Liquid crystals are phases of matter with properties lying somewhere between a liquid and a crystal. The simplest liquid crystal, the nematic, has local orientation like a crystal but flows like a liquid. This unique combination of properties makes liquid crystals a fruitful source of materials in the creation of devices. Most famously, LCD displays are liquid crystalline; you are most likely reading this description by light shone through a liquid crystal!
Moving beyond immediate technological applications, the nature of liquid crystalline order makes it fertile ground for exploring topological and geometrical phenomena in physics. Modern experiments can realise a wealth of topological objects on microscopic lengthscales in liquid crystals. Imagine tying a knot in a piece of string as long as a strand of hair is wide, such knots can be realised in nematics, where the string itself is a singularity, a topological defect. Other examples include Hopf solitons, which are also knotted configurations as well as a whole host of topologically twisted structures in chiral liquid crystals, known as cholesterics.
Investigating these structures is of basic scientific interest, their investigation reveals deep connections to other areas of physics and mathematics as well as giving new properties of these phases, but beyond this they have great potential for the creation of a new generation of topologically inspired devices. This is because these singularites and solitons are robust, they cannot be gotten rid of without tearing or otherwise performing a singular operation on the material, much like you cannot unlink two loops without tearing one apart. This robustness makes them ideal for the creation of micro and nanoscale devices.
The purpose of this project is to use tools from algebraic and geometric topology to explore these topological configurations, knots and solitons, and give new theoretical characterisations. Current theories in the literature are elementary and known to be incomplete ; they cannot account for the morpohological richness found in modern experiments. This project will work on developing new theories of these materials based on the concepts and ideas of contact topology . The project will begin by classifying and characterise knotted and linked singularities in cholesteric liquid crystals by mapping it onto a problem of isotopy classification in contact topology. Building on this, the project will explore other directions, including interpretation of experimental results and studies of reconnection processes, where the knot type of a singularity changes. Along the way it is likely that new soliton-like structures will be found, with the potential for collaborative experimental work to explore them in the laboratory.
Tools used in the project will be theoretical, computational or a mixture of the two, according to the problem, as well as the preference of the student. Theoretical techniques used will draw from algebraic and contact topology, differential geometry as well as analytic calculations. The computational tools will be numerical simulation as well as energy landscape analysis.
There will be several collaborative opportunities during the project, depending on the direction taken, working with other groups at the University of Bristol as well as at other leading institutions in the UK, Israel and the United States.
For informal enquiries about the project please contact [email protected]
For enquiries about the application process contact [email protected]
How to apply:
Please make an online application for this project at http://www.bris.ac.uk/pg-howtoapply
. Please select Physics PhD on the Programme Choice page. You will be prompted to enter details of this specific project in the ‘Research Details’ section of the form.
Anticipated start date: September 2019
Candidate requirements: A first degree in physics or a related subject, normally at a level equivalent to at least UK upper second-class honours, or a relevant postgraduate master's qualification.
See international equivalent qualifications on the International Office website: http://www.bristol.ac.uk/international/countries/
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: T Machon, New Journal of Physics. 19, 113030 (2017).