### Abstract

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein-Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Original language | English (US) |
---|---|

Article number | 053005 |

Journal | New Journal of Physics |

Volume | 20 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2018 |

### Fingerprint

### Keywords

- Dirac phonons
- ghost phonons
- spacetime
- topological phononics
- twistor theory

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*20*(5), [053005]. https://doi.org/10.1088/1367-2630/aaba18

**Spacetime representation of topological phononics.** / Deymier, Pierre A; Runge, Keith A; Lucas, Pierre; Vasseur, Jérôme O.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 20, no. 5, 053005. https://doi.org/10.1088/1367-2630/aaba18

}

TY - JOUR

T1 - Spacetime representation of topological phononics

AU - Deymier, Pierre A

AU - Runge, Keith A

AU - Lucas, Pierre

AU - Vasseur, Jérôme O.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein-Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

AB - Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein-Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

KW - Dirac phonons

KW - ghost phonons

KW - spacetime

KW - topological phononics

KW - twistor theory

UR - http://www.scopus.com/inward/record.url?scp=85048061993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048061993&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/aaba18

DO - 10.1088/1367-2630/aaba18

M3 - Article

AN - SCOPUS:85048061993

VL - 20

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 5

M1 - 053005

ER -