Dynamics of Vortices and Active Matter on Structured Substrates

This work investigates various physical problems under the general category of particles being driven over an ordered or disordered substrate. The general problem has clear applications to frictional phenomena, ranging from stick-slip motion to earthquakes; here we consider more novel scenarios taken from the fields of superconductivity and biophysics.

The 'conformal crystal' structure is investigated in the context of superconducting vortex pinning. This 2D structure is generated mathematically by a conformal transformation of a regular hexagonal lattice, and possesses local hexagonal ordering,but globally features a density gradient in one dimension and an arching structure in the other dimension. A vortex pinning array based on this structure is shown to have superior magnetization and transport properties as compared to other previously considered pinning arrays, and is used to construct a highly effective ratchet for vortices.

An Archimedean pinning structure, with two characteristic length scales, is also considered, as an intermediate case between periodic pinning with a single length scale, and conformal pinning with a continuum of scales due to the density gradient. Magnetization studies reveal a variety of novel vortex states at integer and fractional matching fields, which are not present in either periodic or conformal pinning.

Finally, an nanoassembly experiment is simulated where the particles affect the substrate, as opposed to the more common reverse scenario which underlies the other topics in this work. The energy of run-and-tumble active matter particles (such as E. coli bacteria undergoing chemotactic motion) is harnessed to push together two movable walls arranged in a Casimir geometry.