Suppression of Andreev conductance in a topological insulator-superconductor nanostep junction

When two three-dimensional topological insulators (TIs) are brought close to each other with their surfaces aligned, the surfaces form a line junction. Similarly, three TI surfaces, not lying in a single plane, can form an atomic-scale nanostep junction. In this paper, Andreev reflection in a TI-TI-superconductor nanostep junction is investigated theoretically. Because of the existence of edge states along each line junction, the conductance for a nanostep junction is suppressed. When the incident energy (ε) of an electron is larger than the superconductor gap (Δ), the Andreev conductance in a step junction is less than unity while for a plane junction it is unity. The Andreev conductance is found to depend on the height of the step junction. The Andreev conductance exhibits oscillatory behavior as a function of the junction height with the amplitude of the oscillations remaining unchanged when ε=0, but decreasing for ε=Δ, which is different from the case of the plane junction. The height of the step is therefore an important parameter for Andreev reflection in nanostep junctions, and plays a role similar to that of the delta potential barrier in normal metal-superconductor plane junctions.