Torsional topology and fermion-like behavior of elastic waves in phononic structures

A one-dimensional block-spring model that supports rotational waves is analyzed within Dirac formalism. We show that the wave functions possess a spinor and a spatio-temporal part. The spinor part leads to a non-conventional torsional topology of the wave function. In the long-wavelength limit, field theoretical methods are used to demonstrate that rotational phonons can exhibit fermion-like behavior. Subsequently, we illustrate how information can be encoded in the spinor-part of the wave function by controlling the phonon wave phase.