Theories of low-energy quasi-particle states in disordered d-wave superconductors

The physics of low-energy quasi-particle excitations in disordered d-wave superconductors is a subject of ongoing intensive research. Over the last decade, a variety of conceptually and methodologically different approaches to the problem have been developed. Unfortunately, many of these theories contradict each other, and the current literature displays a lack of consensus on even the most basic physical observables. Adopting a symmetry-oriented approach, the present paper attempts to identify the origin of the disagreement between various previous approaches, and to develop a coherent theoretical description of the different low-energy regimes realized in weakly disordered d-wave superconductors. We show that, depending on the presence or absence of time-reversal invariance and the microscopic nature of the impurities, the system falls into one of four different symmetry classes. By employing a field-theoretical formalism, we derive effective descriptions of these universal regimes as descendants of a common parent field theory of Wess–Zumino–Novikov–Witten type. As well as describing the properties of each universal regime, we analyse a number of physically relevant crossover scenarios, and discuss reasons for the disagreement between previous results. We also touch upon other aspects of the phenomenology of the d-wave superconductor such as quasi-particle localization properties, the spin quantum Hall effect, and the quasi-particle physics of the disordered vortex lattice.