Periodic wave functions and number of extended states in random dimer systems

The electronic properties for a one-dimensional random dimer model (RDM) with a- and b-type atoms are studied within a tight-binding on-site model. We carry out a perturbative calculation on the energy spectrum for two different situations (a) epsilon(a)-epsilon(6)=t and (b) epsilon(a)-epsilon(b)=2t, where epsilon(a) and epsilon(b) are the site energies of a- and b-type atoms, respectively, t is a nearest-neighbor matrix element. Let Delta E(i)=\E-i-epsilon(s)\, where s=a or b, E-i is the ith eigenenergy; we find that Delta E(i) for E-i around epsilon(a) or epsilon(b) equals 1.3m/N and 8.5m(2)/N-2 for cases (a) and (b), respectively, where in is the period of wave functions and N is the number of total states. Interestingly, by using the results of Delta E(i), we find root N and 0.34 root N extended electronic states in RDM for cases (a) and (b), respectively.