Majorana fermions in superconducting nanowires without spin-orbit coupling

Kjærgaard, Morten; Wölms, Konrad; Flensberg, Karsten

doi:10.1103/physrevb.85.020503

Cited by 197 publications

(160 citation statements)

References 28 publications

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“…In these recent Majorana proposals, the presence of the helical order was either assumed a priori [13,[23][24][25][26][27][28] or shown to exist in rather limited situations [14][15][16]. In this Letter, we revisit the claims of the emergent self-tuned topological superconductivity in magnetic chains in realistic experimental conditions.…”

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confidence: 85%

“…If correct, this is a breakthrough in the prospective realization of non-Abelian topological phases of matter, and hence of great importance. A helical spin texture is a crucial ingredient also in most other proposals for topological superconductivity [17][18][19][20][21][22].In these recent Majorana proposals, the presence of the helical order was either assumed a priori [13,[23][24][25][26][27][28] or shown to exist in rather limited situations [14][15][16]. In this Letter, we revisit the claims of the emergent self-tuned topological superconductivity in magnetic chains in realistic experimental conditions.…”

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confidence: 86%

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Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

et al. 2014

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We theoretically obtain the phase diagram of localized magnetic impurity spins arranged in a one-dimensional chain on top of a one-or two-dimensional electron gas. The interactions between the spins are mediated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism through the electron gas. Recent work predicts that such a system may intrinsically support topological superconductivity without spin-orbit coupling when a helical spin-density wave is spontaneously formed in the spins, and superconductivity is induced in the electron gas. We analyze, using both analytical and numerical techniques, the conditions under which such a helical spin state is stable in a realistic situation in the presence of disorder. We show that (i) it appears only when the spins are coupled to a (quasi-) 1D electron gas, and (ii) it becomes unstable towards the formation of (anti) ferromagnetic domains if the disorder in the impurity spin positions δR becomes comparable with the Fermi wave length. We also examine the stability of the helical state against Gaussian potential disorder in the electronic system using a diagrammatic approach. Our results suggest that in order to stabilize the helical spin state and thus the emergent topological superconductivity under realistic experimental conditions, a sufficiently strong Rashba spin-orbit coupling, giving rise to Dzyaloshinskii-Moriya interactions, is required.PACS numbers: 73.21. Hb, 71.10.Pm, 74.78.Fk Magnetism originating from interactions between magnetic atoms mediated by delocalized electrons (the so-called RKKY interaction) represents an important problem in modern condensed matter physics [1] and has been a subject of intense research [2][3][4][5][6][7]. In this Letter, we consider the specific case of a helical spin density wave (SDW) that might appear in a one-dimensional chain of magnetic atoms that are coupled to a metal or a superconductor. The issue of RKKY-induced magnetism has recently taken on a new and unexpected interesting perspective in the physics of non-Abelian Majorana bound states (Majoranas) [8,9], with the recent claims of the natural (i.e. self-tuned) emergence of Majorana modes in a chain of states induced by magnetic atoms at the surface of a superconductor, see Fig. 1. A Majorana-carrying topological superconducting phase should emerge in this system without the tuning of any external parameters due to the existence of an RKKY-stabilized helical order in conjunction with s-wave superconductivity [13][14][15][16]. If correct, this is a breakthrough in the prospective realization of non-Abelian topological phases of matter, and hence of great importance. A helical spin texture is a crucial ingredient also in most other proposals for topological superconductivity [17][18][19][20][21][22].In these recent Majorana proposals, the presence of the helical order was either assumed a priori [13,[23][24][25][26][27][28] or shown to exist in rather limited situations [14][15][16]. In this Letter, we revisit the claims of the emergent self-tuned topological supercon...

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confidence: 85%

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confidence: 86%

Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

et al. 2014

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“…155 Remarkably, clever routes to engineering a topological phase in systems without spin-orbit coupling were even devised recently. 156,157 The key idea can be understood by rewriting our original wire Hamiltonian in Eq. (64) in terms of rotated operatorsψ = e imαxσ y ψ:…”

Section: 97mentioning

confidence: 99%

“…The required non-uniform Zeeman field in the latter setup can be generated using an array of magnetic nanoparticles deposited on a superconductor 156 or by coupling a set of magnetic gates to a wire 157 . Finally, we note that one can engineer a 1D topological superconducting state with cold fermionic atoms using optical Raman transitions (to generate effective spinorbit coupling and Zeeman fields) and a proximity effect with a bulk molecular BEC.…”

Section: 97mentioning

confidence: 99%

New directions in the pursuit of Majorana fermions in solid state systems

2012

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The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review article highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one-and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals, and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects, and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

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“…In semiconductor wires with SOC-based effective p-wave pairing, the energetically isolated MBSs do not survive the transition to 2D, but rather evolve into edge states with increasing wire width [42,43]. Without SOC, a helical magnetic texture can still produce MBSs in 1D sys- tems [23,44,45]. The MBSs may then survive the transition to 2D, but spread entirely along opposite edges, precluding braiding.…”

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Wireless Majorana Bound States: From Magnetic Tunability to Braiding

et al. 2016

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We propose a versatile platform to investigate the existence of Majorana bound states (MBSs) and their nonAbelian statistics through braiding. This implementation combines a two-dimensional electron gas formed in a semiconductor quantum well grown on the surface of an s-wave superconductor, with a nearby array of magnetic tunnel junctions (MTJs). The underlying magnetic textures produced by MTJs provide highly-controllable topological phase transitions to confine and transport MBSs in two dimensions, overcoming the requirement for a network of wires. Obtained scaling relations confirm that various semiconductor quantum well materials are suitable for this proposal. PACS numbers: 74.78.Na,74.25.Ha,74.45.+c In condensed-matter systems Majorana bound states (MBSs) are emergent quasiparticles with exotic non-Abelian statistics and particle-antiparticle symmetry [1][2][3][4][5][6][7]. Elucidating their properties is further motivated by the prospect to use them for fault-tolerant quantum computing [8][9][10]. Typical material systems envisioned for experimental implementations of MBSs include superconducting regions [11] such as those relying on the native p-wave pairing in a vortex core [12], Sr 2 RuO 4 [13,14], and Bechgaard salts [15]. They can also occur with common proximity-induced s-wave pairing when combined with a nontrivial spin structure, which can be provided by spin-orbit coupling (SOC) and magnetic textures [16][17][18][19][20][21][22][23][24] to yield an effective p-wave pairing.Impressive advances in fabricating complex superconducting systems for an unambiguous detection of MBSs remain actively debated [23,[25][26][27][28][29][30]. Observed MBS signatures, such as a zero-bias tunneling conductance peak, may have other origins [31][32][33][34][35] and should be supplemented by additional measurements [36][37][38][39][40]. However, those signatures do not directly probe non-Abelian statistics [2][3][4]8]. While realizing the non-Abelian braiding statistics under exchange would provide both an ultimate proof for the MBS existence and the key element for topological quantum computing, even theoretical schemes imply a significant complexity to implement such braiding [10]. Exchanging vortices on the surface of the p-wave superconductor to close the braiding loop would require an experimental tour de force. Frequently examined one-dimensional (1D) superconductor/semiconductor wire systems avoid the need for challenging vortex manipulation, but that geometry alone is insufficient. Braiding statistics are ill-defined in 1D and complex wire networks must be used instead of single wires, posing additional obstacles [10,41].To address these challenges, in Fig. 1 we propose a versatile platform to realize MBSs and enable their braiding in 2D superconductor/semiconductor systems without the need for wire networks. This proposal seemingly contradicts prior knowledge. In semiconductor wires with SOC-based effective p-wave pairing, the energetically isolated MBSs do not survive the transition to 2D, but rather ev...

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Majorana fermions in superconducting nanowires without spin-orbit coupling

Cited by 197 publications

References 28 publications

Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

New directions in the pursuit of Majorana fermions in solid state systems

Wireless Majorana Bound States: From Magnetic Tunability to Braiding

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