Green's function approach to the impurity state in the Lieb lattice

Abstract

Wavefunction of an impurity attached to the Lieb lattice is considered by directly computing the Green's function (GF) for the nearest-neighbor tight-binding model. By replacing the lattice GF with a GF array including all the nine GFs defining on the three-atom unit cell of the Lieb lattice, an accurate and efficient numerical technique is developed. Agreement of both the real and imaginary components of the GF between numerical simulation of the lattice GF and continuum-space Fourier transformation is achieved in the whole resonant-energy range. Both results demonstrate that the wavefunction amplitude decays in a power-law pattern while the resonant energy is small and it decays in a pattern stronger than the power law and weaker than exponentially while the resonant energy is large. The decaying exponents depend on the adatom type and location in the unit cell, which directly modifies the temperature-dependent conductance under the variable-range hopping theory.