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

No abstract

We study the influence of spin on the quantum interference of interacting electrons in a singlechannel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of electron-electron interaction and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.

We study the effects of quasiparticle interactions on disorder-induced localization of Dirac-like nodal excitations in superconducting high-Tc cuprates. As suggested by the experimental ARPES and terahertz conductivity data in Bi2Sr2CaCu2O 8+δ , we focus on the interactions mediated by the order parameter fluctuations near an incipient second pairing transition d → d + is. We find interaction corrections to the density of states, specific heat, and conductivity as well as phase and energy relaxation rates and assess the applicability of the recent localization scenarios for noninteracting random Dirac fermions to the cuprates.In the past few years, the problem of disordered twodimensional (2D) Dirac fermions received much of attention, as it provides an effective description for the random bond Ising model, network models of Quantum Hall plateau transitions, and some other statistical problems. Also, dynamical Dirac fermions can be used to conveniently describe low-energy excitations in a variety of correlated systems, such as p-wave (e.g., Ru 2 SrO 4 ) and layered d-wave (high-T c cuprates) superconductors and superfluids (He 3 ), and zero-gap semiconductors (e.g., graphene sheets).The Hamiltonian of a generic disordered gapless superconductor and, in particular, planar d-wave system, possesses an additional discrete symmetry of charge conjugation which gives rise to as many as seven novel random Gaussian ensembles corresponding to different patterns of spin rotational and time reversal symmetry breaking [1]. Moreover, in a stark contrast with the conventional case of a normal metal with extended Fermi surface the density of states (DOS) of the non-interacting Dirac fermions in a 2D d-wave superconductor is strongly affected by disorder [2]. Furthermore, depending on the concrete model for disorder, such as isotropic versus predominantly forward potential impurity scattering, the DOS of the random Dirac fermions can exhibit different low-energy asymptotic behaviors even within the same random ensemble [3][4][5][6][7][8].The multitude of different regimes and crossovers predicted for the non-interacting random Dirac fermions raises a question about their observability in such realistic d-wave systems as the high-T c superconductors where quasiparticle interactions are believed to be important. Moreover, the localization theory still remains incomplete without an extra input in the form of quasiparticle dephasing rate which controls the magnitude of disorder-induced localization corrections in the infinite system.Thus far, despite the continuing progress in understaning of the non-interacting (de)localization phenomena in the d-wave systems, the above issues did not receive enough attention. In the present paper, we fill in this gap by investigating the effects of physically relevant quasiparticle interactions on the localization properties of the Dirac-like nodal excitations in the superconducting cuprates.In the Nambu spinor representation, the quasiparticle (retarded) Green function reads aŝ( 1) where we intro...

A simple way to investigate theoretically the Raman spectra (RS) of nonpolar nanoparticles is proposed. For this aim we substitute the original lattice optical phonon eigenproblem by the continuous Klein-Fock-Gordon-like equation with Dirichlet boundary conditions. This approach provides the basis for the continuous description of optical phonons in the same manner how the elasticity theory describes the longwavelength acoustic phonons. Together with continuous reformulation of the bond polarization model it allows to calculate the RS of nanoparticles without referring to their atomistic structure. It ensures the powerful tool for interpreting the experimental data, studying the effects of particle shape and their size distribution. We successfully fit recent experimental data on very small diamond and silicon particles, for which the commonly used phonon confinement model fails. The predictions of our theory are compared with recent results obtained within the dynamical matrix method -bond polarization model (DMM-BPM) approach and an excellent agreement between them is found. The advantages of the present theory are its simplicity and the rapidity of calculations. We analyze how the RS are affected by the nanoparticle faceting and propose a simple power law for Raman peak position dependence on the facets number. The method of powder RS calculations is formulated and the limitations on the accuracy of our analysis are discussed. arXiv:1806.08100v1 [cond-mat.mes-hall]

The RKKY interaction between rare-earth (RE) ions in high-T c superconductors is considered at T ≪ T c . It is shown that this interaction consists of two terms: conventional oscillating one and the positive term, which is proportional to the gap function and decreases in the 2D case inversely proportional to the distance. In the antiferromagnetic state of the RE subsystem this positive interaction gives rise for frustrations which diminishes the Neel temperature. In the case of strongly anisotropic gap function this frustration produces two different values of the effective nearest neighbor exchange coupling between RE ions along the a and b. This anisotropy has been established experimentally in Ref. [6][7][8].