Investigation of Planckian behavior in a high-conductivity oxide: PdCrO2.

The layered delafossite metal PdCrO[Formula: see text] is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO[Formula: see text] layers. At high temperatures, T, it has a T-linear resistivity which is not seen in the isostructural but nonmagnetic PdCoO[Formula: see text]. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate "Planckian metal" physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio, and studying the sources of its high-temperature entropy. The T-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10[Formula: see text] of the Planckian value of k[Formula: see text]T/[Formula: see text].

Low-symmetry nonlocal transport in microstructured squares of delafossite metals.

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, additional 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 nonintuitive at first sight, we show that they can be understood within a nonlocal Landauer-Büttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of nonlocal transport can be resolved for squares of linear dimension of nearly 100 µm, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated.

Directional ballistic transport in the two-dimensional metal PdCoO2.

In an idealized infinite crystal, the material properties are constrained by the symmetries of the unit cell. The point-group symmetry is broken by the sample shape of any finite crystal, but this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from an anisotropic Fermi surface are needed. Here we show how a strongly facetted Fermi surface and the long quasiparticle mean free path present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. We fabricate bar-shaped transport devices narrower than the mean free path from single crystals using focused ion beam milling, such that the ballistic charge carriers at low temperatures frequently collide with both of the side walls that define the channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and a transverse voltage appears in zero magnetic field. Using ballistic Monte Carlo simulations and a numerical solution of the Boltzmann equation, we identify the orientation of the narrow channel as the source of symmetry breaking.

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 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.

Granular segregation in a thin drum rotating with periodic modulation.

We present the results of an experimental investigation into the effects of a sinusoidal modulation of the rotation rate on the segregation patterns formed in thin drum of granular material. The modulation transforms the base pattern formed under steady conditions by splitting or merging the initial streaks. Specifically, the relation between the frequency of modulation and the rotation rate determines the number of streaks which develop from the base state. The results are in accord with those of Fiedor and Ottino [J. Fluid. Mech. 533, 223 (2005)10.1017/S0022112005003952], and we show that their ideas apply over a wide range of parameter space. Furthermore, we provide evidence that the observed relationship is maintained for filling fractions far from 50% and generalize the result in terms of the geometry of the granular deposit.