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