Antiferromagnetic nuclear spin helix and topological superconductivity in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts /><mml:none /><mml:mn>13</mml:mn></mml:mmultiscripts></mml:math>nanotubes

Hsu, Chia-Hsiang; Stano, Peter; Klinovaja, Jelena; Loss, Daniel

doi:10.1103/physrevb.92.235435

Cited by 49 publications

(46 citation statements)

References 111 publications

(263 reference statements)

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“…below). This is in contrast to nonhelical systems, where multiple Goldstone modes associated with the SU(2) symmetry emerge in the magnon spectrum [61,80,81,88,89].…”

Section: A Rkky Interaction and Spiral Nuclear Spin Ordermentioning

confidence: 84%

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

et al. 2018

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The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.

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“…below). This is in contrast to nonhelical systems, where multiple Goldstone modes associated with the SU(2) symmetry emerge in the magnon spectrum [61,80,81,88,89].…”

Section: A Rkky Interaction and Spiral Nuclear Spin Ordermentioning

confidence: 84%

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

et al. 2018

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“…The induced superconductivity then becomes of the topological p-wave type, and Majorana bound states appear at the two ends of the 1D wire. A system with such a spiral magnetic order is indeed equivalent [12][13][14][15][16][17][18]21,[28][29][30][33][34][35][36][37] to the original proposals for topological superconductivity in nanowires [7,8]. Remarkably, by this mechanism, the topological superconducting phase emerges naturally as the ground state without any fine tuning.…”

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confidence: 78%

Self-stabilizing temperature-driven crossover between topological and nontopological ordered phases in one-dimensional conductors

Braunecker

Simon

2015

Phys. Rev. B

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We present a self-consistent analysis of the topological superconductivity arising from the interaction between self-ordered localized magnetic moments and electrons in one-dimensional conductors in contact with a superconductor. We show that, due to a gain in entropy, there exists a magnetically ordered yet nontopological phase at finite temperatures that is relevant for systems of magnetic adatom chains on a superconductor. The spin-orbit interaction is taken into account, and we show that it causes a modification of the magnetic order, yet without affecting the topological properties. Introduction. Topological superconductors have received much attention recently, partly because they host exotic low energy excitations such as Majorana bound states [1-3], whose non-Abelian statistics are attractive for topological quantum computation [4,5]. As a remarkable feature, topological superconductivity can be created artificially by contacting specific materials with a conventional s-wave superconductor. For instance, it arises at the interface between the surface states of a three-dimensional topological insulator and an s-wave superconductor [6], in one-dimensional (1D) semiconducting wires with a strong spin-orbit interaction (SOI) and a Zeeman magnetic field with proximitized superconductivity [7][8][9][10][11], or in arrays of magnetic nanoparticles or magnetic adatoms on top of a superconducting surface [12][13][14][15][16][17][18][19][20][21][22], such as iron adatoms on lead [23][24][25].The systems we consider in this Rapid Communication exhibit a topological phase emerging from self-organization of magnetic moments embedded in 1D conductors with proximity induced superconductivity. This situation may apply to semiconducting wires with extrinsic magnetic impurities or intrinsic moments such as nuclear spins, or a conducting wire made of magnetic adatoms on a superconducting surface. Due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediated through the electrons, the magnetic moments can undergo an ordering transition below a temperature T * and form a spiral with a spatial period characterized by the wave number 2k m (see Fig. 1) such that k m = k F , for k F the Fermi momentum. This ordering mechanism was first demonstrated for normal conductors [26,27], then conjectured [13] and selfconsistently demonstrated [28][29][30] for the superconducting case. These results were corroborated recently by showing that the spiral order persists beyond the RKKY limit, and k m stays close to k F , as long as k F is away from commensurate band fillings and the coupling strength A between magnetic moments and electrons remains smaller than the electron bandwidth [31,32].The locking of k m to k F has important consequences. The magnetic spiral forms a periodic superstructure that causes a part of the electrons to undergo a spin-selective Peierls transition [33] to a nonconducting spiral electron spin density wave, whereas the remaining conducting electron states become helical (spin filtered). The induced supercon...

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“…It is well established that a Zeeman splitting, induced by the exchange interaction with impurities in this case, is a necessary ingredient but the magnetic order of the chain is unknown. Interaction between the magnetic impurities mediated by the quasiparticles of the superconductor induces a helical order with a pitch of 2k F [25,26,27,28]. Such a helical order is sufficient to drive the system into the topological phase.…”

Section: Chains Of Magnetic Impurities: Theorymentioning

confidence: 99%

Majorana fermions in magnetic chains

Pawlak

Hoffman

Klinovaja

et al. 2019

Progress in Particle and Nuclear Physics

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Majorana fermions have recently garnered a great attention outside the field of particle physics, in condensed matter physics. In contrast to their particle physics counterparts, Majorana fermions are zero energy, chargeless, spinless, composite quasiparticles, residing at the boundaries of so-called topological superconductors. Furthermore, in opposition to any particles in the standard model, Majorana fermions in solid-state systems obey non-Abelian exchange statistics that make them attractive candidates for decoherence-free implementations of quantum computers. In this review, we report on the recent advances to realize synthetic topological superconductors supporting Majorana fermions with an emphasis on chains of magnetic impurities on the surface of superconductors. After outlining the theoretical underpinning responsible for the formation of Majorana fermions, we report on the subsequent experimental efforts to build topological superconductors and the resulting evidence in favor of Majorana fermions, focusing on scanning tunneling microscopy and the hunt for zero-bias peaks in the measured current. We conclude by summarizing the open questions in the field and propose possible experimental measurements to answer them.

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Antiferromagnetic nuclear spin helix and topological superconductivity inC13nanotubes

Cited by 49 publications

References 111 publications

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

Self-stabilizing temperature-driven crossover between topological and nontopological ordered phases in one-dimensional conductors

Majorana fermions in magnetic chains

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