A relativistic treatment about the existence of band gaps in one-dimensional disordered systems

Abstract

We have investigated the relativistic criteria for the occurrence of band gaps in one-dimensional disordered systems, with the intention of elucidating the circumstances under which the relativistic effects would be significant with respect to various issues concerned with band gaps in such systems. Our model consists of an infinite chain of atoms lacking long range order, the atomic potentials being represented by rectangular wells or barriers. Our treatment is a relativistic generalisation of a non-relativistic approach due to Borland [ Proc. Phys. Soc. 78, 926 (1961)]. We find that the relativistic effects on various aspects concerning the occurrence of band gaps in our models, are quite significant. Also, we show that there exists an upper limit to the deviation parameter for occurrence of band gaps in disordered systems, for both relativistic and non-relativistic cases.