Extended States in a One-dimensional Generalized Dimer Model

TL;DR

This paper analyzes a one-dimensional tight-binding model with two impurities, deriving conditions for extended states and showing how to design systems with resonant energies near the Fermi level.

Contribution

It provides analytical expressions for impurity energies and demonstrates the existence of extended states in a generalized dimer model.

Findings

Extended states occur at specific energies.

Number of resonant states scales with host sites.

Designing systems with resonant energy near E_F is feasible.

Abstract

The transmission coefficient for a one dimensional system is given in terms of Chebyshev polynomials using the tight-binding model. This result is applied to a system composed of two impurities located between $N$ sites of a host lattice. It is found that the system has extended states for several values of the energy. Analytical expressions are given for the impurity site energy in terms of the electron's energy. The number of resonant states grows like the number of host sites between the impurities. This property makes the system interesting since it is a simple task to design a configuration with resonant energy very close to the Fermi level $E_F$.