An opportunity to become involved in a new area of physics.
This project looks at a new physical system for studying topological physics, using networks of radio frequency transmission lines made
from coaxial cables. The underpinning theory is our discovery of a mapping from these networks to tight binding Hamiltonians of solid
state physics - we can, for example, make an analogue of a graphene lattice, where the radio frequency transmission mimics the behaviour
of electrons in real graphene. An important property of these Hamiltonians is that they have a symmetry, known as chiral symmetry,
which leads to a non-trivial topological classification, with different structures having different topologies. As a consequence,
we can use our networks to investigate topological physics concepts, such as topologically protected states, whose energies remain
completely unchanged when we add disorder to a structure. In the case of graphene, we are currently looking at how making structures with
different topologies, by changing the way that we connect the edges, as a tube, torus or even mobius strip.
Looking forward, I am planning to investigate other topologically interesting lattices, such as the Kagome lattice, and making
structures with different symmetries, such as particle-hole symmetry, which have different sorts of topological properties. I also have
some fun ideas for making structures which cannot normally exist in the three dimensional Euclidean space we live in, for example, four
dimensional lattices, and an octagonal tiling of the hyperbolic plane. These are possible because of the (literal) flexibility of the cables
we work with.
The project has a strong theoretical component, to obtain a deeper understanding of the topological properties of the structures in which
we are interested. However, the unique feature of our networks is that we can perform experimental studies of topological physics, so ideally
I would like to recruit a student with interest in both aspects. The balance between theory and experiment can be weighted according
preference.
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