Electronic structure of vortices pinned by columnar defects

Mel’nikov, A. S.; Самохвалов, А. В.; Zubarev, M. N.

doi:10.1103/physrevb.79.134529

Cited by 33 publications

(38 citation statements)

References 40 publications

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“…In our situation, this condition is not satisfied, and it is possible to apply perturbation theory in orders of the vectorpotential A to account for the magnetic field. Equations (29) and (30) for the zero-energy wave functions valid for U = 0 can be used to evaluate the corresponding matrix elements. However, it is easy to check that these matrix elements are identically zero.…”

Section: B Tunneling Spectroscopy Of the Corementioning

confidence: 99%

Tunneling spectrum of a pinned vortex with a robust Majorana state

et al. 2014

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We study a heterostructure which consists of a topological insulator and a superconductor with a hole. The hole pins a vortex. The system supports a robust Majorana fermion state bound to the vortex core. We investigate the possibility of using scanning tunneling spectroscopy (i) to detect the Majorana fermion in the proposed setup and (ii) to study excited states bound to the vortex core. The Majorana fermion manifests itself as a magnetic-field dependent zero-bias anomaly of the tunneling conductance. Optimal parameters for detecting Majorana fermions have been obtained. In the optimal regime, the Majorana fermion is separated from the excited states by a substantial gap. The number of zero-energy states equals the number of flux quanta in the hole; thus, the strength of the zero-bias anomaly depends on the magnetic field. The lowest energy excitations bound to the core are also studied. The excited states spectrum differs from the spectrum of a typical Abrikosov vortex, providing additional indirect confirmation of the Majorana state observation.

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Section: B Tunneling Spectroscopy Of the Corementioning

confidence: 99%

Tunneling spectrum of a pinned vortex with a robust Majorana state

et al. 2014

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“…This gives the possibility of using this approach for a more complicated situation, for example, a vortex pinned by the cylindrical defects [20].…”

Section: Resultsmentioning

confidence: 99%

Localized states near the Abrikosov vortex core in type-II superconductors within zero-range potential model

Kulinskii¹,

Panchenko²

2015

Nanosist.: fiz. him. mat.

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We propose to treat the lowest bound states near the Abrikosov vortex core in type-II superconductors on the basis of the self-adjoint extension of the Hamiltonian of Aharonov-Bohm type with the localized magnetic flux. It is shown that the Hamiltonian for the excitations near the vortex core can be treated in terms of the generalized zero-range potential method when the magnetic field penetration depth δ is much greater than the coherence length ξ i.e. in the limit κ = δ/ξ ≫ 1. In addition, it is shown that in this limit it is the singular behavior of d∆/dr| r=0 and not the details of the order parameter ∆(r) profile that is important. In support of the proposed model, we reproduce the spectrum of the Caroli-de Gennes-Matricon states and provide direct comparison with the numerical calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921]. In contrast to the empirical formula for the energy of the ground state in Hayashi, N. we use no fitting parameter. The parameters for the boundary conditions are determined in a self-consistent manner with Caroli-de Gennes-Matricon formula.

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“…This is justified in the bulk since the sample size is of order of ξ. Although the Andreev's bound states are typically inhomogeneous, the effect of their inhomogeneity on the order parameter is still smaller than that of the continuum states even for small sizes [9]. We will later investigate the stability of the solutions with respect to variations to s (r).…”

Section: Basic Equationsmentioning

confidence: 99%

“…This means that the boundary condition on the amplitudes is consistent with a zero order parameter at the boundary point in the self-consistency equation (see details in ref. [9] and references therein).…”

Section: Basic Equationsmentioning

confidence: 99%

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Majorana states in a p-wave superconducting ring

Rosenstein¹,

Shapiro²,

Shapiro³

2013

EPL

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The spectrum of excitations of the chiral superconducting ring with internal and external radii R i , R e (comparable with coherence length ξ) trapping a unit flux Φ 0 is calculated . We find within the Bogoliubov-deGennes approach that there exists a pair of precisely zero energy states when 2k ⊥ (R e − R i ) /π is integer (here k ⊥ is the momentum component in the disk plane while k ⊥ ξ > 1 ). They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon.

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Electronic structure of vortices pinned by columnar defects

Cited by 33 publications

References 40 publications

Tunneling spectrum of a pinned vortex with a robust Majorana state

Tunneling spectrum of a pinned vortex with a robust Majorana state

Localized states near the Abrikosov vortex core in type-II superconductors within zero-range potential model

Majorana states in a p-wave superconducting ring

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