Title: Hidden Symmetries in Distortions
Abstract:

Symmetry is a fundamental tool in physical sciences. An introductory course in materials science, solid-state physics, or chemistry begins with an introduction to symmetry. Distortions are ubiquitous in materials, ranging from molecular and crystal lattice vibrations, mechanical deformations, phase transitions, protein reconfigurations and others.  One set of atomic configuration can rearrange to another configuration under an external stimuli, such as temperature, fields, and stresses. Representation theory is extensively used to study distortions and symmetry of distortions in materials.

In this talk, I propose a new antisymmetry operation called distortion-reversal (DR) symmetry, 1*, that reverses a distortion field. With this additional symmetry, we find that we can formulate distortion space groups and point groups (similar to magnetic groups), and ascribe them to a whole range of distortion phenomena such as the vibration modes of a water molecule, the a to b transition of quartz, oxygen diffusion on graphene, and phase transitions and domain wall motion in a ferroelectric or a ferromagnetic system.  If a material exhibits distortions as well as magnetic phenomena, then both 1* and 1' are relevant, and we can describe the structure using double antisymmetry space groups (DASG’s).  The 17,803 DASG’s were recently listed by the VanLeeuwen, Huang, Litvin, and Gopalan. 

We can ascribe distortion space and point groups to a general distortion of a discrete collection of objects as well as to continuous quantities such as electronic wavefunctions. An important consequence of ascribing distortion groups to a generalized distortion is that it can predict a change in any property tensor of a material system in response to a distortion. I will discuss how the application of distortion symmetry can extend vastly from crystals and biomolecules, to metamaterials, electronic structure calculations such as Berry phase, to even generalized motion in Euclidean and curvilinear spaces.