Low-frequency vibrational modes anomalies and rigidity: A key to understanding the glass and the electronic properties of flexible materials from a topological perspective

Abstract

Using rigidity (constraint) theory of glasses, the effects of low-frequency vibrational modes anomalies in the glass transition are studied. It is discussed how the possibility of tailoring by chemical doping the number of low-frequency modes gives clues about how to determine the glass transition temperature and glass formation ability. In particular, we present the effects of floppy modes in the specific heat, entropy, internal energy below glass transition, as well as a discussion of the thermodynamical effects above the glass transition. All the previous results can be extended to include the Boson peak, since it can also be understood from a rigidity point of view as a dilution of bonds in an over-constrained network. Finally, we discuss how a new subject is emerging: floppy modes effects in the electronic properties of flexible systems. Such relationship provides a natural connection with topological insulators and two dimensional materials like graphene.