phasons

Phasons are collective excitations in certain aperiodic crystals, most notably quasicrystals and incommensurately modulated structures, that represent fluctuations of the phase of the order parameter rather than ordinary lattice displacements (phonons). In practical terms, a phason changes the relative arrangement of motifs or tiles without altering their local surroundings.

In the theoretical description of quasiperiodic order, phasons arise from the higher-dimensional or internal-space (perpendicular-space) description of the structure. Shifts in this internal space correspond to real-space rearrangements of the tiling or density-modulation pattern. In one-dimensional modulated structures, the phason relates to sliding the phase of the density wave; in higher dimensions, it manifests as local tile flips or rearrangements of the quasiperiodic pattern.

Physically, phason dynamics can be gapless in ideal models, yielding low-energy phason modes, but real materials often exhibit pinning by impurities or defects that can create a finite phason gap and lead to diffusive motion. Phason fluctuations contribute to characteristic diffuse scattering near Bragg peaks and influence the dynamic response observed in scattering experiments. In charge-density waves, the phason is the phase mode of the CDW, and external fields can drive phason motion, producing nonlinear transport.

Experimental evidence for phasons comes from X-ray and neutron scattering showing diffuse intensity associated with phason fluctuations, as well as time-resolved measurements of phason relaxation. The concept of phasons is central to understanding aperiodic order and the dynamical behavior of modulated and quasiperiodic materials under temperature, stress, and fields.