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The Anderson transition of Bogoliubov-de Gennes (BdG) quasiparticles insuperconducting state has been studied theoretically for last three decades.However, its experimental proof is lacking. In particular, the relationship ofthe superconducting order-parameter fluctuations and the Anderson transition ofBdG quasiparticles have not been well understood. Our study, based on scanningtunneling microscopy measurements, investigates how BdG quasiparticles becomeAnderson-localized and delocalized as a function of energy and applied magneticfield in a quasi-two-dimensional Fe-based superconductor with sufficientzero-bias BdG quasiparticles. The anomalous multifractal spectra based on thespatial distributions of the pairing gaps and the coherent peak heights suggestthat superconducting fluctuations play a key role in the delocalization ofin-gap BdG quasiparticles. Our real-space Hartree-Fock-BCS-Anderson simulationsand renormalization group analysis with pairing fluctuations supportquasiparticle localization and suggest that enhanced pairing fluctuations leadto delocalization of BdG quasiparticles and "weak localization" ofphase-fluctuating Cooper pairs in quasi-two-dimensional disorderedsuperconductors. The present study proposes that the 10-fold way classificationscheme has to be generalized to take order-parameter fluctuations in actualquantum matter. Also, it shed light on how ac energy loss due to quasiparticlesat Fermi level can be controlled in a quasi-2d superconductor with sufficientpairing fluctuation.

Anderson transition of in-gap quasiparticles in a quasi-two-dimensional disordered superconductor