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Transport of electrons in a bulk metal is usually well captured by theirparticle-like aspects, while their wave-like nature is commonly harder toobserve. Microstructures can be are fully designed to reveal the quantum phase,for example mesoscopic metal rings resembling interferometers. Here we report anew type of phase coherent oscillation of the out-of-plane magnetoresistance inthe layered delafossites PdCoO$_2$ and PtCoO$_2$. The oscillation period isequivalent to that determined by the magnetic flux quantum, $h/e$, threading anarea defined by the atomic interlayer separation and the sample width. Thephase of the electron wave function in these crystals appears remarkably robustover macroscopic length scales exceeding 10$\mu$m and persisting up to elevatedtemperatures of $T$>50K. We show that, while the experimental signal cannot beexplained in a standard Aharonov-Bohm analysis, it arises due to periodicfield-modulation of the out-of-plane hopping. These results demonstrateextraordinary single-particle quantum coherence lengths in the delafossites,and identify a new form of quantum interference in solids.

$h/e$ Oscillations in Interlayer Transport of Delafossites