Hierarchical structure formation in layered superconducting systems with multi-scale inter-vortex interactions

Varney, Christopher; Sellin, Karl; Wang, Qingze; Fangohr, Hans; Babaev, Egor

doi:10.1088/0953-8984/25/41/415702

Cited by 29 publications

(56 citation statements)

References 43 publications

(61 reference statements)

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“…As some vortices are now closer to each other while being further away from others, the effective Majorana tunneling couplings become not only anisotropic, but also staggered. This can in general occur in the presence of a periodic background potential, but it could also arise due to multiscale interactions in superconductors [44] or be induced in an optical lattice setting through long-range dipolar interactions [28]. As we will show below, it may also occur spontaneously due to a possible dimerizing instability arising from the oscillations in the pairwise vortex interactions.…”

Section: B Dimerization Of the Vortex Latticementioning

confidence: 92%

Perturbed vortex lattices and the stability of nucleated topological phases

2014

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We study the stability of nucleated topological phases that can emerge when interacting non-Abelian anyons form a regular array. The studies are carried out in the context of Kitaev's honeycomb model, where we consider three distinct types of perturbations in the presence of a lattice of Majorana mode binding vortices -spatial anisotropy of the vortices, dimerization of the vortex lattice and local random disorder. While all the nucleated phases are stable with respect to weak perturbations of each kind, strong perturbations are found to result in very different behavior. Anisotropy of the vortices stabilizes the strong-pairing like phases, while dimerization can recover the underlying non-Abelian phase. Local random disorder, on the other hand, can drive all the nucleated phases into a gapless thermal metal state. We show that all these distinct behavior can be captured by an effective staggered tight-binding model for the Majorana modes. By studying the pairwise interactions between the vortices, i.e. the amplitudes for the Majorana modes to tunnel between vortex cores, the locations of phase transitions and the nature of the resulting states can be predicted. We also find that due to oscillations in the Majorana tunneling amplitude, lattices of Majorana modes may exhibit a Peierls-like instability, where a dimerized configuration is favored over a uniform lattice. As the nature of the nucleated phases depends only on the Majorana tunneling, our results are expected to apply also to other system supporting localized Majorana mode arrays, such as Abrikosov lattices in p-wave superconductors, Wigner crystals in Moore-Read fractional quantum Hall states or arrays of topological nanowires.

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Section: B Dimerization Of the Vortex Latticementioning

confidence: 92%

Perturbed vortex lattices and the stability of nucleated topological phases

2014

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“…Generalizations to multiple repulsive length scales in layered systems or caused by stray fields were discussed in 39 . In thin films intervortex interaction acquires also 1/r repulsion at long ranges due to the magnetic field outside the sample, similarly to single-component case.…”

Section: Multi-band Superconductorsmentioning

confidence: 99%

“…The ground state values of the fields |ψ i | and ϕ ij of system (39) are found by minimizing the potential energy…”

Section: Macroscopic Separation In Domains Of Different Brokenmentioning

confidence: 99%

Type-1.5 superconductivity in multicomponent systems

Babaev

Carlström

Силаев

et al. 2017

Physica C: Superconductivity and its Applications

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In general a superconducting state breaks multiple symmetries and, therefore, is characterized by several different coherence lengths ξ i , i = 1, ..., N . Moreover in multiband material even superconducting states that break only a single symmetry are nonetheless described, under certain conditions by multi-component theories with multiple coherence lengths. As a result of that there can appear a state where some coherence lengths are larger and some are smaller than the magnetic field penetration length λ:state was recently termed "type-1.5" superconductivity. This breakdown of type-1/type-2 dichotomy is rather generic near a phase transition between superconducting states with different symmetries. The examples include the transitions between U (1) andstates or between U (1) and U (1) × Z 2 states. The later example is realized in systems that feature transition between s-wave and s + is states. The extra fundamental length scales have many physical consequences. In particular in these regimes vortices can attract one another at long range but repel at shorter ranges. Such a system can form vortex clusters in low magnetic fields. The vortex clustering in the type-1.5 regime gives rise to many physical effects, ranging from macroscopic phase separation in domains of different broken symmetries, to unusual transport properties.

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“…This leads to a complete new kind of superconductor, the so-called type-1.5 superconductors [29], which allow coexistence of various properties of type-I and type-II superconductors. Type-1.5 materials can be made by placing a thin layer of type-I material onto a thin layer of type-II material [31][32][33][34]. For more articles about type-1.5 superconductors, see [27,35,36].…”

Section: Macroscopic Model For An Intermediate State Between Type-mentioning

confidence: 99%

A macroscopic model for an intermediate state between type-I and type-II superconductivity

Bockstal

Slodička

2015

Numer. Methods Partial Differential Eq.

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A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type-I and type-II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen's model. The nonlinearity is coming from the power law relation by Rhyner. The well-posedness of the problem is discussed under low regularity assumptions and the error estimate for a semi-implicit time-discrete scheme based on backward Euler approximation is established. In the proofs, the monotonicity methods and the Minty-Browder argument are used.

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Hierarchical structure formation in layered superconducting systems with multi-scale inter-vortex interactions

Cited by 29 publications

References 43 publications

Perturbed vortex lattices and the stability of nucleated topological phases

Perturbed vortex lattices and the stability of nucleated topological phases

Type-1.5 superconductivity in multicomponent systems

A macroscopic model for an intermediate state between type-I and type-II superconductivity

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