Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice

Abstract

We investigate a number of fermionic condensate phases on the honeycomb lattice, to determine whether topological defects (vortices and edges) in these phases can support bound states with zero energy. We argue that topological zero modes bound to vortices and at edges are not only connected, but should in fact be \emph{identified}. Recently, it has been shown that the simplest s-wave superconducting state for the Dirac fermion approximation of the honeycomb lattice at precisely half filling, supports zero modes inside the cores of vortices (P. Ghaemi and F. Wilczek, 2007). We find that within the continuum Dirac theory the zero modes are not unique neither to this phase, nor to half filling. In addition, we find the \emph{exact} wavefunctions for vortex bound zero modes, as well as the complete edge state spectrum of the phases we discuss. The zero modes in all the phases we examine have even-numbered degeneracy, and as such pairs of any Majorana modes are simply equivalent to one ordinary fermion. As a result, contrary to bound state zero modes in $p_x+i{p}_y$ superconductors, vortices here do \emph{not} exhibit non-Abelian exchange statistics. The zero modes in the pure Dirac theory are seemingly topologically protected by the effective low energy symmetry of the theory, yet on the original honeycomb lattice model these zero modes are split, by explicit breaking of the effective low energy symmetry.

arXiv commentFinal version including numerics, accepted for publication in PRB

References in corpus (33)

• The electronic properties of graphene
• 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
• Topological Insulators in Three Dimensions
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Electronic States of Graphene Nanoribbons
• Bipolar supercurrent in graphene
• Boundary conditions for Dirac fermions on a terminated honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Fermion zero modes on vortices in chiral superconductors
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Superconducting states of pure and doped graphene
• Anyons and the quantum Hall effect - a pedagogical review
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Observing Majorana Bound States in p-wave Superconductors Using Noise Measurements in Tunneling Experiments
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron-electron interactions in graphene sheets
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Edge states and tunneling of non-Abelian quasiparticles in the nu=5/2 quantum Hall state and p+ip superconductors
• Zero modes of two-dimensional chiral p-wave superconductors
• Proximity Induced Superconductivity and Multiple Andreev Reflections in Few-Layer-Graphene
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors
• Magnetic-Field-Driven Superconductor-Insulator-Type Transition in Graphite
• Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Predicted signatures of p-wave superfluid phases and Majorana zero modes of fermionic atoms in RF absorption
• Spin-Hall effect in triplet chiral superconductors and graphene

Cited by in corpus (45)

• Topological Insulators
• Majorana fermions in a tunable semiconductor device
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Dirac materials
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Vortices and Other Topological Solitons in Dense Quark Matter
• Quantizing Majorana Fermions in a Superconductor
• Josephson current in graphene: the role of unconventional pairing symmetries
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• Topological insulator in the core of the superconducting vortex in graphene
• Detecting Majorana bound states
• Majorana fermions in pinned vortices
• Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state
• Unsolved problems in particle physics
• Dirac Green's function approach to graphene-superconductor junctions with well defined edges
• The quantum valley Hall effect in proximity-induced superconducting graphene: an experimental window for deconfined quantum criticality
• Supersolidity of cold-atom Bose-Fermi mixtures in optical lattices
• Creating p-wave superfluids and topological excitations in optical lattices
• Detection of Majorana edge states in topological superconductors through the non-Fermi-liquid effects induced in an interacting quantum dot
• Proximity induced interface bound states in superconductor-graphene junctions
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
• Classification of massive and gapless phases in bilayer graphene
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Majorana Fermions in Periodically Driven Semiconductor-Superconductor Heterostructure
• Majorana edge modes of topological exciton condensate with superconductors
• Zero-energy states of massive Dirac equation in magnetic fields
• Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene
• Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension
• Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice
• Majorana zero modes bound to a vortex line in a topological superconductor
• Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
• Competing orders in the Dirac-like electronic structure and the non-linear sigma model with the topological terms
• Realization of a vortex in the Kekule texture of molecular Graphene, at a Y junction where 3 domains meet
• Chiral d-wave superconducting state in the core of a doubly quantized s-wave vortex in graphene
• Evolution of pairing from weak to strong coupling on a honeycomb lattice
• Gapless vortex bound states in superconducting topological semimetals
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Current Density of Majorana Bound States
• On a Solution to the Dirac Equation with a Triangular Potential Well
• Local breaking of the spin degeneracy in the vortex states of Ising superconductors: Induced antiphase ferromagnetic order