On the propagation of Dirac fermions in graphene with strain-induced inhomogeneous Fermi velocity

Abstract

We consider systems described by the two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the wave packets. The analogy with known reflectionless quantum systems is pointed out. Furthermore, with the use of the qualitative spectral analysis, we discuss how inhomogeneous strains can be used to create waveguides for valley polarized transport of partially dispersionless wave packets.arXiv:1912.00675v1 [cond-mat.mes-hall]

Critical behavior for point monopole and dipole electric impurities in uniformily and uniaxially strained graphene

“…When we turn on the strain such that λ < 1, collapse occurs for impurities of smaller size. The quoted value λ =0.9 is consistent with the reported values of strain for which the graphene membrane can be contracted before folding 41 . According to 35,38 , this value for λ would obtain by tensile deformations around ε = 10% either along the zigzag direction or the armchair direction.…”

Critical behavior for point monopole and dipole electric impurities in uniformly and uniaxially strained graphene

“…When we turn on the strain such that λ < 1, collapse occurs for impurities of smaller size. The quoted value λ = 0.9 is consistent with the reported values of strain for which the graphene membrane can be contracted before folding [41]. According to [35,38], this value for λ would be obtained by tensile deformations around ε = 10% along either the zigzag direction or the armchair direction.…”

Complex Supersymmetry in Graphene

“…To confine or control the charge carriers in a graphene sample, electromagnetic fields have to be applied [11][12][13][14]; it has been shown that mechanical deformations can be used as well for that purpose [15][16][17][18][19]. To explore and enrich the configurations where the Dirac equation can be solved exactly (or quasiexactly), supersymmetric quantum mechanics have been used from different approaches [20][21][22][23][24][25][26][27][28][29][30][31][32].…”