Continuum Theory of Excitation Spectra of Topologically Disordered Systems

Abstract

We propose a continuum treatment of random networks with odd rings near the antibonding .bound. An analogy with nematic liquid crystals is demonstrated in which Rivier lines play the role of disclination lines. The state density is expressed in terms of fluctuations of gauge fields associated with Rivier lines. There has been a great interest lately on the effects of topological disorder on the spectra of elementary excitations in amorphous materi­ als. , ),2) An important aspect characterizing such topological disorder is the existence of closed lines threading through odd rings. 3 ) The so­ called Rivier lines are known to lead to drastic reductions in density of states near the antibond­ ing limit.I),2) Here we present a continuum treat­ ment which is hoped to provide further insights into this important problem. We adopt a simple one· electron problem on a random network consisting of N sites which is described in Ref. 1). The Schrodinger equation for a set of amplitudes {aJ where j designates a site on the network is given in some dimensionless units by