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We study the properties of an anisotropically paired superconductor in the presence of a specularly reflecting surface. The bulk stable phase of the superconducting order parameter is taken to have−y 2 symmetry. Contributions by order parameter components of different symmetries vanish in the bulk, but may enter in the vicinity of a wall. We calculate the self-consistent order parameter and surface free energy within the quasiclassical formulation of superconductivity. We discuss, in particular, the dependence of these quantities on the degree of order parameter mixing and the surface to lattice orientation. Knowledge of the thermodynamically stable order parameter near a surface is a necessary precondition for calculating measurable surface properties which we present in a companion paper.

We present calculations of the tunneling density of states in an anisotropically paired superconductor for two different sample geometries: a semi-infinite system with a single specular wall, and a slab of finite thickness and infinite lateral extent. In both cases we are interested in the effects of surface pair breaking on the tunneling spectrum. We take the stable bulk phase to be of d x 2 −y 2 symmetry. Our calculations are performed within two different band structure environments: an isotropic cylindrical Fermi surface with a bulk order parameter of the form ∆ ∼ k 2x − k 2 y , and a nontrivial tight-binding Fermi surface with the order parameter structure coming from an anti-ferromagnetic spin-fluctuation model. In each case we find additional structures in the energy spectrum coming from the surface layer. These structures are sensitive to the orientation of the surface with respect to the crystal lattice, and have their origins in the detailed form of the momentum and spatial dependence of the order parameter. By means of tunneling spectroscopy, one can obtain information on both the anisotropy of the energy gap, |∆(p)|, as well as on the phase of the order parameter, ∆(p) = |∆(p)|e iϕ(p) .

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%'e use Eilenberger's quasiclassical equations to compute the self-consistent local density of states of an isolated vortex in an extreme type-II superconductor. %e include the contributions from both the scattering states and the bound states and consider a two-dimensional Fermi surface. The local density of states as a function of energy shows a double-peak structure: (a) there is one peak at E =5 at all distances from the vortex core and (b) a second peak at lower energies due to bound states in the core. This low-energy peak appears at successively lower energy as one moves closer to the core, giving rise to the enhancement of the zero-bias differential conductivity at the vortex core reported by Hess et al.