Delocalization transitions in disordered media

Abstract

The study of crystalline solids and condensed matter physics at large concerns itself with the new behaviors and phases of matter exhibited by elementary particles, atoms, and molecules by virtue of being assembled into a structure. These phases arise from complex microscopic behaviors, which makes it is difficult to establish rigorous quantitative models. The analysis of certain phases is greatly simplified in the presence of symmetries. These symmetries can be non-spatial (time-reversal, particle-hole) or spatial (rotation, inversion, reflection). For example, topological phases ofmatter are easily characterized and classified by the symmetries of the system. Symmetries constrain the band structure of a system, and as a result produce certain quantized responses, such as surface modes on an otherwise insulating bulk. Since these surface modes are related to the symmetry of the bulk, this phenomenon is known as bulk-edge correspondence. So long as the symmetries protecting the topological phase are respected and the energy gap of the insulating bulk remains open, bulk-edge correspondence persists in the presence of disorder. This disorder can be non-structural (appliedmagnetic field), involve part of the structure (impurities) or the entire structure, such as in amorphous systems.....