Impurity states ind-wave superconductors with a competing antiferromagnetic interaction

Abstract

Impurity states in d-wave superconductors with a competing antiferromagnetic ͑AF͒ order are investigated by solving the Bogoliubov-de Gennes equations. The potential scattering (PS) model with moderate strength and the Anderson impurity (AI) model with on-site hybridization are employed to describe the weak impurities. In zero external field, the impurity-induced AF order is rather weak and both models are able to give rise to impurity resonant states with close energy and similar profile of the local density of states. In the mixed state, the effect of magnetic-field-induced AF order on the impurity quasiparticle excitation is also examined. We find that the response of the impurity state to the presence of a local AF order is quite different for the two impurity models when a superconducting vortex is pinned by the impurity. For the PS model, the impurity resonance is subtly dependent on the sign and strength of the scattering potential, while for the AI model in the strong hybridization regime, the low-lying resonance is pinned near the Fermi level within the small gap opened by the AF order and is insensitive to the strength of the coupling between the impurity spin and the conduction electron. Based on our numerical results, we think that the two models give rise to different behaviors of the impurity resonances for both the nickel and zinc impurities in the magnetic field and the prospective scanning tunneling microscopic observation might give a clue to the dominant mechanism of the impurity states in the high-T c cuprates.

Impurity-induced states in conventional and unconventional superconductors

“…The Kondo effect in these systems where the host single particle density of states follows a power law, has been studied intensively Hirschfeld, 1992, 1994;Bulla et al, 2000Bulla et al, , 1997Fradkin, 1996, 1997;Chen and Jayaprakash, 1995;Gonzalez-Buxton and Ingersent, 1998;Han et al, 2002Han et al, , 2004Ingersent, 1996;Ingersent and Si, 1998;Itoh, 1993;Logan and Glossop, 2000;Polkovnikov, 2002;Polkovnikov et al, 2001;Vojta and Bulla, 2001;Withoff and Fradkin, 1990;Zhang et al, 2001;Zhu and Ting, 2001a,b).…”

“…Gapless systems like d-wave superconductors with the low-energy quasiparticle density of states following the power law, N (E) ∝ |E| r with the exponent r > 0, constitute a marginal situation. The Kondo effect in these systems where the host single particle density of states follows a power law, has been studied intensively Hirschfeld, 1992, 1994;Bulla et al, 2000Bulla et al, , 1997Fradkin, 1996, 1997;Chen and Jayaprakash, 1995;Gonzalez-Buxton and Ingersent, 1998;Han et al, 2002Han et al, , 2004Ingersent, 1996;Ingersent and Si, 1998;Itoh, 1993;Logan and Glossop, 2000;Polkovnikov, 2002;Polkovnikov et al, 2001;Vojta and Bulla, 2001;Withoff and Fradkin, 1990;Zhang et al, 2001;Zhu and Ting, 2001a,b). 7 Fradkin and co-workers Fradkin, 1996, 1997;Withoff and Fradkin, 1990) first employed a combination of the poor man's scaling argument and the large-N approach to the case of spin-1 2 (impurity degeneracy N = 2) for 0 < r ≤ 1, an showed that a Kondo effect takes place only when the electron-impurity exchange J exceeds a critical value.…”

Effect of disorder on the pairing properties of electron-doped high-Tcsuperconductors

“…͑ii͒ We use the conventional mean-field BdG equations, in which the strong correlated effect is not considered. Though a more relevant method in which the strong correlations are more or less included 43 deserves to be developed, the reproduction of many features observed in high-T c cuprates by the mean-field BdG equations 20,22,25,29,30,35,39 suggests that this method has captured some important physics of high-T c cuprates.…”

“…This supercell technique is well established and has been applied to study the effect of various inhomogeneities such as impurities and surfaces in high-T c superconductors. 22,29,30 The filling factor n = ͚ i ͗c i, † c i, ͘ / N x N y is fixed at 1.14 ͑electron doping ␦ = 0.14͒ and temperature is chosen to be T =10 −4 . From the obtained eigenvalues and eigenfunctions of many random disorder configurations, we can calculate the statistical and configurational averages of physical quantities.…”

Impurity resonance peaks in the vortex core of cuprate superconductors with induced spin density wave order

“…24 It is worth to mention that the LDOS at the impurity site has been studied for weak scattering potential. 25 Finally, we will study the effect of band structure by varying the next-nearest-neighbor hopping tЈ. As illustrated in This implies that the impurity potential of V imp = 10 is strong enough to induce a local SDW order.…”