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The wave nature of conducting electrons in solids can be revealed through interference effects. In layered materials, these effects are most often seen in in-plane transport. By contrast, Putzke et al. studied electronic transport perpendicular to the conductive layers in the ultraclean delafossites PdCoO2 and PtCoO2. When an in-plane magnetic field was applied, the electrical resistance exhibited periodic oscillations as a function of field magnitude. The findings can be explained through a model that requires that the electronic waves remain coherent over macroscopic distances.Science, this issue p. 1234Microstructures can be carefully designed to reveal the quantum phase of the wave-like nature of electrons in a metal. Here, we report phase-coherent oscillations of out-of-plane magnetoresistance in the layered delafossites PdCoO2 and PtCoO2. The oscillation period is equivalent to that determined by the magnetic flux quantum, h/e, threading an area defined by the atomic interlayer separation and the sample width, where h is Planck’s constant and e is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10 micrometers and persisting up to temperatures of T gt; 50 kelvin. We show that the experimental signal stems from a periodic field modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in delafossites.
