Effect of Surface Andreev Bound States on the Bean-Livingston Barrier ind-Wave Superconductors

Abstract

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.

Phase diagram of geometricd-wave superconductor Josephson junctions

“…An increasing importance of surface Andreev bound states with decreasing temperature has also been found in a previous work on the influence of the surface Andreev bound states on the Bean-Livingston barrier. 28 The backflowing surface currents dominate at low temperatures T as well as for small widths w of the junction. This leads to negative values of the current-phase relations 29 and even to negative critical currents.…”

Enhancement of the field of first flux penetration due to Andreev bound states in Bi2Sr2CaCu2Beek1, Böhmer2, Kończykowski3 2010Physica C: Superconductivity and its Applications0000View full textAdd to dashboardCite

“…Below 50 K, a slight enhancement of the field of first flux penetration, H p , is found when the edge normals are oriented at 45°with respect to the principal (ab) crystal axes, rather than parallel to them. We discuss this effect in terms of a role of Andreev bound states (Iniotakis et al, 2008 [1]). …”

“…In the d-wave layered superconductor Bi 2 Sr 2 CaCu 2 O 8þd ; H p below 50 K is enhanced when the normals to the lateral crystal edges are oriented along the gap nodes. We attribute this effect to the anisotropy of the Meissner current due to the presence of Andreev bound states [1]. …”

“…In Bi 2 Sr 2 CaCu 2 O 8þd , this corresponds to a surface normal at 45°with respect to the ða; bÞ axes. The quasiparticle current carried by the bound states in response to the application of an external magnetic field H a is expected to partially compensate the Meissner current, thereby increasing the Bean-Livingston (BL) barrier [1] and the field of first flux penetration H p .…”

Modification of Born impurity scattering near the surface ofd-wave superconductors and influence of external magnetic field

“…In this case, a counter-flowing paramagnetic current is generated by the surface states, which increases with decreasing temperature and may even lead to a reversal of the current flow at the surface resulting in an anomalous Meissner effect 12,15 . This effect has recently been shown to have a strong influence on the Bean-Livingston surface barrier for entrance of vortices into the superconductor 16 .…”