Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application toCuxBi2Se3

Andreev bound states (ABSs) ubiquitously emerge as a consequence of non-trivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties such as Majorana fermions and odd-frequency pairing. A unified concept behind ABSs originates from a soliton state in the one-dimensional Dirac equation with mass domain wall and interplay of ABSs with symmetry and topology enrich their physical characteristics. We make an overview of ABSs with a special focus on superfluid 3 He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as the mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity and the anomalous magnetic response. The marriage of the superfluid 3 He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with ABSs. This article is part of the theme issue ‘Andreev bound states’.

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Spin-dependent zero-bias peak in a hybrid nanowire-quantum dot system: Distinguishing isolated Majorana fermions from Andreev bound states

Physical Review B ◽

10.1103/physrevb.99.155159 ◽

2019 ◽

Vol 99 (15) ◽

Cited By ~ 15

Author(s):

L. S. Ricco ◽

M. de Souza ◽

M. S. Figueira ◽

I. A. Shelykh ◽

A. C. Seridonio

Keyword(s):

Quantum Dot ◽

Bound States ◽

Majorana Fermions ◽

Zero Bias ◽

Andreev Bound States

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Platform of chiral Majorana edge modes and its quantum transport phenomena

Communications Physics ◽

10.1038/s42005-019-0250-5 ◽

2019 ◽

Vol 2 (1) ◽

Cited By ~ 1

Author(s):

James Jun He ◽

Tian Liang ◽

Yukio Tanaka ◽

Naoto Nagaosa

Keyword(s):

Quantum Transport ◽

Bound States ◽

Majorana Fermions ◽

Two Dimensional ◽

Quasi Particle ◽

One Dimensional ◽

Solid States ◽

Topological Superconductors ◽

Wide Range ◽

Majorana Modes

AbstractMajorana fermions, as electronic quasi-particle modes in solid states, have been under the focus of research due to their exotic physical properties. While the evidence of Majorana fermions as zero-dimensional bound states has been well established, the existence of one-dimensional Majorana modes is still under debate. The main reason is that the current theoretical proposals of platforms supporting such states are very challenging experimentally. Here, we propose a method to create two-dimensional topological superconductors with a heterostructure of ferromagnet, topological insulator thin film and superconductor. We show that such a system supports one-dimensional chiral Majorana edge modes in a wide range of parameters which is readily achievable in experiments. We further propose a new transport measurement to detect these modes.

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