h/e Oscillations in Interlayer Transport of Delafossites

Microstructures 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 the out-of-plane magnetoresistance in the layered delafossites PdCoO₂ and PtCoO₂. The oscillation period is equivalent to that determined by the magnetic flux quantum, <em>h/e</em>, threading an area defined by the atomic interlayer separation and the sample width; here <em>h</em> is Planck’s constant and <em>e</em> is the charge of an electron. The phase of the electron wave function appears robust over length scales exceeding 10mm and persisting up to temperatures of T&gt;50K. 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 the delafossites.