# Characterizations of topological superconductors: Chern numbers, edge states and Majorana zero modes

@article{Liu2017CharacterizationsOT,
title={Characterizations of topological superconductors: Chern numbers, edge states and Majorana zero modes},
author={Xiao-Ping Liu and Yuan Zhou and Yi-Fei Wang and Chang-de Gong},
journal={arXiv: Mesoscale and Nanoscale Physics},
year={2017}
}
• Xiao-Ping Liu, +1 author C. Gong
• Published 28 September 2017
• Physics
• arXiv: Mesoscale and Nanoscale Physics
The topological properties in topological superconductors are usually characterized by the bulk Chern numbers, edge-state spectra, and Majorana zero modes. Whether they are equivalent or inequivalent is not well understood. Here, we investigate this issue with focus on a checkerboard-lattice model combining the Chern insulator and chiral $p$-wave superconductivity. Multiple topologically superconducting phases with Chern numbers up to $\mathcal{N}=4$ are produced. We explicitly demonstrate the…
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## References

SHOWING 1-10 OF 48 REFERENCES
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
• Physics, Medicine
Scientific reports
• 2016
A rich phase diagram is established for these topological superconducting states and multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.
Classification of topological insulators and superconductors in three spatial dimensions
• Physics
• 2008
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial
Topological insulators and superconductors
• Physics
• 2011
Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the
Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition
• Physics
• 2015
Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through
Topological superconductor with a large Chern number and a large bulk excitation gap in single-layer graphene
• Physics
• 2016
We show that a two-dimensional topological superconductor (TSC) can be realized in a hybrid system with a conventional $s$-wave superconductor proximity-coupled to a quantum anomalous Hall (QAH)
Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures.
• Physics, Medicine
Physical review letters
• 2010
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.
Chiral topological superconductor from the quantum Hall state
• Physics
• 2010
The chiral topological superconductor in two dimensions has a full pairing gap in the bulk and a single chiral Majorana state at the edge. The vortex of the chiral superconducting state carries a
Superconducting proximity effect and majorana fermions at the surface of a topological insulator.
• Physics, Medicine
Physical review letters
• 2008
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.
Majorana mode in vortex core of Bi2Te3/NbSe2 topological insulator-superconductor heterostructure
Majorana fermions have been intensively studied in recent years for their importance to both fundamental science and potential applications in topological quantum computing1,2. Majorana fermions are
Fermion zero modes on vortices in chiral superconductors
The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting