Quasiparticle resonant states induced by a unitary impurity in ad-wave superconductor

Abstract

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-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: (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 ξ0; (ii) For the particle-hole asymmetric case, an asymmetric splitting of the zeroenergy peak is intrinsic to a system with a small value of kF ξ0.PACS numbers: 74.25.Jb, 74.50.+r, 73.20.Hb It is now well established [1] that high-T c superconductors (HTSC's) have essentially a d x 2 −y 2 -wave pairing symmetry. In conventional s-wave superconductors, nonmagnetic impurities affect neither the transition temperature nor the superfluid density as dictated by the Anderson theorem [2]. But in a d-wave superconductor (DWSC) with nodes of the energy gap, such impurities can cause a strong pair-breaking effect [3]. Recently, the local electronic properties in the immediate vicinity of an isolated non-magnetic impurity in a DWSC has become the topic of increased investigation [4][5][6][7][8][9][10][11][12][13][14][15][16], as these properties may provide a distinctive signature for the pairing symmetry. It has been theoretically predicted by Balatsky, Salkola and co-workers [7,8] that, in a DWSC, a single nonmagnetic impurity can generate quasiparticle resonant states at subgap energies. They showed that, for a moderately strong impurity, an asymmetry of the resonance peak near the Fermi energy is induced by the fact that the impurity locally breaks the particle-hole symmetry. However, their theory says that increasing the impurity strength pushes the resonance peak toward the Fermi level, so that, in the unitary limit, the resonance occurs right on the Fermi level, and only a single symmetric zero-energy peak (ZEP) occurs in the LDOS near the impurity. It has also been shown by a finite-size diagonalization [10] that, in the unitary limit, the lowest eigenvalues are essentially zero, indicative of the appearance of zero-energy states (ZES's). Note that, in Ref.[10], the chemical potential µ was taken to be at the center of the tight-binding energy band (i.e., µ = 0), so that the system has a particle-hole symmetry. This symmetry is also upheld in the continuum-theory treatment of impurities [7,8] where the self-consistent t-matrix approximation is employed. A question which arises naturally is whether, in the unitary limit, the "ZEP" in the LDOS due to the "ZES's" has an asymmetric splitting or not, when particle-hole symmetry is broken in the system. Recently, Tanaka et al.[15] concluded with their numerical study that such a splitting is still present, whereas Tsuchiura et al. [16] made an opposite conclusion in their numerical study, and asserted that the system studied by Tanaka et al. was too small for their results to be re...

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