Louis J. Buchholtz

Thermodynamics of a d-wave superconductor near a surface

We study the properties of an anisotropically paired superconductor in the presence of specularly reflecting surface. The bulk stable phase of the superconducting order parameter is taken to have dx2-y2 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.

The effect of surfaces on the tunneling density of states of an anisotropically paired superconductor

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 dx2−y2 symmetry. Our calculations are performed within two different band structure environments: an isotropic cylindrical Fermi surface with a bulk order parameter of the form Δ ∼ kx2−ky2, and a nontrivial tight-binding Fermi surface with the order parameter structure coming from an antiferromagnetic 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, ¦Δ(p)¦, as well as on the phase of the order parameter, Δ(p) = ¦Δ(p)¦ eiϕ(p).

Superfluid3He-B in a realistic thin film. Gap and critical current

We examine3He-B confined to a thin film on a rough substrate with a freestanding upper surface by using quasiclassical techniques. First, the dependence of the gap on surface roughness, film width, and boundary condition formulation is examined in detail for the current-free state. The evaluation is conducted using both the “Randomly Rippled Wall” and the “Thin Dirty Layer” surface models in order to compare them. Second, the current bearing state for a submicron film resting on a rough substrate is calculated using the “Thin Dirty Layer” surface model. Several unusual and previously unreported features appear in both cases. Numerical estimates of the critical current densities are in favorable agreement with corresponding experiments.

Aspects of the Quasiclassical t-Matrix Boundary Condition

We apply the t-matrix boundary conditions of Rainer to study the critical current of superfluid 3He confined to a thin channel between realistic rough surfaces using quasiclassical techniques. Rainers conditions lead directly to a simple, stable and comprehensive algorithm for solving the quasiclassical equations which we present in detail. The conditions yielded physical results in all cases studied and their ease of use permitted an exhaustive search through the phase space of solutions. A robust metastable state appears for narrow channel widths suggesting the possibility of two different critical currents.

Critical current states of superfluid 3He in a realistic channel

Abstract Recent experimental results have motivated renewed studies of superfluid 3He in confined geometries. A novel boundary condition by Rainer (Recent Progress in Many-Body Theories, Vol. 1, Plenum Press, New York, 1988) is applied for the first time to superfluid 3He in such configurations. Our study of the critical current in a thin channel with very diffuse boundaries served as a rigorous test of the boundary condition and verified its physicality in every detail observed. We observed a phase transition from a ‘bulk B phase-like’ to a ‘planar-like’ state for sufficiently narrow channels. This state is, apparently, absolutely stable only for channels thinner than the critical width. Nonetheless, it competed with the expected slab solution at all calculated widths and proved highly metastable.

Tunneling density of states ind-wave superconductors with rough surfaces

We discuss the novel surface states which may occur near a boundary in ad-wave superconductor and how these states are affected by surface diffusivity. The surface roughness is taken into account via the “Randomly Rippled Wall Model”, and all calculations are performed within the quasiclassical theory of superconductivity. We consider a uniaxial system with abulk order parameter ofdx2−y2 symmetry. Our analysis focuses on the emergence of surface states of a symmetry other than that of the stable bulk phase when more than one attractive symmetry channel is present. The conditions for the stability of the various surface states and their impact on the tunneling characteristics are discussed.

3He-B in a realistic thin film: Current on a rough substrate

Abstract We calculate the supercurrent of B-phase superfluid3He confined to a film of thickness .3μ and resting on a highly diffuse substrate with a freestanding upper surface. We observe two distinct critical currents. The first critical current coincides with the abrupt vanishing of the gap component parallel to the direction of flow. The system retains global phase stability up to a second and final critical current. Comparison with results computed in the limit of a specular substrate shows crucial differences.

3He-B in a thin film: A comparison of boundary conditions

Abstract We calculate the gap function of stationary B-phase 3 He confined to a thin film and resting on a diffuse substrate with a freestanding upper surface. We employ two different formulations of the boundary conditions describing rough walls and compute the gap for various widths and surface roughnesses. Both formulations predict the abrupt vanishing of the perpendicular gap component at a width of about 2.5 coherence lengths irrespective of surface diffusivity. The parallel gap component persists down to a much smaller width which is quite roughness sensitive.

Superfluid 3HeB in a realistic thin film: Gap function

Abstract This paper reports a calculation of superfluid in a planar film with one diffusely reflecting surface and a facing specular surface. The intent of this work is to demonstrate the use of the nonlinear Quasiclassical boundary conditions in a fully selfconsistent calculation of the superfluid gap function for a realistic anduseful geometry. The diffusely scattering boundary surface was represented by the versatile “RandomlyRippledWall” model. We display results for various surface qualities and film thicknesses.

Superfluid 3He B at a rough surface: Density of states

Abstract The density of states for 3.5. Superfluid 3 He  Bat a rough wall is calculated from the quasiclassical equations using the full nonlinear boundary conditions and the “Randomly Rippled Wall” model. Increased surface roughness leads to a substantially enhanced total density of states at sub gap energies as well as to a more complicated spectrum structure. The calculation provides a sensitive test of boundary condition validity and demonstrates the ready applicability of the nonlinear boundary conditions.