Abstract
Particle–wave duality suggests we think of electrons as waves stretched
across a sample, with wavevector k proportional to their momentum.
Their arrangement in 'k-space', and in particular the shape of the
Fermi surface, where the highest-energy electrons of the system reside,
determine many material properties. Here we use a novel extension
of Fourier-transform scanning tunnelling microscopy to probe the
Fermi surface of the strongly inhomogeneous Bi-based cuprate superconductors.
Surprisingly, we find that, rather than being globally defined, the
Fermi surface changes on nanometre length scales. Just as shifting
tide lines expose variations of water height, changing Fermi surfaces
indicate strong local doping variations. This discovery, unprecedented
in any material, paves the way for an understanding of other inhomogeneous
characteristics of the cuprates, such as the pseudogap magnitude,
and highlights a new approach to the study of nanoscale inhomogeneity
in general.
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