Majorana fermions in honeycomb lattices

Dutreix, C.; Guigou, M.; Chevallier, Denis; Bena, Cristina

doi:10.1140/epjb/e2014-50243-9

Cited by 41 publications

(44 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Importantly, these analytical phase diagrams confirm the numerical predictions discussed in Refs. [45,60]. Note that this feature of the doping near the van Hove singularities is also visible in Fig.…”

Section: (Stretched) Graphenesupporting

confidence: 62%

Topological spin-singlet superconductors with underlying sublattice structure

Dutreix

2017

Phys. Rev. B

View full text Add to dashboard Cite

Majorana boundary quasiparticles may naturally emerge in a spin-singlet superconductor with Rashba spinorbit interactions, when a Zeeman magnetic field breaks time-reversal symmetry. Their existence and robustness against adiabatic changes is deeply related, via a bulk-edge correspondence, to topological properties of the band structure. The present paper shows that the spin-orbit may be responsible for topological transitions when the superconducting system has an underlying sublattice structure, as it appears in a dimerized Peierls chain, graphene, and phosphorene. These systems, which belong to the Bogoliubov-de Gennes class D, are found to have an extra symmetry that plays the role of the parity. It enables the characterization of the topology of the particle-hole symmetric band structure in terms of band inversions. The topological phase diagrams this leads to are then obtained analytically and exactly. They reveal that, because of the underlying sublattice structure, the existence of topological superconducting phases requires a minimum doping fixed by the strength of the Rashba spin-orbit. Majorana boundary quasiparticles are finally predicted to emerge when the Fermi level lies in the vicinity of the bottom (top) of the conduction (valence) band in semiconductors such as the dimerized Peierls chain and phosphorene. In a two-dimensional topological superconductor based on (stretched) graphene, which is semimetallic, Majorana quasiparticles cannot emerge at zero and low doping, that is, when the Fermi level is close to the Dirac points. Nevertheless, they are likely to appear in the vicinity of the van Hove singularities.

show abstract

Section: (Stretched) Graphenesupporting

confidence: 62%

Topological spin-singlet superconductors with underlying sublattice structure

Dutreix

2017

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…We note that our analysis is similar to that used to find edge states in graphene 80,81 and other systems 82,83 , except that we are considering Majorana fermions rather than ordinary fermions 84 . We will find the wave functions of these states by solving Eqs.…”

Section: Phase Diagram For Edge Statesmentioning

confidence: 99%

Majorana edge modes in the Kitaev model

2014

View full text Add to dashboard Cite

We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes of the model in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic δ-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic d-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice.

show abstract

“…A detailed analysis of the dependence of the topological phase diagram on the value of the spin-orbit coupling for a perpendicular magnetic field was presented in Ref. [39]. We would like to emphasize that unlike the case of a perpendicular field [39], the band structure is gapless (same as for a square lattice with an in-plane field [28]), and chiral Majorana edge modes can form, as shown in Fig.…”

Section: Infinite Ribbonsmentioning

confidence: 96%

“…[33,34] However, its almost negligible spin-orbit, [35][36][37][38] as well as the difficulty to obtain large dopings 1 , do not make graphene a choice Majorana candidate. In previous works, it has been proposed that Majorana states can form in infinite graphene ribbons either in the presence of a spin-orbit coupling, or of an inhomogeneous magnetic field [39,40], however these proposals present an important drawback in the necessity to access dopings close to the bottom of the band or the Van Hove singularities [39][40][41], both being far from experimental reach. Moreover, an infinitely-long ribbon is not a realistic description of an experimental system, and the finite longitudinal dimension needs to be taken into account in the formation of the Majorana fermions, together with the transversal one.…”

Section: Introductionmentioning

confidence: 99%

Formation of Majorana fermions in finite-size graphene strips

Kaladzhyan

Bena

2017

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We investigate the formation of Majorana fermions in finite-size graphene strips with open boundary conditions in both directions, in the presence of an in-plane magnetic field and in the proximity of a superconducting substrate. We show that for long enough strips the Majorana states can form in the presence of a Rashba-like spin-orbit coupling, as well as in the presence of an inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in which Majorana states arise solely close to the bottom of the band and the Van Hove singularities, for finite-size systems this can happen also at much smaller doping values, close to the Dirac points, and depends strongly on the type of the short edges of the systems (e.g. armchair vs. zigzag), as well as on the width of the ribbons.

show abstract

Majorana fermions in honeycomb lattices

Cited by 41 publications

References 42 publications

Topological spin-singlet superconductors with underlying sublattice structure

Topological spin-singlet superconductors with underlying sublattice structure

Majorana edge modes in the Kitaev model

Formation of Majorana fermions in finite-size graphene strips

Contact Info

Product

Resources

About