Magnetic field response of an STM tip containing artificial holes

Within the framework of three-dimensional (3D) Ginzburg–Landau (GL) formalism, the magnetic response of a nanoscale conical superconducting scanning tunneling microscope (STM) tip containing artificial holes is studied. Cuboid holes are pierced parallel to the axis of the cone, and their number and size are varied while the dimensions of the tip, the temperature, and the GL parameter are kept constant. The vortex configurations are identified from isosurface plots of the order parameter, its phase, the Cooper-pair density, and the supercurrent density. It is found that the holes lower the vortex entry field and that their ability to pin flux increases with size: a large hole accommodates a quantum of vorticity, whereas a small hole only guides the vortices, whose cores remain in the superconducting region. Increasing the number of holes removes low-vorticity states from the stable sequence, enhances the surface critical field, and sustains the diamagnetic response up to higher magnetic fields. The results show how artificial defects can be used to control vortex matter in superconducting tips employed in scanning tunneling microscopy.