Theory of rough surface effects on the anisotropic BCS states

Nagato, Yasushi; Higashitani, Seiji; Yamada, Kotaro; Nagai, Katsuhiko

doi:10.1007/bf00754654

Cited by 65 publications

(92 citation statements)

References 20 publications

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“…We use the quasi-classical theory 16,17) developed for the study of pwave Fermi superfluids. We calculate the self-consistent order parameter, the surface mass current and the surface density of states.…”

Section: -15)mentioning

confidence: 99%

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Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

2011

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We discuss the rough surface effects on a two-dimensional chiral kx + iky superconductor. The atomic scale roughness at the surface is considered using the random S matrix model. The roughness effects on the self-consistent order parameter, the surface mass current and the surface density of states are studied using the quasi-classical theory. We find that the surface mass current is suppressed by the surface roughness. The surface density of states shows a quite similar behavior to that of superfluid 3 He B phase. When the surface is specular, the surface Andreev bound states form a band which fills the bulk energy gap ∆ bulk . When the surface becomes diffusive, there occurs a sharp upper edge of the surface bound states band and there opens a sub-gap between the edge and the bulk energy gap. We show that this sub-gap is induced by the repulsion between the surface bound states and the propagating Bogoliubov quasi-particles through the second order process of roughness.KEYWORDS: 2-D Chiral Superconductor, Edge States, Surface Demsity of States, Superfluid 3 He-BThe 2-dimensional chiral k x + ik y state is known as a model system for Sr 2 RuO 4 superconducting state. 1)When there is a surface along the y axis, there occur gapless surface Andreev bound states as in other p-waveand d-wave 4) pairing systems, because the k x component of the order parameter changes its sign under the surface reflection. The surface bound states in chiral system are known to carry spontaneous mass flow along the surface.5, 6) Recently, surface bound states are recognized as edge states which reflect the topological nature of the bulk pairing state. A lot of attention has been paid to the surface Andreev bound states from this aspect. 6-15)In this paper, we consider the effects of atomic scale surface roughness on the chiral k x + ik y state. We use the quasi-classical theory 16,17) developed for the study of pwave Fermi superfluids. We calculate the self-consistent order parameter, the surface mass current and the surface density of states. The surface density of states shows quite a similar behavior to that in the 3-dimensional BW state.17) Existence of the order parameter component parallel to the surface disperses the surface bound state energy. The bound states, therefore, form a band below the bulk energy gap ∆ bulk . When the surface is specular, the band completely fills the bulk energy gap. When the surface becomes diffusive, however, there occurs a sharp upper edge of the band and there opens a sub-gap between the edge and the bulk energy gap. The band edge energy ∆ * increases as the roughness is reduced. Similar sub-gap has been known in the BW state. 17-19)The sub-gap was first reported by Zhang 18) who treated the surface roughness using the thin dirty layer model. He suggested that the sub-gap is due to the suppression of the parallel component of the order parameter by the roughness. However, Nagato et al. 17) found that this sub-gap also occurs when the order parameter is assumed to be spatially constant. Although t...

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Section: -15)mentioning

confidence: 99%

“…16,17,23) The surface is characterized by an S-matrix for the quasiparticles at the Fermi level in the normal state…”

Section: -19)mentioning

confidence: 99%

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

2011

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“…7, 26, we develop an alternative analytical method, which is based on Riccati formulation of the quasiclassical theory. 27,28,29,30,31,32,33) In the next section, we present the framework of quasiclassical theory of superconductivity. In §3, impurity problem of s-wave vortex core is considered.…”

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Phase-Sensitive Impurity Effects in Vortex Core of Moderately Clean Chiral Superconductors

Kato

2000

J. Phys. Soc. Jpn.

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We study impurity effects in vortex core of two-dimensional moderately clean superconductors within the quasiclassical theory. The impurity scattering rate Γ(E) of the Andreev bound states in vortex core with +1 vorticity of p-wave superconductors with d =ẑ (px + ipy) is suppressed, compared to the normal state scattering rate Γn in the energy region Γwith scattering phase shift δ0 (|δ0| ≪ 1) and the pair-potential in bulk ∆∞. Further we find that Γ(E)/Γn for p-wave superconductors with d =ẑ (px − ipy) is at most O(E/∆∞). These results are in marked contrast to the even-parity case (s,d-wave), where Γ(E)/Γn is known to be proportional to ln(∆∞/E) . Parity-and chirality-dependences of impurity effects are attributed to the Andreev reflections involved in the impurity-induced scattering between bound states. Implications for the flux flow conductivity is also discussed. Novel enhancement of flux flow conductivity is expected to occur at T ≪ E δ for d =ẑ (px + ipy) and at T ≪ ∆∞ for d =ẑ (px − ipy).

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“…In numerical studies of boundary problems similar techniques were used [18,19]. Also a scattering matrix approach, which is related to the randomly rippled wall model [21], was applied to disordered surfaces [22]; the solution was given in a Born-like approximation. Except for models with unitary scatterers [20], all calculations show a broadening of the ZBCP due to disorder.…”

Section: Introductionmentioning

confidence: 99%

d-wave superconductors near surfaces and interfaces: A scattering matrix approach within the quasiclassical technique

2001

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A recently developed method [A. Shelankov and M. Ozana, Phys. Rev. B 61, 7077 (2000)] is applied to investigate d-wave superconductors in the vicinity of (rough) surfaces. While this method allows the incorporation of arbitrary interfaces into the quasiclassical technique, we discuss, as examples, diffusive surfaces and boundaries with small tilted mirrors (facets). The properties of the surface enter via the scattering matrix in the boundary condition for the quasiclassical Green's function. The diffusive surface is described by an ensemble of random scattering matrices. We find that the fluctuations of the density of states around the average are small; the zero bias conductance peak broadens with increasing disorder. The faceted surface is described in the model where the scattering matrix couples m in-and m out-trajectories (m ≥ 2). No zero bias conductance peak is found for [100] surfaces; the relation to the model of Fogelström et al. [Phys. Rev. Lett. 79, 281 (1997)] is discussed.

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Theory of rough surface effects on the anisotropic BCS states

Cited by 65 publications

References 20 publications

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

Phase-Sensitive Impurity Effects in Vortex Core of Moderately Clean Chiral Superconductors

d-wave superconductors near surfaces and interfaces: A scattering matrix approach within the quasiclassical technique

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