Research themes

We are focused on understanding and exploiting the topological properties of structures to achieve specific combinations of desirable and exotic physical properties in new materials and devices.  Such structured materials, which possess properties not occurring in the natural world, are called topological metamaterials.

We explore material topology in real space, and how it can lead to strong, lightweight materials, and also material topology in reciprocal space, leading to topologically protected modes and channels.

Topological Design in Mechanical and Vibration Engineering

We employ topological design (such as topology optimisation) of materials to enable weight reduction, combined with properties such as sound damping in acoustic metamaterials, temperature or magnetic field activation using shape memory alloys (e.g. magnetic shape memory materials); elastic/structural metamaterials (e.g. auxetic structures, negative Poisson’s ratio).

Topological Design in Quantum Physics and Technology

Topological physics is primarily concerned with topological properties of the band structure of materials, such as electric conductivity in the Hall effect, or its optical analogues in photonic materials. Our research covers a range of topological quantum physics, from highly abstract (such as synthetic dimensions in ultracold atoms and photonic devices) to applications of density functional theory in new topologies for metal-organic frameworks for improved battery materials.

Topological Design in Electromagnetism and Photonics

Topologically structured electromagnetic fields offer new ways of transferring and encoding information, in principle even extending to many bits for a single photon. Furthermore, topologically designed photonic metamaterial waveguides do not have the problems of waveguides made from traditional ferrite materials, opening up the possibility of creating completely new photonic and microwave devices.

Topological Design in Health and the Life Sciences

Topologically structured materials offer great possibilities for flexible medical implants that adapt to the shapes of our bodies.  Furthermore, many disruptive biological processes, such as fibrillation of the heart, can be understood and addressed using topological methods.

Topological Design in Soft Matter and Chemistry

Topology plays an important role in the ordering of soft materials such as liquid crystals.  2-dimensional magnetic and liquid crystal films support Skyrmions – stable topological excitations proposed as bits for low-energy data storage, and are analogous to topological excitations studied in high-energy physics, originally proposed by Prof Tony Skyrme (Birmingham Professor 1964-1987).  We are exploring various other topological structures such as 3D isostatic colloidal crystals.

Topological Design in Mathematical, Computational and Data Sciences

The mathematical study of the duality between symplectic and algebraic geometry and its higher genus generalisation, is finding wide application, for example in theoretical physics to model correlation functions and in theoretical neuroscience to model the network of synaptic connections between neurons in the brain.  Other more established techniques, such as persistent homology, are being used to analyse the existence of 2D holes and 3D voids in single molecule membrane microscopy of cell membrane structures.

Topological Design in Manufacturing and 3D Printing

Traditional forming and machining manufacturing techniques have led to a barrier to the creativity of the design engineer. Our research is exploring how to exploit the geometric freedom of topological design and knowledge of the constraints which are material, platform and parameter dependent, with inspiration taken from developmental biology to lead to new manufacturing processes.