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Particle-wave duality suggests we think of electrons as waves stretchedacross a sample, with wavevector k proportional to their momentum. Theirarrangement in "k-space," and in particular the shape of the Fermi surface,where the highest energy electrons of the system reside, determine manymaterial properties. Here we use a novel extension of Fourier transformscanning tunneling microscopy to probe the Fermi surface of the stronglyinhomogeneous Bi-based cuprate superconductors. Surprisingly, we find thatrather than being globally defined, the Fermi surface changes on nanometerlength scales. Just as shifting tide lines expose variations of water height,changing Fermi surfaces indicate strong local doping variations. Thisdiscovery, unprecedented in any material, paves the way for an understanding ofother inhomogeneous characteristics of the cuprates, like the pseudogapmagnitude, and highlights a new approach to the study of nanoscaleinhomogeneity in general.

Imaging nanoscale Fermi surface variations in an inhomogeneous superconductor