On phase transitions in two-dimensional disordered systems

Abstract

The low-energy limits of models with disorder are frequently described by sigma models. In two dimensions, most sigma models admit either a Wess-Zumino-Witten or a theta term. When such a term is present the model can have a stable critical point with gapless excitations. We describe how such a critical point appears, in particular in two-dimensional superconductors with disorder. The presence of such terms is required by the underlying (anomalous) symmetries of the original electron model. This indicates that the usual symmetry classes of disordered systems in two dimensions can be further refined. Conversely, our results also indicate that models previously thought to be in different universality classes are in fact the same once the appropriate extra terms are included.

5 pages, new material on d_{x^2-y^2} superconductors, and an addition on the spin quantum Hall effect

References in corpus (2)

• Quasiparticle localization in superconductors with spin-orbit scattering
• Localization-delocalization transition of disordered d-wave superconductors in class CI

Cited by in corpus (17)

• Classification of topological insulators and superconductors in three spatial dimensions
• Electron transport in disordered graphene
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• Integrable sigma models with theta=pi
• Wave function statistics and multifractality at the spin quantum Hall transition
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• Interaction effects on 2D fermions with random hopping
• Disordered d-wave superconductors with interactions
• Effect of nonmagnetic disorder on criticality in the "dirty" U(1) spin liquid
• Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian
• Localization-delocalization transition of disordered d-wave superconductors in class CI
• Large N spin quantum Hall effect
• Quasiparticle Delocalization Induced by Novel Quantum Interference in Disordered d-Wave Superconductors
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Role of the impurity-potential range in disordered d-wave superconductors
• Phase diagram of disordered fermion model on two-dimensional square lattice with $\pi$-flux
• Two-dimensional Dirac fermions with random axial-vector potential