Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled s-wave superconductors

Hui, Hoi-Yin; Brydon, P. M. R.; Sau, Jay D.; Tewari, Sumanta; Sarma, S. Das

doi:10.1038/srep08880

Cited by 77 publications

(84 citation statements)

References 38 publications

(71 reference statements)

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“…103 There have been several theoretical analyses of this ferromagnetic nanowire Majorana platform [104][105][106][107][108] showing that such a system is indeed generically capable of supporting MZMs without any need for fine tuning of the chemical potential, i.e., the system is always in the topological phase as the spin splitting V x is always much larger than Δ and μ. Although potentially an important development, more data (particularly, at lower temperatures, higher induced superconducting gap values and longer wires) would be necessary before any firm conclusion can be drawn about the experiment of ref.…”

Section: Signatures Of Mzms In Topological Superconductorsmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

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We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localised at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic MZMs in solid-state systems. We also discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC. We describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC. INTRODUCTIONTopological quantum computation 1,2 is an approach to faulttolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called 'anyons'. Anyons braid non-trivially: two counterclockwise exchanges do not leave the state of the system invariant, unlike in the cases of bosons or fermions. Anyons can arise in two ways: as localised excitations of an interacting quantum Hamiltonian 3 or as defects in an ordered system.

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Section: Signatures Of Mzms In Topological Superconductorsmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

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“…MBS is a unique quasiparticle excitation of topological SC carrying zero energy and zero total angular momentum, which appears at ends of one-dimensional systems or at vortex cores, where the SC gap is closed [13][14][15][16][20][21][22][23][24][25][26][27][28]. The unique property of equivalence between particle and antiparticle, which renders MBS noble for advanced applications, makes them difficult to be identified [9,[29][30][31].…”

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Evolution of Density of States and a Spin-Resolved Checkerboard-Type Pattern Associated with the Majorana Bound State

Kawakami

2015

Phys. Rev. Lett.

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In terms of Bogoliubov-de Gennes approach, we investigate Majorana bound state (MBS) in vortex of proximity-induced superconductivity on the surface of topological insulator (TI). Mapping out the local density of states (LDOS) of quasiparticle excitations as a function of energy and distance from vortex center, it is found that the spectral distribution evolves from "V"-shape to "Y"-shape with emergence of MBS upon variation of chemical potential, consistent with the STM/STS measurement in a very recent experiment [Xu et al., Phys. Rev. Lett. 114, 017001 (2015)] on Bi2Te3 thin layer on the top of NbSe2. Moreover, we demonstrate that there is a "checkerboard" pattern in the relative LDOS between spin up and down channels, which maps out directly the quantum mechanical wave function of MBS. Therefore, spin-resolved STM/STS technique is expected to be able to provide phase sensitive evidence for MBS in vortex core of topological superconductor.

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“…While it becomes clear theoretically that MBSs appear at vortex cores in two-dimensional (2D) topological SCs and ends of 1D ones realized in various hybrid systems [14][15][16][17][18][19][20][21][22][23], to nail them down conclusively in experiments remains challenging [10,[24][25][26].…”

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Helical Spin Texture and Interference of Majorana Bound States in One-Dimensional Topological Superconductor

Kawakami

2016

J. Phys. Soc. Jpn.

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We investigate one-dimensional (1D) Majorana bound states (MBSs) realized in terms of the helical edge states of a 2D quantum spin-Hall insulator (QSHI) in a heterostructure with a superconducting substrate and two ferromagnetic insulators (FIs). By means of Bogoliubov-de Gennes approach we demonstrate that there is a helical spin texture in the MBS wave function with a pitch proportional to the Fermi momentum of the helical edge states of QSHI . Moreover, simultaneous detection on local density of states by scanning tunneling microscopy and spectroscopy at a position close to one FI edge and at the midpoint between two FIs can not only map out the energy spectrum ±E cos(φ/2), but also prove experimentally that the two quasiparticle excitations do not mix with each other as protected by the parity conservation associated with the MBSs.Introduction.-Considerable efforts have been devoted to search for peculiar zero-energy quasiparticle excitations in topological superconductors (SCs) [1][2][3][4], which, getting name of Majorana bound states (MBSs) due to the equivalence to their antiparticles [5,6], can realize non-Abelian quantum statistics useful for establishing decoherence-free topological quantum computation [7][8][9][10][11][12][13]. While it becomes clear theoretically that MBSs appear at vortex cores in two-dimensional (2D) topological SCs and ends of 1D ones realized in various hybrid systems [14][15][16][17][18][19][20][21][22][23], to nail them down conclusively in experiments remains challenging [10,[24][25][26].Recently experimental works have been reported on local density of states (LDOS) associated with MBSs explored by scanning tunneling microscopy and spectroscopy (STM/STS). In a system of iron (Fe) chains on the lead (Pb) substrate, high-resolution spectroscopic images signal zero-energy quasiparticle states localized at the ends of Fe chains, as expected with the emergence of MBSs [27]. In a hybrid device made of a NbSe 2 substrate and a thin film of 3D topological insulator (TI) Bi 2 Te 3 , LDOS at vortex cores as a function of energy and the distance from vortex center evolves from "V"-shape to "Y"-shape with increasing thickness of the TI film, reflecting the appearance of MBSs [28]. By means of Bogoliubov-de Gennes (BdG) approach the present authors confirmed this LDOS evolution, and meanwhile revealed a "checkerboard" pattern in the relative LDOS between spin up and down channels inside vortex cores. The latter property can be explored experimentally by spin-resolved STM/STS, which may identify MBSs as individual quantum states [29].The spin oscillations in MBS wave function in a vortex core are governed by the conservation of total angular momentum, which has contributions from orbital and spin angular momenta as well as the phase winding of superconducting vortex. It is then interesting to ask whether a spin texture exists in 1D MBS where orbital angular momentum and superconducting phase

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Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled s-wave superconductors

Cited by 77 publications

References 38 publications

Majorana zero modes and topological quantum computation

Majorana zero modes and topological quantum computation

Evolution of Density of States and a Spin-Resolved Checkerboard-Type Pattern Associated with the Majorana Bound State

Helical Spin Texture and Interference of Majorana Bound States in One-Dimensional Topological Superconductor

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