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h/e oscillations in interlayer transport of delafossites

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Science  12 Jun 2020:
Vol. 368, Issue 6496, pp. 1234-1238
DOI: 10.1126/science.aay8413

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Coherent electronic waves

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. 1234

Abstract

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 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 > 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.

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