Topological indices, defects and Majorana fermion in chiral superconductors

Abstract

We study theoretically the role of topological invariants to protect the Majorana fermions in a model of two-dimensional chiral superconductors which belong to class D of topological periodic table. A rich phase diagram is revealed. Each phase is characterized by the topological invariants for 2d (Z) and 1d (Z2), which lead to the Majorana fermion at the edge of the dislocation and the core of the vortex. Interference of the Majorana fermions originated from the different topological invariants is studied. The stability of the Majorana fermion with respect to the interlayer coupling, i.e., in 3d, is also examined.

arXiv comment5 pages, 4 figures

References in corpus (49)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Topological Insulators with Inversion Symmetry
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological invariants of time-reversal-invariant band structures
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Topological Crystalline Insulators in the SnTe Material Class
• Majorana fermions in a tunable semiconductor device
• Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator
• Majorana Fermion Induced Resonant Andreev Reflection
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Topological Superconductivity in CuxBi2Se3
• Electrically detected interferometry of Majorana fermions in a topological insulator
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Probing Neutral Majorana Fermion Edge Modes with Charge Transport
• Chiral Topological Superconductor From the Quantum Hall State
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• Unconventional superconductivity on a topological insulator
• Helical Metal Inside a Topological Band Insulator
• On the $Z_2$ classification of Quantum Spin Hall Models
• Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortex matter in a $p_x+i{p}_y$ superconductor
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Orbital dependent superconductivity in Sr_2RuO_4
• Majorana Fermions in Proximity-coupled Topological Insulator Nanowires
• Topological odd-parity superconductors
• Topological spin-current in non-centrosymmetric superconductors
• Hidden quasi one-dimensional superconductivity in Sr${}_2$RuO${}_4$
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application to CuxBi2Se3
• Edge states of Sr${}_2$RuO${}_4$ detected by in-plane tunneling spectroscopy
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Tunneling Conductance and Surface States Transition in Superconducting Topological Insulators
• Unpaired Majorana fermions in a layered topological superconductor

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• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators
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• Dislocation as a bulk probe of higher-order topological insulators
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• Dislocation defect as a bulk probe of monopole charge of multi-Weyl semimetals
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• Detecting Majorana fermions in quasi-one-dimensional topological phases using nonlocal order parameters
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• Chiral zero modes in superconducting nanowires with Dresselhaus spin-orbit coupling
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
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• Dislocation Majorana zero modes in perovskite oxide 2DEG
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• Spontaneous breaking of time-reversal symmetry in topological superconductors
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• ${\mathbf{Z}}_n$ clock models and chains of $so(n{)}_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
• Counting Majorana bound states using complex momenta
• Emergent metallicity at the grain boundaries of higher-order topological insulators
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• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Grain-boundary topological superconductor
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification
• Dynamic melting and condensation of topological dislocation modes
• Hybrid symmetry class topological insulators
• Topological magnonic dislocations modes
• Persistent current in 2D topological superconductors
• Dispersive nodal fermions along grain boundaries in Floquet topological crystals
• Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
• Fragile dislocation modes in obstructed atomic topological phases
• Pairing-induced Momentum-space Magnetism and Its Implication In Optical Anomalous Hall Effect In Chiral Superconductors
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases