Odd rings and tunneling modes in glasses

Abstract

Tunneling modes, elementary excitations of a large class of glasses, are local dynamical signatures of disorder. There is one tunneling mode per odd loop (a necklace through odd rings in the network), decoupled from other loops, and tunneling is forced by gauge invariance of the structure, the symmetry of disorder. Absence of tunneling modes in trivalent glasses (a-As or B 2O 3) is a notable consequence of this model. It is possible to decompose topologically a tetravalent network into a trivalent network, and to add a large proportion of boroxol rings with their characteristic but different dynamical signature.