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Universal characteristics of one-dimensional non-Hermitian superconductors
TLDR
In this article, a non-Bloch band theory for one-dimensional (1D) non-Hermitian topological superconductors is established based on the theory that there exist reciprocal particle and hole loops of generalized Brillouin zone (GBZ).Abstract:
We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone (GBZ) The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect and their values of GBZ satisfy |\beta| = 1 If the non-Hermitian system has skin modes, these modes should be Z2 style, ie, the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively The non-Bloch band theory is applied to two examples, non-Hermitian p- and s-wave topological superconductors Topological phase transitions occur at \beta_{c}= \pm 1 in the two systems In terms of Majorana Pfaffian, a Z2 non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence in non-Hermitian superconductorsread more
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Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
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Non-Abelian Anyons and Topological Quantum Computation
TL;DR: In this article, the authors describe the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the ''ensuremath{
u}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
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Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator
Liang Fu,Charles L. Kane +1 more
TL;DR: It is shown that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.
Journal ArticleDOI
Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices
Vincent Mourik,K. Zuo,Sergey Frolov,Sebastien Plissard,Epam Erik Bakkers,Epam Erik Bakkers,Leo P. Kouwenhoven +6 more
TL;DR: Electrical measurements on indium antimonide nanowires contacted with one normal (gold) and one superconducting (niobium titanium nitride) electrode support the hypothesis of Majorana fermions in Nanowires coupled to superconductors.
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Unpaired Majorana fermions in quantum wires
TL;DR: In this article, a condition for boundary Majorana fermions is expressed as a condition on the bulk electron spectrum, which is satisfied in the presence of an arbitrary small energy gap induced by proximity of a 3D p-wave superconductor.
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