Global phase diagram of two-dimensional Dirac fermions in random potentials

Anderson localization is studied for two flavors of massless Dirac fermions in two-dimensional space perturbed by static disorder that is invariant under a chiral symmetry (chS) and a time-reversal symmetry (TRS) operation which, when squared, is equal either to plus or minus the identity. The former TRS (symmetry class BDI) can, for example, be realized when the Dirac fermions emerge from spinless fermions hopping on a two-dimensional lattice with a linear energy dispersion such as the honeycomb lattice (graphene) or the square lattice with flux per plaquette. The latter TRS is realized by the surface states of three-dimensional Z[sub 2]-topological band insulators in symmetry class CII. Moreover, we argue that physics of Anderson localization in the CII phase can be presented in terms of a non-linear-model (NL[sigma]M) with a Z[sub 2]-topological term. We thereby complete the derivation of topological or Wess-Zumino-Novikov-Witten terms in the NL[sigma]M description of disordered fermionic models in all ten symmetry classes relevant to Anderson localization in two spatial dimensions.