Discrete Gauge Fields for Graphene Membranes under Mechanical Strain
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Discrete Gauge Fields for Graphene Membranes under Mechanical Strain James V. Sloan,1 Alejandro A. Pacheco Sanjuan,2 Zhengfei Wang,3 Cedric M. Horvath,1 and Salvador Barraza-Lopez1 1 Department of Physics. University of Arkansas. Fayetteville, AR 72701, USA, 2 Departamento de Ingeniería Mecánica. Universidad del Norte. Barranquilla, Colombia, 3 Department of Materials Science and Engineering. University of Utah. Salt Lake City, UT 84112, USA ABSTRACT Mechanical strain creates strong gauge fields in graphene, offering the possibility of controlling its electronic properties. We developed a gauge field theory on a honeycomb lattice valid beyond first-order continuum elasticity. Along the way, we resolve a recent controversy on the theory of strain engineering in graphene: there are no K-point dependent gauge fields. INTRODUCTION The interplay of electronic and mechanical properties of graphene membranes is a subject under intense experimental and theoretical investigation [1-7]. Mechanical strain induces gauge fields in graphene that affect the dynamics of charge carriers [3-6,8]. Graphene can sustain elastic deformations as large as 20% [9] resulting in pseudo-magnetic fields that are much larger than magnetic fields available in state-of-the-art experimental facilities [10]. These effects have been experimentally confirmed in strained graphene “nanobubbles” on a metal substrate [11]. In addition to the pseudo-magnetic vector potential As, strain induces a scalar deformation potential Es [8,12,13] that affects the electron dynamics in complex ways. Only in special cases Es=0 [4]. The theory of strain-engineered electronic effects on graphene is semiclassical. The strain-induced pseudo-magnetic field is given by the rotational of the strain-created vector potential: Bs(r) = Rot[As(r)]. The vector potential is incorporated into a spatially-varying pseudospin Hamiltonian Hps(q,r), where Hps(q) is the low-energy expansion of the Hamiltonian in reciprocal space in the absence of strain. The semiclassical approximation is justified when the strain extends over many unit cells and preserves sublattice symmetry [4]. It is also possible to determine the electronic properties directly from a tight-binding Hamiltonian H in real space, without resorting to the semiclassical approximation and without imposing an a priori lattice symmetry. So, while the semiclassical Hps(q,r) is defined in reciprocal space (thus assuming some reasonable preservation of crystalline order), the tight-binding Hamiltonian H in real space is more general. We defer a discussion of specific details to forthcoming publications [14,15] and in the present occasion we focus on presenting our most relevant results, which include expressions for the strain-derived fields given directly in terms of changes between interatomic distances. RELEVANT GEOMETRICAL PARAMETERS
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Figure 1. Lattice vectors and basis vectors change when graphene is under mechanical strain. We show in Figure 1 the relevant information needed for our discussion. The choice of lattice vec
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