Nodal-antinodal dichotomy from pairing disorder in d -wave superconductors

We study the basic features of the local density of states (LDOS) observed in STM experiments on high-Tc d-wave superconductors in the context of a minimal model of a d-wave superconductor which has weakly modulated off-diagonal disorder. We show that the low and high energy features of the LDOS are consistent with the observed experimental patterns and in particular, the anisotropic local domain features at high energies. At low energies, we obtain not only the scattering peaks predicted by the octet model [1], but also weak features that should be experimentally accessible. Finally, we show that the emerging features of the LDOS lose their correspondence with the features of the imposed disorder, as its complexity increases spatially. In recent years, the effect of underlying inhomogeneities in superconductors has been studied intensively. In the context of high temperature superconductors (HTSC), checkerboard local density of states (LDOS) oscillations and strong nanoscale gap inhomogeneity have been observed in scanning tunneling spectroscopy (STS) experiments [2], and signals in dynamical susceptibility measured by neutron scattering have been interpreted as stripe-like nanoscale modulations of charge and spin degrees of freedom [3]. Even though it is still not clear whether these modulations are intrinsic or driven entirely by disorder, it seems plausible that the magnitude of Tc might be strongly related to the very existence of inhomogeneity on the coherence length scale [4, 5], and therefore a deeper understanding of the source of inhomogeneities is important. In the cases of the compounds La2−xBaxCuO4and La2−xSrxCuO4(with Nd or Eu co-doping), inhomogeneities take the form of static long-range stripe-like spin and charge modulations [6–9]. Tunneling spectroscopy has been used to probe states in different regions of momentum and energy, by the help of the Fourier transform scanning tunneling spectroscopy (FT-STS) and the high energy features of the LDOS. At low energies, in the d-wave superconducting state near optimal doping, quasiparticle interference (QPI) observed by FT-STS is dominated by peaks at well-defined wavevectors q i which are consistent with a simple model of Bogoliubov quasiparticles, called the octet model [10, 11]. Even though the qualitative features of the octet model are experimentally robust, a quantitative understanding of the amplitude, location and width of the peaks is not straightforward to obtain and depends rather sensitively on the nature of the scattering medium [12]. A point-like scatterer, for example, in an otherwise homogeneous dSC leads to a landscape of some spot-like and some arc-like dispersive features close to qi in the FT-STS images [13], whereas experimental data appear mostly spot-like. At high energies, local unidirectionality has been observed in domains with size approximately 5a0, close to the superconductor’s coherence length and the domains typically alternate in orientation. This behavior is usually attributed to a disordered charge-density wave (CDW), with some success on demonstrating the emergence of the LDOS patterns from the underlying CDW order. [14].