Unconventional Superconductivity
Cryogenic magnetic microscopy is a very valuable tool in the study of unconventional superconductors (see Kirtley, Fundamental studies of superconductors using scanning magnetic imaging, Reports on Progress in Physics, 2010).
Scanning SQUID magnetometry and susceptometry have helped to elucidate the pairing symmetry in the high-Tc superconductor YBCO [1, 2], place limits on spin-charge separation in high-Tc superconductors [3, 4], place limits on time-reversal symmetry breaking in unconventional superconductors [5, 6], and perform local measurements of diamagnetic susceptibility and critical temperature [7, 8, 9, 10, 11, 12, 13, 14].

Spatially modulated critical temperature in doped strontium titanate. Phys. Rev. B 94, 174516 (2016). 
Spatially modulated diamagnetic susceptibility in thin film LBCO. Phys. Rev. B 98, 014506 (2018). 
Inhomogeneous critical temperature in strontium ruthenate. Phys. Rev. B 98, 094521 (2018). 
Modulated superfluid density in an iron-pnictide superconductor. Phys. Rev. B 81, 184513 (2010). 
Inhomogeneous diamagnetic susceptibility in twinned YBCO near Tc.
