Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms

Westström, Alex; Pöyhönen, Kim; Ojanen, Teemu

doi:10.1103/physrevb.94.104519

Cited by 8 publications

(12 citation statements)

References 56 publications

(96 reference statements)

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“…A chain of magnetic adatoms, ferromagnetically arranged in the presence of spin-orbit coupling and placed on top of a twodimensional conventional superconductor, led to similar results [29] and localized zero energy modes were detected at the edges of adatom chain using STM: being a superconductor, these edge states were interpreted as the Majorana zero energy modes (MZEM) [30]. Other configurations of magnetic impurities such as different chains or islands [27][28][29] also lead to topological properties [54][55][56]. If the magnetic impurities have arbitrary orientations and locations, the pair breaking effect leads to gapless superconductivity and eventually destruction of superconductivity occurs for small concentration of impurities of the order of a few percent [57].…”

Section: Introductionmentioning

confidence: 83%

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

2019

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Topological properties may be induced or changed by the action of disorder. We investigate two examples of this scenario: in the first, by showing that either trivial or topological two-dimensional superconductors, as a result of a static random distribution of magnetic impurities, display topological phases. The second one involves using timedependent perturbations, which also have the general effect of inducing topology and, under appropriate conditions, the appearance of topological properties is shown. In this case, we consider the effect on the topology of onedimensional systems, of time periodic or aperiodic perturbations consisting of kicks of spatially non-homogeneous potentials. One finds different regimes characterized by localized, critical, or extended non-equilibrium states, as a result of the time dependent perturbation. We further carry out the existence and characterization of the topological edge states that occur both in the case of a static and dynamic perturbations. In the case of the static disorder, the topological phases are characterized calculating the real space Chern number and various regimes for the low energy density of states are identified and explained in the context of general properties of the symmetry classes D and C. In the case of a time periodic perturbation (the Floquet regime) we contrast the dynamical localization, and its properties, when using kicks either in the quasiperiodic spatially inhomogeneous potentials of the Aubry-André type or in the case of kicks on the pairing amplitude in the presence of static Aubry-André quasi-disorder. In both, we make use of lattice sizes drawn from the Fibonacci sequence. We also show that aperiodicity in the sequence of time perturbations leads in general to delocalization, a regime characterized by a fully random matrix Hamiltonian with the appropriate symmetry.

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Section: Introductionmentioning

confidence: 83%

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

2019

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“…In this picture, missing impurity sites give rise to vacancy states below the topological band edge and dilute vacancy states eventually drive the system gapless. 29 However, a dilute concentration of defects do not destroy the topological phases.…”

Section: Discussion and Summarymentioning

confidence: 99%

Engineering one-dimensional topological phases onp-wave superconductors

Sahlberg¹,

Westström²,

Pöyhönen³

et al. 2017

Phys. Rev. B

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In this work, we study how, with the aid of impurity engineering, two-dimensional p-wave superconductors can be employed as a platform for one-dimensional topological phases. We discover that, while chiral and helical parent states themselves are topologically nontrivial, a chain of scalar impurities on both systems support multiple topological phases and Majorana end states. We develop an approach which allows us to extract the topological invariants and subgap spectrum, even away from the center of the gap, for the representative cases of spinless, chiral and helical superconductors. We find that the magnitude of the topological gaps protecting the nontrivial phases may be a significant fraction of the gap of the underlying superconductor.

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“…A large effort was therefore made to derive simpler equivalent expressions [12][13][14][15]. Notable is the replacement of the frequency ω integral by ω = 0 and use of the Green's function then to define an effective topological Hamiltonian that correctly captures the topological classification [11,14,15,[59][60][61][62]. The latter is indeed rather intuitive since any Green's function is obtained through matrix elements of the resolvent Ĝ(ω) = (ω − H ) −1 such that H = − Ĝ−1 (0).…”

Section: Topological Hamiltoniansmentioning

confidence: 99%

Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification

Carroll

Braunecker

2021

Phys. Rev. B

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We investigate the topological classification of the subgap bands induced in a two-dimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic or spiral alignments. The wave functions for these bands are composites of Yu-Shiba-Rusinov-type states and magnetic scattering states and have a significant spatial extension away from the magnetic moments. We show that this spatial structure prohibits a straightforward extraction of a Hamiltonian useful for the topological classification. To address the latter correctly, we construct a family of spatially varying topological Hamiltonians for the subgap bands adapted for the broken translational symmetry caused by the chain. The spatial dependence in particular captures the transition to the topologically trivial bulk phase when moving away from the chain by showing how this, necessarily discontinuous, transition can be understood from an alignment of zeros with poles of Green's functions. Through the latter, the topological Hamiltonians reflect a characteristic found otherwise primarily in strongly interacting systems.

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Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms

Cited by 8 publications

References 56 publications

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

Engineering one-dimensional topological phases onp-wave superconductors

Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification

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