Majorana fermions in magnetic chains

Pawlak, Rémy; Hoffman, Silas; Klinovaja, Jelena; Loss, Daniel; Meyer, Ernst

doi:10.1016/j.ppnp.2019.04.004

Cited by 71 publications

(66 citation statements)

References 133 publications

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“…The presence of magnetic impurities on a superconducting surface leads to the emergence of so-called Yu-Shiba-Rusinov (YSR) states [4][5][6][7][8][9], due to the coupling of the localized magnetic moment to the Cooper pairs. In atomic chains, hybridized YSR states develop into bands [10,11], that can give rise to topological superconductivity and consequently to the appearance of Majorana bound states [12][13][14][15][16]. In a recent study by Beck et al [7], an Mn adatom and Mn dimers on Nb(110) were investigated in the superconducting state.…”

Section: Introductionmentioning

confidence: 99%

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

et al. 2021

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We present results for the electronic and magnetic structure of Mn and Fe clusters on Nb(110) surface, focusing on building blocks of atomic chains as possible realizations of topological superconductivity. The magnetic ground states of the atomic dimers and most of the monatomic chains are determined by the nearest-neighbor isotropic interaction. To gain physical insight, the dependence on the crystallographic direction as well as on the atomic coordination number is analyzed via an orbital decomposition of this isotropic interaction based on the spin-cluster expansion and the difference in the local density of states between ferromagnetic and antiferromagnetic configurations. A spin-spiral ground state is obtained for Fe chains along the [11¯0] direction as a consequence of the frustration of the isotropic interactions. Here, a flat spin-spiral dispersion relation is identified, which can stabilize spin spirals with various wave vectors together with the magnetic anisotropy. This may lead to the observation of spin spirals of different wave vectors and chiralities in longer chains instead of a unique ground state.

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Section: Introductionmentioning

confidence: 99%

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

et al. 2021

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“…The above results are consistent with the appearance of the MZM at the topological transition. It should be noted that the presence of those MZM implies unconventional p -wave superconductivity 8 . As a consequence, for our description to be consistent, the topological phase transition ought to be accompanied by the onset of triplet SC amplitudes Δ T .…”

Section: Discussionmentioning

confidence: 99%

Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

et al. 2021

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Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator’s surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.

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“…For this and other relevant aspects that are not covered in this Tutorial, we refer the reader to several excellent comprehensive reviews of the field. [2][3][4][5][73][74][75][76][77][78][79][80][81] The Tutorial is organized as follows: In Sec. II, we introduce some basic notions related to MBSs that will reappear frequently throughout the entire Tutorial.…”

Section: Introductionmentioning

confidence: 99%

Majorana bound states in semiconducting nanostructures

Laubscher,

Klinovaja

2021

Preprint

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In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple 'minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional s-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students-both theorists and experimentalists-seeking to familiarize themselves with some of the basic concepts in the field.

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Majorana fermions in magnetic chains

Cited by 71 publications

References 133 publications

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Majorana bound states in semiconducting nanostructures

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