Resonance State Localized around Nonmagnetic Impurity with Unitarity Scattering in Two-Dimensional<i><i>d</i></i>-Wave Superconductor

Onishi, Yoshifumi; Ōhashi, Y.; Shingaki, Yasunori; Miyake, Kazumasa

doi:10.1143/jpsj.65.675

Cited by 50 publications

(44 citation statements)

References 17 publications

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“…1(a), µ = 0 [23] and γ = 0.80, a single ZEP occurs in the LDOS on the nearest-neighbor site of the impurity, similar to the prediction of the continuum theory [7,8] and the eigenvalue calculation in Ref. [10]. In addition, as a reflection of the particle-hole symmetry, the whole LDOS spectrum is symmetric about E = 0.…”

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“…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.…”

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“…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.…”

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confidence: 99%

“…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.…”

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

et al. 2000

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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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confidence: 99%

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confidence: 99%

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

et al. 2000

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“…7,8,9) Recently, Pan et al observed such a low-energy state around a Zn atom in Bi 2 Sr 2 CaCu 2 O 8+δ using a low-temperature scanning tunneling microscope (STM), showing a fourfold symmetrical structure which is consistent with a d x 2 −y 2 -wave pairing state.…”

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Impurity Site NMR Relaxation in Unconventional Superconductors

Matsumoto

2001

J. Phys. Soc. Jpn.

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Impurity nuclear spin relaxation is studied theoretically. A single impurity generates a bound state localized around the impurity atom in unconventional superconductors. With increasing impurity potential, the relaxation rate T −1 1 is reduced by the impurity potential. However, it has a peak at low temperatures due to the impurity bound state. The peak disappears at nonimpurity sites. The impurity site NMR measurement detecting a local electronic structure just on the impurity atom is very useful for identifying the unconventional pairing states. KEYWORDS: NMR, NQR, unconventional superconductivity, impurityThe study of unconventional superconductors has become one of the most attractive issues in recent condensed matter physics. These materials include heavy fermion compounds, high-T c cuprates, organic superconductors and the recently discovered Sr 2 RuO 4 . A great effort has been made to detect the unconventional superconductivity by several probes: specific heat measurement, tunneling spectroscopy, nuclear magnetic resonance (NMR), π-junction and so on. NMR experiments were important in the early stage of studying the unconventional superconductivity. It is well known that T −1 1 in s-wave superconductors has a Hebel-Slichter peak just below T c , while it does not exhibit this feature in unconventional superconductors. On the other hand, it was also reported that the peak can be suppressed by the strong damping effect even for a s-wave state.

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The importance of self-consistency in determining interface properties of SIN and DIN structures

Martin¹,

Annett²

1999

Superlattices and Microstructures

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We develop a method to solve the Bogoliubov-de Gennes equation for superconductors self-consistently, using the recursion method. The method allows the pairing interaction to be either local or nonlocal corresponding to s-and d-wave superconductivity, respectively. Using this method, we examine the properties of various SIN and DIN interfaces. In particular, we self-consistently calculate the spatially varying density of states and the superconducting order parameter. We see that changing the strength of the insulating barrier at the interface, does not, in the case of an s-wave superconductor, dramatically change the low-energy local density of states in the superconducting region near the interface. This is in stark contrast to what we see in the case of a DIN interface where the local particle density of states is changed dramatically. Hence we deduce that in calculating such properties as the conductance of SIN and DIN structures it is far more important to carry out self-consistent calculations in the d-wave case.

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Resonance State Localized around Nonmagnetic Impurity with Unitarity Scattering in Two-Dimensionald-Wave Superconductor

Cited by 50 publications

References 17 publications

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

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

Impurity Site NMR Relaxation in Unconventional Superconductors

The importance of self-consistency in determining interface properties of SIN and DIN structures

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