The low-energy density of states (DOS) of disordered 2D d-wave superconductors is extremely sensitive to details of both the disorder model and the electronic band structure. Using diagrammatic methods and numerical solutions of the Bogoliubov-de Gennes equations, we show that the physical origin of this sensitivity is the existence of a novel diffusive mode with momentum close to (π, π) which is gapless only in systems with a global nesting symmetry. We find that in generic situations, the DOS vanishes at the Fermi level. However, proximity to the highly symmetric case may nevertheless lead to observable non-monotonic behavior of the DOS in the cuprates.Introduction. An understanding of the quasiparticle (QP) excitations in the d-wave superconducting state of the high-T c superconductors is essential for the elucidation of transport properties, for determining how the ground state deviates from the BCS model, and for describing the instability of the lightly doped antiferromagnetic state to superconductivity. It has been known for some time that the influence of disorder on the QP states is quite different from ordinary superconductors, in part due to the gap symmetry and in part due to low dimensionality. Nersesyan et al. have shown that these two features conspire to introduce logarithmic divergences in all orders of the perturbation theory [1]. Since then, several groups have attempted nonperturbative treatments of the "2D dirty d-wave problem", arriving at a surprisingly diverse set of results. 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.

In crystalline nanoparticles, the Raman peak is downshifted with respect to the bulk material and has asymmetric broadening. These effects are straightly related to the finite size of nanoparticles, giving the perspective to use Raman spectroscopy as the size probe. By combining the dynamical matrix method (DMM) and the bond polarization model (BPM), we develop a new (DMM− BPM) approach for the description of Raman spectra of nanoparticle powders. The numerical variant of this approach is suitable for the description of small particles, whereas its analytical version is simpler to implement and allows one to obtain the Raman spectra of arbitrary-sized particles. Focusing on nanodiamond powders, the DMM−BPM theory is shown to fit the most recent experimental data much better than the commonly used phonon confinement model.

We study the effect of correlations between impurity potentials in different layers on the Coulomb drag in a double-layer electron system. It is found that for strongly correlated potentials the drag in the diffusive regime is considerably enhanced as compared to conventional predictions. The appropriate experimental conditions are discussed, and the new experiments are suggested.Comment: 7 pages, 1 figur