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Intense work studying the ballistic regime of electron transport in two dimensional systems based on semiconductors and graphene had been thought to have established most of the key experimental facts of the field. In recent years, however, new forms of ballistic transport have become accessible in the quasi-two-dimensional delafossite metals, whose Fermi wavelength is a factor of 100 shorter than those typically studied in the previous work, and whose Fermi surfaces are nearly hexagonal in shape, and therefore strongly faceted. This has some profound consequences for results obtained from the classic ballistic transport experiment of studying bend and Hall resistances in mesoscopic squares fabricated from delafossite single crystals. We observe pronounced anisotropies in bend resistances and even a Hall voltage that is strongly asymmetric in magnetic field. Although some of our observations are non-intuitive at first sight, we show that they can be understood within a non-local Landauer-B\"uttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of non-local transport can be resolved for squares of linear dimension of nearly 100 $\mu$m, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated., Comment: 23 pages, 9 figures (including supplementary information)

Funding: This project was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant no. 715730, MiTopMat) and also was supported by the Max Planck Society. A.P.M. and R.M. acknowledge support from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147). M.D.B., P.M., and V.S. acknowledge studentship funding from the EPSRC under grant no. EP/L015110/1. A.S. was supported by the Israel Science Foundation, the European Research Council (Project LEGOTOP), and the DFG through projectno.CRC-183. M.K. acknowledges support from the SIRIUS irradiation facility through project no. EMIR 2019 18-7099. 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. Postprint

The delafossite metals PdCoO2, PtCoO2, and PdCrO2 are among the highest conductivity materials known, with low-temperature mean free paths of tens of microns in the best as-grown single crystals. A key question is whether these very low resistive scattering rates result from strongly suppressed backscattering due to special features of the electronic structure or are a consequence of highly unusual levels of crystalline perfection. We report the results of experiments in which high-energy electron irradiation was used to introduce point disorder to the Pd and Pt layers in which the conduction occurs. We obtain the cross section for formation of Frenkel pairs in absolute units, and cross-check our analysis with first-principles calculations of the relevant atomic displacement energies. We observe an increase of resistivity that is linear in defect density with a slope consistent with scattering in the unitary limit. Our results enable us to deduce that the as-grown crystals contain extremely low levels of in-plane defects of approximately 0.001%. This confirms that crystalline perfection is the most important factor in realizing the long mean free paths and highlights how unusual these delafossite metals are in comparison with the vast majority of other multicomponent oxides and alloys. We discuss the implications of our findings for future materials research.