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

Abstract

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.

One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology

“…Recently, extrinsic topological phononic crystals have demonstrated the astonishing property of non-reciprocity and backscattering-immune edge states and bulk states establishing classical equivalents of topological electronic insulators. The non-conventional topology of elastic waves in an intrinsic topological phononic structure has been associated with the notion of duality in the quantum statistics of phonons (i.e., boson vs. fermion) [4,5]. In the current paper, we illustrate the topological properties of elastic waves in the two classes of topological phononic structures.…”

“…There exists two-classes of phonon structures possessing non-conventional topology, namely intrinsic and extrinsic systems. Time-reversal symmetry in intrinsic systems [4][5][6][7][8][9][10][11][12][13][14] is broken through internal resonance or symmetry breaking structural features (e.g., chirality) and without addition of energy from the outside. Energy is added to extrinsic topological systems to break time reversal symmetry [15][16][17][18][19][20].…”

“…For instance, at k = 0, the antisymmetric mode is represented by a standing wave which enforces a strict relation between the amplitude of a forward propagating wave and a backward propagating wave. This characteristic was shown [4,5] to be representative of Fermion-like behavior of phonons. As k Ñ 8 , ω Ñ`βk , the first two terms in Equation (5) go to zero and only one direction of propagation (backward) is supported by the medium (third and fourth terms in Equation (5)).…”

“…Topological electronic [1], electromagnetic [2,3], and phononic crystals [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] all have demonstrated unusual topologically constrained properties. In phononic crystals and acoustic metamaterials, symmetry breaking is linked to constraints on the topological form of acoustic wave functions.…”

Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

“…Phononic structures have also been shown recently to possess non-conventional topology as well as topologically constrained propagative properties. These properties have been achieved by breaking time-reversal symmetry through internal resonance or symmetry breaking structural features (e.g., chirality) [9][10][11][12][13][14][15][16][17][18][19] and without addition of energy from the outside. Energy can also be added to extrinsic topological elastic systems to break time reversal symmetry.…”