Quantum oscillations in a confined electron gas

Abstract

When metals are structured on nanometre length scales, their electrons are subject to confinement effects: the response of a confined electron gas is governed by Friedel oscillations¹ of the electron density and Rudermann–Kittel–Kasuya–Yosida oscillations² of the spin density. Spatial oscillations of electron density have been observed directly at surfaces (in the vicinity of defects and steps) by scanning tunnelling spectroscopy^3,4. But it has proved more difficult to probe such oscillations in bulk materials and over large distances⁵. Here we report the detection of quantum oscillations in a three-dimensional electron gas confined to a half space by a surface. To facilitate this detection, we have inserted an atomically thin ferromagnetic cobalt film at a variable distance τ from the surface of a copper single crystal. The cobalt film induces⁵ a total spin polarization P in the conduction electrons of the copper and, by virtue of the confining effects of the copper–vacuum interface, P varies as a function of τ. Our measurements of P reveal both quantum oscillations (the wavelengths of which are governed by the extremal diameters of the copper Fermi surface) and a decay with τ that are consistent with theoretical expectations². These observations show that a consequence of improving the quality of nanostructured materials is that long-range quantum interactions can emerge more effectively, so that even distant boundaries and defects can become pivotal in determining physical properties.