Impurity Scattering and Magnetic Field Influence on a Nodal Surface of a d-Wave Superconductor

In the present work the surface of d-wave superconductors is studied. In such superconductors zero-energy Andreev bound states (ABSs) may appear at the surface depending on the orientation of the d-wave with respect to the surface normal. Existence of these states influences the properties of the superconductor on the length scale of the coherence length, the spatial extension of the bound states. Surface roughness, surface disorder, or diffuse scattering as well as an external magnetic field at the surface may affect the bound states and consequently the surface properties. Based on Eilenberger equations we perform self-consistent calculations in three different cases: in the presence of impurities, in the presence of an external magnetic field, and a combination of these two cases. We focus on the influence of bulk impurity scattering in the Born approximation limit. We show that the impurity scattering around zero energy is significantly increased near the surface as compared to the bulk due to the presence of ABSs. This leads to a larger broadening of the ABSs than expected from the scattering rate in the bulk and consequently a decrease of the peak height of the local density of states at zero energy. Due to the anomalous Meissner current flowing at the nodal surface, the magnetic field initially increases before the normal Meissner screening sets in and eventually screens out the magnetic field exponentially. The field increase is stronger at low temperatures and leads to an increase in the modulus of the vector potential towards low temperatures. The result is a nonmonotonous temperature dependence of the vector potential at the surface. Since the vector potential is proportional to the superfluid velocity, the size of the peak splitting in the local density of states is directly influenced by such a behavior of the vector potential. We observe that the splitting is large both for low temperatures and close to the critical temperature. As a result also the peak height has a nonmonotonous temperature dependence. Considering the Born impurity scattering in the presence of an external magnetic field, we show that the peak height in the local density of states at the surface is strongly reduced due to the scattering rate. The peak width also grows with decreasing mean-free path. However, the size of the peak splitting remains almost unaffected. The presence of the surface ABSs also has a significant influence on the nonlinear Meissner effect. The nonlinear response coefficient in the bulk of a d-wave superconductor is known to show an upturn at low temperatures following a 1/T law in a clean system. However we show that the contribution of the surface ABSs to the nonlinear response coefficient follows an inverse T-cube law, which will ultimately dominate. Considering the total inductance, a quantity which actually is probed in typical intermodulation experiments, we show that the crossover from bulk dominated behavior to surface dominated behavior occurs at a comparatively high temperature. Also at this point the nonlinear coefficient changes the sign. Such temperatures are readily available in intermodulation experiments and make them a tool to study surface ABSs. Furthermore, in order to check the validity of the numerical calculations and obtain a physical understanding of the results, we present a model to solve the problem analytically.

Author

• Zare, Aida

Identifier

hdl:10900/49641

OAI record oai:identifier

https://publikationen.uni-tuebingen.de/oai/request?verb=GetRecord&metadataPrefix=mets&identifier=oai%3Apublikationen.uni-tuebingen.de%3A10900%2F49641