Nature of the extended states in one-dimensional random trimers

By using a Kronig-Penney model, we examined in this paper the extended states of a non-interacting electron in one-dimensional n-mers randomly placed in a crystal. We found at the most in each band of the energy spectrum n−1 resonances corresponding to extended states of the n-mers. Such resonances become narrower of the crystal support is constituted of potential wells instead of barriers. We studied also the Anderson transition near the two resonances of the random trimer in the first allowed band of the crystal support. We found that this transition is slower at the left side rather than the right side of the first resonance while it behaves similarly for the second one. This is due to the nature of the eigenstates for each resonance. We then examined the wave functions at these resonances where the first one is not like Bloch-waves but the second one looked like the crystal wave function with slight distortions. These features are discussed in detail.