Imaging superconducting vortex cores and lattices with a scanning tunneling microscope

The observation of vortices in superconductors was a major breakthrough in developing the conceptual background for superconducting applications. Each vortex carries a flux quantum, and the magnetic field decreases radially from the center. Techniques used to make magnetic field maps, such as magnetic decoration, give vortex lattice images in a variety of systems. However, strong type II superconductors allow penetration of the magnetic field over large distances, of the order of the magnetic penetration depth lambda. Superconductivity survives up to magnetic fields where, for imaging purposes, there is no magnetic contrast at all. Static and dynamic properties of vortices are largely unknown at such high magnetic fields. Reciprocal space studies using neutron scattering have been employed to obtain insight into the collective behavior. But the microscopic details of vortex arrangements and their motion remain difficult to obtain. Direct real-space visualization can be made using scanning tunneling microscopy and spectroscopy (STM/S). Instead of using magnetic contrast, the electronic density of states describes spatial variations of the quasiparticle and pair wavefunction properties. These are of the order of the superconducting coherence length xi, which is much smaller than lambda. In principle, individual vortices can be imaged using STM up to the upper critical field where vortex cores, of size xi, overlap. In this review, we describe recent advances in vortex imaging made with scanning tunneling microscopy and spectroscopy. We introduce the technique and discuss vortex images that reveal the influence of the Fermi surface distribution of the superconducting gap on the internal structure of vortices, the collective behavior of the lattice in different materials and conditions, and the observation of vortex lattice melting. We consider challenging lines of work, which include imaging vortices in nanostructures, multiband and heavy fermion superconductors, single layers and van der Waals crystals, studying current-driven dynamics and the liquid vortex phases.