Non Possum Comprimi Ergo Sum: Skyrmions and Edge States in the Quantum Hall Effect

Abstract

When the chemical potential of an electron system has a discontinuity at a density $n^{*}$, the system is said to be incompressible and a finite energy is required to create mobile charges in the bulk of the system. The quantum Hall effect is associated with incompressibilities in a two-dimensional electron system that occur at magnetic-field dependent densities, $n^{*}(B)$. In these notes we discuss two aspects of the physics of quantum Hall systems that follow directly from this association.