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We utilize a combination of vector magnetic field and scanning tunnelingmicroscopy to elucidate the 3D field-based electronic phase diagram of acorrelated iron-based superconductor, LiFeAs. We observe, under azero-field-cooled method, an ordered hexagonal vortex lattice ground-state incontrast to the disordered lattice observed under a field-cooled method. Ittransforms into a four-fold-symmetric state by increasing c-axis field anddistorts elliptically upon tilting the field in-plane. The vortex latticetransformations correlate with the field dependent superconducting gap thatcharacterizes the Cooper pairing strength. The anisotropy of the vortex latticeagrees with the field enhanced Bogoliubov quasiparticle scattering channel thatis determined by the pairing symmetry with respect to its Fermi surfacestructure. Our systematic tuning of the vortex lattice symmetry and study ofits correlation with Cooper pairing demonstrates the many-body interplaybetween the superconducting order parameter and emergent vortex matter.

Vector field controlled vortex lattice symmetry in LiFeAs