Topological Skyrmion Research Articles

Topological excitation in the fractional quantum Hall system

Two kinds of topological excitations, vortices and skyrmions, are studied in the frame of Ginzburg–Landau theory. We obtain the rigorous relation between the topological excitation and the order parameters in the fractional quantum Hall systems. We also discuss the evolution of the vortices in fractional quantum Hall systems.

An Effective Field Theory Model to Describe Nuclear Matter in Heavy-Ion Collisions

Relativistic mean field theory with mesons σ, ω, π and ρ mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is a composite object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear σ-model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions.

Skyrmion excitations in quantum Hall systems

Using finite size calculations on the surface of a sphere we study the topological (skyrmion) excitation in quantum Hall system with spin degree of freedom at filling factors around $\nu=1$. In the absence of Zeeman energy, we find, in systems with one quasi-particle or one quasi-hole, the lowest energy band consists of states with $L=S$, where $L$ and $S$ are the total orbital and spin angular momentum. These different spin states are almost degenerate in the thermodynamic limit and their symmetry-breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron interaction and the skyrmion shrinks to a spin texture of finite size. We have calculated the energy gap of the system at infinite wave vector limit as a function of the Zeeman energy and find there are kinks in the energy gap associated with the shrinking of the size of the skyrmion. breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron

Theory of the overhauser effect in ferro- and antiferromagnets

Pions and magnons — the Goldstone bosons of the strong interactions and of magnetism — share a number of common features. Pion and magnon fields couple anomalously to electromagnetism through the conserved Goldstone-Wilczek current of their topological Skyrmion excitations. In the pion case, this coupling gives rise to the decay of the neutral pion into two photons. In the magnon case, the anomalous coupling leads to photonmagnon conversion in an external magnetic field. A measurement of the conversion rate in quantum Hall ferromagnets determines the anyon statistics angle of baby-Skyrmions. If photon-magnon conversion also occurs in antiferromagnets, baby-Skyrmions carry electric charge and may represent the Cooper-pairs of high-temperature superconductors.