Self-similar Charge Transport in Gapped Graphene

Abstract

A new type of self-similar potential is used to study a multibarrier system made of graphene. Such potential is based on the traditional middle third Cantor set rule combined with a scaling of the barriers height. The resulting transmission coefficient for charge carriers, obtained using the quantum relativistic Dirac equation, shows a surprising self-similar structure. The same potential does not lead to a self-similar transmission when applied to the typical semiconductors described by the non-relativistic Schrödinger equation. The proposed system is one of the few examples in which a self-similar structure produces the same pattern in a physical property. The resulting scaling properties are investigated as a function of three parameters: the height of the main barrier, the total length of the system and the generation number of the potential. These scaling properties are first identified individually and then combined to find general analytic scaling expressions.

7 pages

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Cited by in corpus (2)

• Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons
• Multifractal wave functions of charge carriers in graphene with folded deformations, ripples or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudomagnetic fields