Erratum: Majorana fermions in superconducting nanowires without spin-orbit coupling [Phys. Rev. B<b>85</b>, 020503(R) (2012)]

Kjærgaard, Morten; Wölms, Konrad; Flensberg, Karsten

doi:10.1103/physrevb.90.059901

Cited by 47 publications

(78 citation statements)

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“…A chain of such adatoms creates many Shiba states that can hybridize and form a band, which can itself support zero-energy MFs at the ends of the chain [17,21]. Alternatively, when the magnetic exchange energy is small compared to the inter-adatom coupling, a one-dimensional band with helical magnetic order, via the Ruderman-KittelKasuya-Yosida interaction [18][19][20], is formed in the adatom chain itself that, analogously to a one-dimensional quantum wire with proximity-induced superconductivity [26][27][28], can form MFs at the ends of the chain [22].…”

Section: Introductionmentioning

confidence: 99%

Topological phases of inhomogeneous superconductivity

2016

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We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions induced by a one-dimensional system with magnetic impurities brought into close proximity to an s-wave superconductor. When the magnetic exchange energy is larger than the inter-impurity electron hopping we model the effective system as a chain of coupled Shiba states, while in the opposite regime, the effective system is accurately described by a quantum wire model. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange energy, that the system is able to support a single pair of Majorana fermions with one Majorana fermion on the left end of the system and one on the right end. When the modulation of superconductivity is large compared to the magnetic exchange energy, the Shiba chain returns to a trivially gapped regime while the quantum wire enters a new topological phase capable of supporting two pairs of Majorana fermions.

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Section: Introductionmentioning

confidence: 99%

Topological phases of inhomogeneous superconductivity

2016

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“…However, a qualitative understanding of the topological properties can be achieved along the lines of Ref. [23]. When a particle is moving in a uniformly rotating planar magnetic field of a constant magnitude, the Hamiltonian is unitary equivalent with a one describing particle experiencing a Rashba spin-orbit coupling and a constant field.…”

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confidence: 99%

“…A lattice of magnetic impurity sites on top of s-wave superconductors could provide very clean and controlled system to study MBS [19,20]. Semiconductor nanowires in the proximity of arrays of nanomagnets also give rise to topological properties similar to those in spin-orbit coupled wires [21][22][23]. The physical mechanism of topological superconductivity in magnetic systems and spin-orbit coupled systems rely on lifting the spin degeneracy of charge carriers leading to an effective p-wave pairing in the low energy corner.…”

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confidence: 99%

“…When a particle is moving in a uniformly rotating planar magnetic field of a constant magnitude, the Hamiltonian is unitary equivalent with a one describing particle experiencing a Rashba spin-orbit coupling and a constant field. The effective Rashba constant is given by α = 2 θ 2m , where θ is the rate of change of the field angle as a function of the wire coordinate [23]. In the geometry of Fig.…”

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confidence: 99%

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Majorana states and devices in magnetic structures

Ojanen

2013

Phys. Rev. B

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The pursuit for Majorana fermions is one of the top priorities in condensed matter physics at the moment. In this work we propose a new method of fabricating Majorana Josephson devices in systems with a weak or no spin-orbit coupling and without external magnetic fields. Our proposal is based on curved semiconductor wires in the proximity of superconducting elements and a small number of nanomagnets. With this method it is possible to fabricate devices that are not feasible by employing straight topological wire segments. The proposed method is naturally scalable and opens up a possibility for a systematic fabrication of arrays of Majorana states where a pair of Majorana states is obtained from a single magnet.

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“…In addition, the recent ground-breaking experiment in ferromagnetic chains presented persuasive signatures of topological superconductivity [15]. Magnetic realizations of topological superconductivity have attracted attention, since they commonly circumvent the need for materials with strong spin-orbit coupling or exotic superconducting pairing [16][17][18][19][20][21][22]. Shiba chains are particular representatives of magnetic topological systems with special advantages.…”

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confidence: 99%

Tuning topological superconductivity in helical Shiba chains by supercurrent

Röntynen

Ojanen

2014

Phys. Rev. B

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Recent experimental investigations of arrays of magnetic atoms deposited on top of a superconductor have opened a new chapter in the search for topological superconductivity. We generalize the microscopic model derived by Pientka et al. [Phys. Rev. B 88, 155420 (2013)] to accommodate the effects of finite supercurrent in the host material. Previously it was discovered that helical chains with nonplanar textures are plagued by a gapless phase. We show that by employing supercurrent it is possible to tune the chain from the gapless phase to the topological gapped phase. It is also possible to tune the chain between the trivial and the topological gapped phase, the size of which may be dramatically increased due to supercurrent. For planar textures supercurrent mainly contributes to proliferation of the gapless phase. Our predictions, which could be probed in scanning tunneling microscope experiments, are encouraging for the observation and manipulation of Majorana states. Introduction. Finding novel realizations for topological superconductivity and accompanying Majorana states has become a major source of inspiration in quantum condensed matter physics [1][2][3]. The possibility of engineering Majorana bound states (MBS), particlelike entities that could serve as building blocks of topological quantum computation [4][5][6][7], has been the primary driving force in the recent developments. Magnetic Shiba chains [8][9][10][11][12][13][14], consisting of arrays of magnetic atoms deposited on top of a superconducting host material, were recognized as promising candidates for topological superconductivity. In addition, the recent ground-breaking experiment in ferromagnetic chains presented persuasive signatures of topological superconductivity [15]. Magnetic realizations of topological superconductivity have attracted attention, since they commonly circumvent the need for materials with strong spin-orbit coupling or exotic superconducting pairing [16][17][18][19][20][21][22]. Shiba chains are particular representatives of magnetic topological systems with special advantages. Nearby magnetic atoms form effectively one-dimensional (1D) band that may undergo a topological phase transition to a 1D topological superconductor with Majorana end states, similar to nanowire realization [23][24][25][26]. Shiba chains are exceptionally disorder free and allow accessing the local density of state (LDOS) in scanning tunneling microscope (STM) experiments, enabling spatial mapping of the Majorana wave functions.Previous work on Shiba chains mostly employed a shortrange hopping model which obeys the correct symmetries and captures some qualitative features of the topological properties [8][9][10][11]. A substantial step was taken by Pientka et al., who provided a microscopic derivation of a long-range hopping model [12,13] for helical magnetic order [27], arising possibly from the Ruderman-Kittel-Kasuya-Yosida (RKKY) and the spin-orbit interaction. The iron-based Shiba chains in the recent experiment were found to be ferromagnetic. ...

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Erratum: Majorana fermions in superconducting nanowires without spin-orbit coupling [Phys. Rev. B85, 020503(R) (2012)]

Cited by 47 publications

References 0 publications

Topological phases of inhomogeneous superconductivity

Topological phases of inhomogeneous superconductivity

Majorana states and devices in magnetic structures

Tuning topological superconductivity in helical Shiba chains by supercurrent

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