Many properties of metals, semiconductors and superconductors are determined by the shape of their Fermi surface — the surface in momentum space that separates filled electron states from unfilled states at absolute zero temperature. In superconductors, a detailed knowledge of the Fermi surface is essential for an understanding of their physical properties, including their ability to conduct electricity with resistance. However, most techniques for measuring the Fermi surface of superconductors only produce spatially averaged data, rather than information on how the surface changes on nanometre length scales.

In recent years a number of groups have used scanning tunnelling microscopy (STM) to study the properties of high-temperature cuprate superconductors in greater detail, including spatial variations in the superconducting energy gap and the influence of dopant atoms. Now, Eric Hudson and colleagues at MIT, Nagoya University and the Brookhaven National Laboratory have extended a technique called Fourier-transform STM to image variations in the Fermi surface of bismuth-based cuprate superconductors at the nanoscale (Nature Phys. 5, 213–216; 2009).

STM can be used to measure the local density of states for electrons — which is related to conductance — as a function of energy and position in two dimensions. These maps can then be Fourier transformed to learn more about the Fermi surface. Hudson and co-workers found that the Fermi surface changes on the nanoscale, as these images of the conductance (left) and energy gap (right) show. Each image is 60 nm across; red corresponds to a high conductance and a small gap. The nanoscale variations in the Fermi surface are thought to be due to variations in the distribution of dopants in the superconductor.