Quasiparticle scattering and local density of states in the d-density wave phase

Jian‐Xin Zhu, T. K. Lee, C. S. Ting +1 more

The quasiparticle resonant states around a single nonmagnetic impurity with unitary scattering in a d-wave superconductor is studied by solving the Bogoliubov--de Gennes equations based on a $t\ensuremath{-}J$ model. Both the spatial variation of the order parameter and the local density of states (LDOS) around the impurity have been investigated. We find that (i) a particle-hole symmetric system has a single symmetric zero-energy peak in the LDOS regardless of the size of the superconducting coherence length ${\ensuremath{\xi}}_{0};$ (ii) for the particle-hole asymmetric case, an asymmetric splitting of the zero-energy peak is intrinsic to a system with a small value of ${k}_{F}{\ensuremath{\xi}}_{0}.$

P. J. Hirschfeld

Bodo Huckestein

Alexander V. Balatsky, M. I. Salkola

The absence of localization of impurity-induced low-energy quasiparticle states in a 2D d-wave superconductor is shown for any amount of disorder in the limit of unitary scatterers. This result follows from the fact that a unitary impurity produces a marginally bound state at zero energy which decays as a power law along the nodes of the d-wave energy gap. Consequently, for finite density of impurities, the impurity-induced states are coupled by long-range overlaps yielding extended quasiparticle states below a characteristic energy scale ${\ensuremath{\omega}}_{c}$. Simple scaling arguments suggest that ${\ensuremath{\omega}}_{c}\ensuremath{\propto}{e}^{{\ensuremath{-}c/n}_{\mathrm{imp}}}$, with ${n}_{\mathrm{imp}}$ the impurity density and c a positive constant.

Indranil Paul, A. D. Klironomos, Michael R. Norman

We illustrate the importance of many-body effects in the Fourier-transformed local density of states (FT-LDOS) of $d$-wave superconductors from a model of electrons coupled to an Einstein mode with energy ${\ensuremath{\Omega}}_{0}$. For bias energies significantly larger than ${\ensuremath{\Omega}}_{0}$, the quasiparticles have short lifetimes due to this coupling and the FT-LDOS is featureless if the electron-impurity scattering is treated within the Born approximation. In this regime, it is important to include boson exchange for the electron-impurity scattering, which provides a ``step down'' in energy for the electrons and allows for long lifetimes. This many-body effect produces qualitatively different results, namely the presence of peaks in the FT-LDOS, which are mirrors of the quasiparticle interference peaks which occur at bias energies smaller than $\ensuremath{\sim}{\ensuremath{\Omega}}_{0}$. The experimental observation of these quasiparticle mirages would be an important step forward in elucidating the role of many-body effects in FT-LDOS measurements.

Franz Mohling, James C. Rainwater