Enhanced Antiferromagnetic Exchange between Magnetic Impurities in a Superconducting Host

Yao, Norman Y.; Glazman, L. I.; Demler, Eugene; Lukin, Mikhail D.; Sau, Jay D.

doi:10.1103/physrevlett.113.087202

Cited by 74 publications

(91 citation statements)

References 47 publications

(81 reference statements)

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“…3), and large and negative near the jumps which are associated with the sin 2 θ/2 term in Eq. (39). Note that also for the pairing strength, the strict logarithmic divergences are cut off for large but finite ξ 0 on a scale of 1/ξ 0 .…”

Section: B Large Coherence Lengthmentioning

confidence: 99%

“…(39) and (41) for h k and ∆ k can also be specified to the limit of large ξ 0 a. The dispersion h k follows from Eq.…”

Section: B Large Coherence Lengthmentioning

confidence: 99%

“…The magnitude of the correction is of order δJ(i − j) ∼ ∆/(k F r ij ) 2 and thus small at any r ij ξ 0 . The presence of deep Shiba states enhances the correction; 39 in the limit α → 1, its absolute value reaches a maximum of the order of ∆/(k F r ij …”

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confidence: 99%

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Topological superconducting phase in helical Shiba chains

2013

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Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless p-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase.

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Section: B Large Coherence Lengthmentioning

confidence: 99%

“…(39) and (41) for h k and ∆ k can also be specified to the limit of large ξ 0 a. The dispersion h k follows from Eq.…”

Section: B Large Coherence Lengthmentioning

confidence: 99%

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Topological superconducting phase in helical Shiba chains

2013

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“…The interaction between localized spins is exponentially suppressed in this case. However, it was shown that antiferromagnetic interaction in s-wave superconductors gets enhanced due to the formation of Yu-Shiba-Rusinov bound states [35], already at distances between localized spins smaller than the coherence length. We expect similar results for TIs.…”

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confidence: 99%

RKKY interaction on surfaces of topological insulators with superconducting proximity effect

Zyuzin

Loss

2014

Phys. Rev. B

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We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities on the surface of a three-dimensional topological insulator with proximity induced superconductivity. A superconductor placed on the top of the topological insulator induces a gap in the surface electron states and gives rise to a long-ranged in-plane antiferromagnetic RKKY interaction. This interaction is frustrated due to strong spin-orbit coupling, decays as 1/r for r < ξ, where r is the distance between two magnetic impurities and ξ the superconducting coherence length, and dominates over the ferromagnetic and Dzyaloshinskii-Moriya type interactions for r > ξ. We find the condition for the Yu-Shiba-Rusinov intragap states that are bound to the magnetic impurities. Motivated by the intense research on the interplay of topological insulators (TI), magnetism, [10][11][12][13][14][15][16][17][18], and superconductivity [1,19,20], we study here the RKKY interaction between magnetic impurities (localized spins) on the surface of a three-dimensional TI with proximity induced superconductivity, see Fig. 1. The effect of strong spin-orbit interaction at the surface of a TI on the RKKY interaction without superconductivity is well-studied theoretically [10][11][12][13][14][15]. If the system is at the charge neutrality point, i.e., the chemical potential is at the Dirac point, it is predicted that the localized spins can form a ferromagnetic order with magnetization pointing normal to the surface of the TI, if the out-of-plane anisotropy of the RKKY interaction is stronger than the in-plane one. Out-of-plane ferromagnetic order breaks time-reversal symmetry and opens energy band gaps in the surface states. On the other hand, the in-plane interaction is frustrated. It may result in a spin-glass state [21,22] if the in-plane anisotropy is stronger than the out-of plane one [14].The effect of magnetic impurities deposited on the surface of a TI on the band gap and the resulting magnetic order is under experimental debate [23][24][25][26][27][28][29][30]. Alternatively, the locally induced electronic spin density can be measured by NV-center atomic force microscope tips, allowing one to experimentally probe the spin-spin correlations independently of the magnetic impurities on the surface [31]. The method of spin-polarized scanning tunneling microscope for probing the surface magnetic properties of TI is well established experimentally [30].In the present paper, we consider an s-wave superconductor placed on the surface of a three-dimensional TI. The proximity effect can lead to a gap in the density

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“…Moving the tip away from the sample one can recover the dephasing and relaxation rates that are governed by thermal excitations, whose density is ∼ e −∆0/T . This long dephasing rate makes localized spin states in superconductors an appealing framework for various quantum computing applications, including those based on Majorana fermions [19,20].…”

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confidence: 99%

Nonequilibrium theory of tunneling into a localized state in a superconductor

Martin

2014

Phys. Rev. B

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A single static magnetic impurity in a fully-gapped superconductor leads to the formation of an intragap quasiparticle bound state. At temperatures much below the superconducting transition, the energy relaxation and spin dephasing of the state are expected to be exponentially suppressed. The presence of such a state can be detected in electron tunneling experiments as a pair of conductance peaks at positive and negative biases. Here we show, that for an arbitrarily weak tunneling strength, the peaks have to be symmetric with respect to the applied bias. This is in contrast to the standard result in which the tunneling conductance is proportional to the local (in general particle-hole asymmetric) density of states. The asymmetry can be recovered if one allows for either a finite density of impurity states, or if impurities are coupled to another, non-superconducting, equilibrium bath.

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Enhanced Antiferromagnetic Exchange between Magnetic Impurities in a Superconducting Host

Cited by 74 publications

References 47 publications

Topological superconducting phase in helical Shiba chains

Topological superconducting phase in helical Shiba chains

RKKY interaction on surfaces of topological insulators with superconducting proximity effect

Nonequilibrium theory of tunneling into a localized state in a superconductor

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