Aharonov–Bohm interferences from local deformations in graphene

Abstract

One of the most interesting aspects of graphene is the tied relation between structural and electronic properties. The observation of ripples in the graphene samples both free standing and on a substrate has given rise to a very active investigation around the membrane-like properties of graphene and the origin of the ripples remains as one of the most interesting open problems in the system. The interplay of structural and electronic properties is successfully described by the modelling of curvature and elastic deformations by fictitious gauge fields that have become an experimental reality after the suggestion that Landau levels can form associated to strain in graphene and the subsequent experimental confirmation. Here we propose a device to detect microstresses in graphene based on a scanning-tunneling-microscopy setup able to measure Aharonov-Bohm interferences at the nanometer scale. The interferences to be observed in the local density of states are created by the fictitious magnetic field associated to elastic deformations of the sample.PACS numbers: I. LATTICE DEFORMATIONS AND FICTITIOUS MAGNETIC FIELDS IN GRAPHENE.Since graphite monolayers started to be isolated in a controlled way [1,2], graphene has been an optimal playground to test the most exciting ideas in condensed matter [3]. A great deal of attention was initially paid to its striking electronic properties, but it was soon realised that the structural and mechanical properties can be even more interesting both from a fundamental point of view as well as for applications [4]. The modelling of curvature by gauge fields in graphene was suggested in the early publications associated to topological defects needed to form the fullerene structures [5,6]. The main idea was that the phase acquired by an electron circling a pentagonal defect is the same as that arising when circling a solenoid with the appropriate magnetic flux in analogy with the Aharonov-Bohm effect. The fictitious magnetic fields were later applied to model the observed ripples [7][8][9] and elastic deformations [10][11][12][13][14][15]. The state of the art and an updated list of references can be found in [16].A turn of screw took place when the fictitious magnetic field became an experimental reality after the suggestion that Landau levels can form associated to strain in graphene [17,18] and their subsequent observation in [19]. The formation of Landau levels requires very high values of the fictitious magnetic fields and hence very strong deformations of the samples. Fields of up to 300 Tesla were estimated for the observed nano bubbles in [19]. In the present work, we consider the opposite limit where the fields are small and the electronic excitations can still be described in terms of plane waves (rather than Landau levels). As we show below, non-trivial amusing effects can also be generated by fictitious gauge fields in this limit. Specifically, we discuss the realisation of the Aharonov-Bohm (AB) effect via deformation fields and propose a simple scanning-tunneling-microsco...

Discrete differential geometry and the properties of conformal two-dimensional materials

“…where g α (ξ 1 , ξ 2 ) is a tangent vector field, δ αβ is the reference (flat) metric andn = g ξ 1 ×g ξ 2 |g ξ 1 ×g ξ 2 | is the local normal [13,23,26,32,33]. However, peculiarities of how graphene ripples [38,39,40,41,42], slides and adheres [39,43] may be beyond first-order continuum elasticity.…”

“…α pyr is a signed quantity, as follows: Direct inspection of Eqn. (33) indicates that α pyr will be positive for a bulge, and negative for a sag. Similarly, the mean curvature H D -Eqn.…”

“…Specifically, on thinplate continuum elasticity the strain tensor is u αβ = (∂ α u β + ∂ β u α + ∂ α u γ ∂ β u γ + ∂ α z∂ β z)/2, with z an out-of-plane elongation [11,12,13,22,23,32,26,33,34,35,36,37]. There, differential geometry and mechanics couple as:…”

Optical conductivity of curved graphene

“…Another example of possible effects due to the pseudo magnetic fields associated with local deformations of the graphene is given in [18], where the authors propose a device to measure Aharonov-Bohm interferences at the nanometre scale. The interplay between the pseudo-magnetic field and an external real one has been addressed in [19], where it was shown that due to an inherent competition between the two fields, the electric current exhibited spatial inhomogeneity not present when the real magnetic field is zero.…”

“…Curvature in a geometrical approach can be translated into a pseudo magnetic field or, more generally, into pseudo gauge fields which can lead to observable phenomena; see e.g the references [2,16,17,18].…”