We study superconducting microtraps with rectangular shapes for cold atomic gases. We present a general argument why microtraps open if brought close to the surface of the superconductor. We show that for a given width of the strips there exists an optimal thickness under which the closest distance of the microtrap from the superconductor can be achieved. The distance can be significantly improved if the edge enhancement of the supercurrent near edges and corners is exploited. We compare the numerical calculations with results from conformal mapping and show that conformal mapping can often give useful approximate results.

We study the influence of self-consistent Born impurity scattering on the zero-energy Andreev bound states near the surface of a d-wave superconductor with and without an externally applied magnetic field. Without an external magnetic field we show that the effect of Born impurity scattering is stronger at the surface than in the bulk. In the presence of an external magnetic field the splitting of the zero-energy Andreev bound states is shown to have a nonmonotonous temperature dependence. Born impurity scattering does not wash out the peak splitting, but instead the peak splitting is shown to be quite robust against impurities. We also show that a nonzero renormalization of the pair potential appears near the surface.

We show that massive low energy particles traversing a branching zone or a crossing of quantum waveguides may experience a non standard trapping force that cannot be derived from a potential. For interacting cold Bose atoms we report on the formation of a localised Hartree ground state for three prototype waveguide geometries with broken translational symmetry: a cranked L-shaped waveguide L, a T -shaped waveguide T , and the crossing C of two quantum waveguides. The phenomenon is kinetic energy driven and cannot be described within the Thomas-Fermi approximation. Depending on the ratio κ (Γ) of joining lateral tube diameters of the respective waveguides Γ ∈ {C, L, T } delocalisation commences when the particle number N approaches a critical value N (Γ) c . For the case of a binary mixture of two different Bose atom species A and B we observe non standard trapping of both atom species for subcritical particle numbers. A sudden demixing quantum transition takes place as the total particle number N = NA + NB is increased at fixed mixing ratio NA/NB. Depending on the mass ratio mA/mB the heavier atom species delocalises first for a wide range of interaction parameters. The numerical calculations are based on a splitting scheme involving an analytic approximation to the short time asymptotics of the imaginary time quantum propagator of a single particle obeying to Dirichlet boundary conditions at the walls inside the respective waveguides.