Mapping Dimensionality and Directionality of Electronic Behavior in CeCoIn$_{5}$: the Superconducting State

Unconventional superconductors often exhibit anisotropic physical properties that arise from the directional dependence of their order parameters. A prime example is CeCoIn$_{5}$, a heavy fermion $d$-wave superconductor with a rich low-temperature phase diagram consisting of competing and coexisting magnetic and superconducting orders. Here we present dilution refrigerator scanning tunneling microscopy of CeCoIn$_{5}$ cleaved perpendicular to its basal plane. We study superconductivity on the (100) surface, whose normal vector points along the antinode of the superconducting energy gap. The gap magnitude is similar to that observed in the basal plane, with a key difference: it does not exhibit any suppression near step edges. Application of a magnetic field along the [100] direction leads to the formation of anisotropic vortices, and the vortex lattice undergoes a transition at high field before the superconducting state gives way to a pseudogap phase. Our measurements illustrate the directional dependence of the superconducting properties in CeCoIn$_{5}$, and more generally, demonstrate the utility of imaging $d$-wave superconductors along their nodal and antinodal directions.