Transport in the Two-Dimensional Honeycomb Lattice with Substitutional Disorder
In this chapter, we examine the transport properties of the two-dimensional honeycomb lattice with substitutional disorder, using the site quantum percolation model. Like the Anderson localization, the quantum percolation problem is characterized by an Anderson-type Hamiltonian and can therefore be studied using the spectral approach. Here we use the discrete random Schrödinger operator (Eq. 1.3) with a (modified) bimodal probability distributions χ for the random variables ϵi, which is a realistic representation of a doped system where nearest-neighbor interactions dominate. The discussion starts with a brief introduction of basic definitions in the discrete percolation setup together with an overview of some currently established results (Sect. 5.1). The formulation of the quantum percolation problem describing the doped two-dimensional honeycomb lattice is presented in Sect. 5.2. Section 5.3 provides a theoretical and numerical justification for the choice of the (modified) probability distribution of random variables representing doping. Finally, the results from the spectral analysis of lattices with various concentration of doping are provided in Sect. 5.4.
KeywordsSpectral approach Substitutional disorder 2D honeycomb lattice Quantum percolation Doped graphene
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