Paul Leask

I am a postdoctoral researcher in the Condensed Matter Theory division at the KTH Royal Institute of Technology, working in the group of Egor Babaev. I am a theoretical physicist specialising in topological solitons in condensed matter systems, such as superconducting vortices, chiral magnetic skyrmions and liquid crystal hopfions.

Topological solitons are smooth, knot-like lumps of finite energy and are solutions of non-linear PDEs. They are stable against deformations and dissipation, and owe their existence to the topology of the manifold of degenerate vacuum states. They have applications along all length scales, from quantum knots in elementary particles physics, through superconducting vortices in condensed matter systems up to superconducting strings spanning galaxies in cosmology.

From 2020 to 2024, I obtained my doctorate in mathematics from the University of Leeds (under the supervision of Derek Harland and Martin Speight) and was a member of the Leeds Geometry Group. My main research project involved developing on models of nuclear matter as a crystal of topological solitons, such as skyrmions [1,2] or non-linear \(\sigma\)-model solitons stabilized by \(\omega\)-mesons [4,5]. I was particularly interested in the application of these models to cold dense nuclear matter (neutron stars, strange stars & black holes) [3], and finite atomic nuclei [6].

More recently, I have been investigating non-local electrostatic self-interactions of topological quasiparticles in condensed matter systems. These interactions occur as the result of demagnetization in micromagnetic systems [8] and the flexoelectric effect in chiral liquid crystals [9]. In addition, I am interested in probing states of matter in Ginzburg-Landau superconductors with time-reversal symmetry breaking via ultrasound absorption [11]. Currently, I am researching the coexistence of mixed magnetic skyrmion and superconducting vortex states in ferromagnetic superconductors [10].

If you would like to collaborate on any projects, or want to start a new project together, then contact me at palea[at]kth[dot]se.