Quantum-well states in copper thin films

A standard exercise in elementary quantum mechanics is to describe the properties of an electron confined in a potential well. The solutions of Schrödinger's equation are electron standing waves—or ‘quantum-well’ states—characterized by the quantum number n, the number of half-wavelengths that span the well. Quantum-well states can be experimentally realized in a thin film, which confines the motion of the electrons in the direction normal to the film: for layered semiconductor quantum wells, the aforementioned quantization condition provides (with the inclusion of boundary phases) a good description of the quantum-well states. The presence of such states in layered metallic nanostructures isbelieved to underlie many intriguing phenomena, such as the oscillatory magnetic coupling of two ferromagnetic layers across anon-magnetic layer1,2 and giant magnetoresistance3. But our understanding of the properties of the quantum-well states in metallic structures is still limited. Here we report photoemission experiments that reveal the spatial variation of the quantum-well wavefunction within a thin copper film. Our results confirm an earlier proposal4 that the amplitude of electron waves confined in a metallic thin film is modulated by an envelope function (of longer wavelength), which plays a key role in determining the energetics of the quantum-well states.