Abstract
Fractals, a fascinating mathematical concept made popular in the eighties, remained for decades a beautiful scientific curiosity mainly. With the tremendous advances in nanofabrication techniques, such as nanolithography, it has become possible to design self-similar materials with fine structures down to nanometer scale. Here, we investigate the effects of self similarity on quantum electronic transport in graphene Sierpinski carpets. We find that a gap opens up in the electron spectrum in the middle of which lies a flat band of zeros energy modes. Although these states have a zero velocity, a supermetallic phase is found at the neutrality point. For Fermi energy located in the valence/conduction band and in the presence of a small inelastic scattering the system stays metallic and the transport is found strongly anisotropic.
Highlights
We find that a gap opens up in the electron spectrum, in the middle of which lies a flat band of zero-energy modes
Despite the vanishing velocity of these states, a supermetallic phase is revealed at the neutrality point with a conductivity that coincides within a few percent with σ0
In this work we investigate how transport is affected by the self-similarity of the underlying lattice in one of the most remarkable two-dimensional material of the 21st century, graphene [17,18,19,20]
Summary
Next-nearest-neighbor hopping of the order of 10% that breaks particle-hole symmetry. In what follows we make use of the notation ic and f , where L = Lx = Ly = 3ic+1a is the system size and f stands for the degree of fractalization, which varies from 0 (pristine) to its maximum value fmax = ic
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