Introduction to topological superconductivity and Majorana fermions

  title={Introduction to topological superconductivity and Majorana fermions},
  author={Martin Leijnse and Karsten Flensberg},
  journal={Semiconductor Science and Technology},
This short review paper provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some detail the simplest ‘toy model’ in which Majoranas appear, namely a one-dimensional tight-binding representation of a p-wave superconductor, introduced more than 10 years ago by Kitaev. We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their… 

Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations

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One-dimensional semiconducting nanowires with strong spin-orbit coupling coupled to s-wave superconductors, and exposed to external magnetic field have been predicted to support Majorana fermion

Majorana Fermions in Chiral Topological Superconductors

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Majorana nanowires for topological quantum computation

  • P. Marra
  • Physics
    Journal of Applied Physics
  • 2022
Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle–hole symmetric, and

Quasiclassical approach to low-dimensional topological insulators and superconductors

In this work we apply the quasiclassical formalism, an established tool in the context of superconducting heterostructures, to topological insulators and superconductors in one and two dimensions,

A brief review on Majorana bound states in topological superconductors

Topological superconductivity has drawn much attention recently, and most interests are focused on the Majorana bound states existing at the edges of one-dimensional topological superconductors.

Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment

  • T. StanescuS. Tewari
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2013
This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconducting nanowire-superconductor hybrid structures.

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Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed-matter physics. In this Review, we survey the current status of this rapidly developing

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The non-Abelian topological order for superconductors is characterized by the existence of zero-energy Majorana fermions in edges of systems and in a vortex of a macroscopic condensate, which obey

Majorana Fermions in Semiconductor Nanowires

We study multiband semiconducting nanowires proximity coupled with an $s$-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field.

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The experimental realization of Majorana fermions presents an important problem due to their non-Abelian nature and potential exploitation for topological quantum computation. Very recently Sau et

Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures.

The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage, which will be a direct demonstration of the existence of Majorana particles.

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Search for Majorana Fermions in Superconductors

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Realizing a robust practical Majorana chain in a quantum-dot-superconductor linear array

It is shown that Majorana fermions that are protected by a disorder robust topological gap can occur at the ends of a chain of gate-tunable quantum dots connected by s-wave superconductors, and this system provides a very practical and easily realizable experimental platform for the observation of non-abelian Majorana modes.

Unconventional superconductivity on a topological insulator.

It is found that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed.

Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

In proximity to an s-wave superconductor, a one- or two-dimensional, electron- or hole-doped semiconductor with a sizable spin-orbit coupling and a Zeeman splitting can support a topological