Details of Disorder Matter in 2Dd-Wave Superconductors

Abstract

Within numerically exact solutions of the Bogoliubov-de Gennes equations, we demonstrate that discrepancies between predicted low-energy quasiparticle properties in disordered 2D d-wave superconductors occur because of the unanticipated importance of disorder model details and normal state particle-hole symmetry. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-state suppression below an energy scale which appears to be correlated with the corresponding single impurity resonance.

Electron-electron interactions in graphene sheets

“…17 For instance, a sharp divergence of the density of states has been found 18 or a suppression of the density of states at low energies. 19 In graphite, we do not expect a high concentration of charged impurities, which will lead to a strong site disorder.…”

“…Hence, we expect diagonal disorder in pure graphite to be small, leading to minor corrections to the dependence of the density of states on energy, even when nonperturbative terms are included. 17 …”

Narrow depression in the density of states at the Dirac point in disordered graphene

“…Depending on the disorder type and approach, a vanishing, a finite, or an infinite DOS at the Dirac point has been suggested for graphene or related models. 24,25,26,27,28,29,30,31,32,33,34 Also, the interpretation of experimental results is hampered by the uncertainty regarding the precise form of the DOS. Recently, following earlier experimental investigations of the Landau level splitting in high magnetic fields, 35,36 the opening of a spin (Zeeman) gap in the density of states at the Dirac point has been suggested in the interpretation of magneto-transport measurements on graphene sheets.…”

Nesting Symmetries and Diffusion in Disordered d-Wave Superconductors

“…The proposed scenarios predict vanishing [1][2][3], constant [4,5], and divergent [6,7] density of states (DOS) ν(ǫ) as ǫ → 0 (energies are measured from the Fermi level) for apparently similar models. Recently, two of the authors argued [8] on the basis of numerical studies that the d-wave superconductor is fundamentally sensitive to "details" of disorder, as well as to certain symmetries of the normal state Hamiltonian. While this approach was successful in unifying the various analytical treatments, it failed to provide a physical explanation of the origin of this lack of robustness.…”