Electronic properties of Cantor n-ary set random distribution of impurities in graphene

JUAN SEBASTIÁN ARDENGHI; FEDERICO ESCUDERO; ESTELA GONZÁLEZ; PAULA JASEN; ALFREDO JUAN

Palermo

Congreso; Graphene and related Materials: properties and applications-GM-2016; 2016

University of Salerno

The aim of this work is to study the electronic properties of graphene under random impurities which are distributed in the energy line following the Cantor n-ary set box distribution. This implies that for each iteration k, the possible energy values of the random impurities lie in the line segment of the Cantor n-ary set in the interval (-a/2,a/2). By applying the full T-matrix approximation, the electronic density of states is obtained for each iteration k and the limit k -> ∞ limit is taken. A metal-insulator transition is obtained for critical values of a, where a resonance peak in the DOS at the Fermi level is split in two bands that shift towards the band edges when the width a increases. In turn, the electronic density of states for k = 2 only enhance the van Hove singularities, resonant and antiresonant states for k > 2. In the other side, the Cantor set signatures are shown through a spectrum rearrangement for different values of a, where resonant states split in two narrow peaks for k -> ∞. These results are important to study the transport properties in graphene with doped-based fractal superlattices, magnetic or electric barriers or multilayers with triadic patterns and for systems with a hierarchical distribution of energy barriers, where the phenomenon of ultradiffusion appears as a manifestation of the underlying ultrametric topology and where the whole structure of the spectrum is analogous to that of quasiperiodic crystals.