Friedel oscillations at the Dirac cone merging point in anisotropic graphene and graphenelike materials

Dutreix, C.; Bîlteanu, Liviu; Jagannathan, Anuradha; Bena, Cristina

doi:10.1103/physrevb.87.245413

Cited by 24 publications

(26 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One may then reduce this critical doping by stretching the graphene sheet. Indeed, when increasing α up to 1.3, this decreases the energy level at one of the symmetric points Γ 1 , Γ 2 , and Γ 3 , so that the three van Hove singularities are no longer equivalent [49,50,56]. As a consequence, if the Fermi level lies near the lowest van Hove singularities, i.e., µ = 0.7t at Γ 3 in our case, the system may still enter a topological phase.…”

Section: (Stretched) Graphenementioning

confidence: 80%

“…Thus, the upcoming discussion could straightforwardly be generalized to distant neighbor hopping processes. The dimensionless parameter α, which for instance simulates a uniaxial strain, controls the Dirac cone merging transition and the semi-relativistic phenomena it leads to in two dimensions [49,50,56]. Even though such a Lifshitz transition is unrealistic in graphene, contrary to black phosphorus [51], reasonably stretching the graphene sheet turns out to be useful here, because it reduces the minimum doping required to obtain Majorana boundary quasiparticles.…”

Section: (Stretched) Graphenementioning

confidence: 99%

See 1 more Smart Citation

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) Graphenementioning

confidence: 80%

Section: (Stretched) Graphenementioning

confidence: 99%

Topological spin-singlet superconductors with underlying sublattice structure

Dutreix

2017

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…The same hierarchy can be observed in figure 2(d) along the direction going diagonally from the corner along a zigzag axis to the bulk. Corner states present strong similarities with zero-modes associated to localized impurities in anisotropic graphene [35] and will be the subject of further studies.…”

Section: Study Of Armchair Edges In Honeycomb Lattice Under Uniaxial mentioning

confidence: 91%

Manipulation of edge states in microwave artificial graphene

et al. 2014

View full text Add to dashboard Cite

Edge states are an important ingredient in understanding transport properties of graphene nanoribbons. We study experimentally the existence and the internal structure of edge states under uniaxial strain of the three main edges: zigzag, bearded, and armchair. The experiments are performed on artificial microwave graphene flakes, where the wavefunctions are obtained by direct imaging. We show that uniaxial strain can be used to manipulate the edge states: a single parameter controls their existence and their spatial extension into the ribbon. By combining a tight-binding approach and topological arguments, we provide an accurate description of our experimental findings. A new type of zero-energy state appearing at the intersection of two edges, namely the corner state, is also observed and discussed.

show abstract

“…For example, a semi-Dirac dispersion relation, i.e. a dispersion that scales linearly with the momentum in one direction and quadratically in the orthogonal one, would lead to 1/ √ r decaying oscillations [60]. On the other hand, the phase θ ξ (q), which characterizes the momentum dependence of the Bloch spinors, is not involved in the interferences on the sublattice of the impurity, namely A 1 .…”

Section: Localized Impurity On Sublattice Amentioning

confidence: 99%

Friedel oscillations at the surfaces of rhombohedralN-layer graphene

Dutreix¹,

Katsnelson²

2016

Phys. Rev. B

View full text Add to dashboard Cite

The low-energy physics of rhombohedral N-layer graphene mainly arises on the external layers, where most of the π electrons are located. Their Bloch band structure defines a two-band semimetal; the dispersion relation scales as ±q N with the momentum norm q in the vicinity of two non-equivalent valleys. In this paper, we address the problem of elastic scattering through a localized impurity located either on the surface of the material or within the bulk, and focus on the quantum interferences it induces on the two external layers. It is apprehended in the framework of a T -matrix approach, both numerically and analytically, regardless of the impurity magnitude, which enables the description of realistic scatters. In rhombohedral multilayer graphene, the impurity induces Friedel oscillations that always decay as 1/r. As a result, monolayer graphene is the only material of the rhombohedral class that exhibits 1/r 2 -decaying Friedel oscillations. The interference patterns are subsequently analyzed in momentum space. This analysis enables a clear distinction between monolayer graphene and multilayer graphene. It also shows that the interference pattern reveals the whole Bloch band structure, and highlights the number of layers stacked in the material, as well as the π-quantized Berry phases that characterize the existence of nodal points in the semimetallic spectrum. Experimentally, these features may be probed from scanning tunneling microscopy, when imaging the local density of states at the surfaces of suspended rhombohedral N-layer graphene.

show abstract

Friedel oscillations at the Dirac cone merging point in anisotropic graphene and graphenelike materials

Cited by 24 publications

References 27 publications

Topological spin-singlet superconductors with underlying sublattice structure

Topological spin-singlet superconductors with underlying sublattice structure

Manipulation of edge states in microwave artificial graphene

Friedel oscillations at the surfaces of rhombohedralN-layer graphene

Contact Info

Product

Resources

About