Catastrophe theory classification of Fermi surface topological transitions in two dimensions

Abstract

We classify all possible singularities in the electronic dispersion of\ntwo-dimensional systems that occur when the Fermi surface changes topology,\nusing catastrophe theory. For systems with up to seven control parameters\n(i.e., pressure, strain, bias voltage, etc), the theory guarantees that the\nsingularity belongs to to one of seventeen standard types. We show that at each\nof these singularities the density of states diverges as a power law, with a\nuniversal exponent characteristic of the particular catastrophe, and we provide\nits universal ratio of amplitudes of the prefactors of energies above and below\nthe singularity. We further show that crystal symmetry restricts which types of\ncatastrophes can occur at the points of high symmetry in the Brillouin zone.\nFor each of the seventeen wallpaper groups in two-dimensions, we list which\ncatastrophes are possible at each high symmetry point.

Topics & Concepts