Gauge field induced by ripples in graphene

Abstract

We study the effects of quenched height fluctuations (ripples) in graphene on the density of states (DOS). We show that at strong ripple disorder a divergence in the DOS can lead to an ordered ground state. We also discuss the formation of dislocations in corrugated systems, buckling effects in suspended samples, and the changes in the Landau levels due to the interplay between a real magnetic field and the gauge potential induced by ripples.

A pseudopotential model for Dirac electrons in graphene with line defects

“…The existence of an energy gap prevents the Klein paradox 6 from taking place, a necessary condition for building nanoelectronic devices made of graphene. Our conclusion supports the results of the authors of [18,21] about the role of the mass term as a factor impeding the Klein tunnelling of chiral electrons through the barrier. The valley polarization for the case β = 0 is still equal to zero.…”

“…3). As is known [18,21], the term in the D=(2+1) Hamiltonian (3) of the model with the σ 3 matrix corresponds to the effective mass of electrons, and as a consequence the electronic spectrum will present a finite energy gap. The existence of an energy gap prevents the Klein paradox 6 from taking place, a necessary condition for building nanoelectronic devices made of graphene.…”

“…These perturbations may arise due to several types of disorder, like topological lattice defects, strains, and curvature. Such defects are expected to exist in graphene, as experiments show a significant corrugation both in suspended samples, in samples deposited on a substrate, and also in samples grown on metallic surfaces (see, e.g., [17], [18], and references therein). Note, in particular, that changes in the distance between the atoms and in the overlap between the different orbitals by strain or bending lead to changes in the nearest-neighbor (N N ) hopping or next-nearest-neighbor (N N N ) hopping amplitude and this results in the appearance of vector potentials A x ( r), A y ( r) (this coupling must take the form of a gauge field with the matrix structure of the Pauli matrices, σ 1 and σ 2 ) and a scalar potential V ( r) in the Dirac Hamiltonian [5], [9], [17].…”

Magnetic moments in the presence of topological defects in graphene

“…Direct observation can be hard due to their very local influence on the electronic properties [23] and the present work provides alternative indirect ways to detect the presence of dislocations of other topological defects through their influence on the magnetic properties. Although the theoretical description of topological defects in the continuum limit was set some time ago [24,25,26] and their influence on the electronic and transport properties of graphene has been studied recently in a number of papers [20,21,27,28,29], their implications on the magnetic structure has not been fully explored.…”