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}
}
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… 
5 Citations

Figures from this paper

Topological magnons in the antiferromagnetic checkerboard lattice
Abstract Topological magnon excitations have attracted much attention in the latter years, and have become a very active area of research. Motivated by this, we investigate here spin Hall and thermal
Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure
We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of
Surface spectra of Weyl semimetals through self-adjoint extensions
We apply the method of self-adjoint extensions of Hermitian operators to the low-energy, continuum Hamiltonians of Weyl semimetals in bounded geometries and derive the spectrum of the surface states
Fermi Arc Criterion for Surface Majorana Modes in Superconducting Time-Reversal Symmetric Weyl Semimetals.
TLDR
If each constant-k_{z} plane, where z is the vortex axis, contains equal numbers of Weyl nodes of each chirality, a generically gapped vortex is predicted and a topological invariant ν=±1 is derived in terms of the Fermi arc structure that signals the presence or absence of surface Majorana fermions.
Interplay of Magnetism and Topological Superconductivity in Bilayer Kagome Metals.
TLDR
This work uses a multistage minimal modeling of the magnetic bands progressively closer to the Fermi energy and shows that dimensional confinement naturally exposes the flatness of band structure associated with the bilayer kagome geometry in a resultant ferromagnetic Chern metal.

References

SHOWING 1-10 OF 48 REFERENCES
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
TLDR
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
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
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
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
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.
TLDR
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
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.
TLDR
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
...
1
2
3
4
5
...