Relativistic Levinson theorem in two dimensions

Dong, Shi‐Hai; Hou, Xi Wen; Zhong, Qi

doi:10.1103/physreva.58.2160

Cited by 68 publications

(44 citation statements)

References 23 publications

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“…This solution, although decaying away from the impurity, is not normalizable. It has the same spatial dependence as the quasi-localized solutions which are induced by radial potentials on 2D Dirac fermions [22]. The matching of localized states described above cannot be generalized to the case t ′ = 0, as the band of edge states is not degenerate in energy [23].…”

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confidence: 98%

Disorder Induced Localized States in Graphene

et al. 2006

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We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors.PACS numbers: 81.05. Uw, 71.27.+a, Introduction. The problem of disorder in systems with Dirac fermions has been studied extensively in the last few years in the context of dirty d-wave superconductors [1]. Dirac fermions are also the elementary excitations of the honeycomb lattice at half-filling, equally known as graphene, which is realized in two-dimensional (2D) Carbon based materials with sp 2 bonding. It is well-known that disorder is ubiquitous in graphene and graphite (which is produced by stacking graphene sheets) and its effect on the electronic structure has been studied extensively [2,3,4,5,6,7,8,9,10,11,12,13]. It has been shown recently [14] that the interplay of disorder and electron-electron interactions is fundamental for the understanding of recent experiments in graphene devices [15]. Furthermore, experiments reveal that ferromagnetism is generated in heavily disordered graphite samples [16,17,18,19,20], but the understanding of the interplay of strong disorder and electron-electron interactions in these systems is still in its infancy. Different mechanisms for ferromagnetism in graphite have been proposed and they are either based on the nucleation of ferromagnetism around extended defects such as edges [2,8,12,13] or due to exchange interactions originating from unscreened Coulomb interactions [21]. Therefore, the understanding of the nature of the electronic states in Dirac fermion systems with strong disorder is of the utmost interest.In the following, we analyze in detail states near the Fermi energy induced by vacancies in a tight-binding model for the electronic states of graphene planes. We show that single vacancies in a graphene plane generate localized states which are sensitive to the presence of particle-hole symmetry breaking. Moreover, a finite density of such defects leads to strong changes in the local and averaged electronic Density Of States (DOS) with the creation of localized states at the Dirac point.The model. We consider a single band model described by the Hamiltonian:

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confidence: 98%

Disorder Induced Localized States in Graphene

et al. 2006

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“…Similar investigations have been carried out in Refs. [16][17][18][19][20][21]. It is worth mentioning that both potentials (2.7) and (2.8) reproduce the φ 4 model in the case p = n = 1.…”

Section: Generalitiesmentioning

confidence: 98%

“…We go on and investigate the threshold or half-bound states, which are states where the fermion field goes to a constant when x → ±∞. Although the wave function is finite when x → ±∞, these states do not decay fast enough to be square-integrable [17][18][19]. Anyway, to find threshold energies we solve the system of equations at x → ±∞.…”

Section: Generalitiesmentioning

confidence: 99%

Fermionic bound states in distinct kinklike backgrounds

Bazeia

Mohammadi

2017

Eur. Phys. J. C

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This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have a similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and we consider two distinct boson-fermion interactions, one motivated by supersymmetry and the other described by the standard Yukawa coupling.

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“…which is a representation of the Levinson theorem for the massive 2D Dirac equation in a central potential, studied previously using the Green's function method [77] and via a utilization of the generalized Sturm-Liouville theorem [78].…”

Section: Formalismmentioning

confidence: 99%

Optimal traps in graphene

et al. 2015

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We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a nonlinear first-order differential equation for scattering phase shift, using the so-called variable-phase method. This allows us to utilize the Levinson theorem, relating scattering phase shifts of a slow particle to its bound states, to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads us to posit the use of "optimal traps" to combat the chiral tunneling found in graphene: this could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find that the s states create a dominant peak in the scattering cross section as the energy tends towards the Dirac point energy, suggesting a dominant contribution to the resistivity.

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Relativistic Levinson theorem in two dimensions

Cited by 68 publications

References 23 publications

Disorder Induced Localized States in Graphene

Disorder Induced Localized States in Graphene

Fermionic bound states in distinct kinklike backgrounds

Optimal traps in graphene

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