In a quantum fluid without an associated lattice, such as ! He, the momentum of the fluid is conserved except where it interacts with the walls of a channel through which it is flowing. As the temperature decreases and the quasiparticle--quasiparticle mean free path within the fluid increases because of the decrease of its quasiparticle scattering rate, interactions with the walls become more probable, and the viscosity and flow resistance increase. This is intuitively at odds with the behavior seen for electrons moving in a crystalline lattice, whose flow resistance decreases as increases. The resolution of this apparent paradox is that coupling to the lattice and its excitations means that the large majority of collisions in the electron fluid (electron--impurity, normal electron--phonon, Umklapp electron--electron and Umklapp electron--phonon) relax momentum, taking the fluid far from the hydrodynamic limit. At least some of these momentum--relaxing collisions are inevitable in any real material. Strictly speaking, momentum of the electron fluid can never be conserved, even in a bulk sample for which boundary scattering is insignificant. This does not, however, mean that the electronic viscosity needs to play no role in determining electrical resistance. A pragmatic benchmark is whether momentum--conserving processes are faster or slower than momentum--relaxing ones. If the electron fluid's momentum is relaxed slowly, it can be thought of as being quasi--conserved, and hydrodynamic signatures might be observable (1--9).The search for hydrodynamic effects in electrons in solids has been given extra impetus by the introduction of the "holographic correspondence" to condensed matter physics (10).This technique introduced the concept of a minimum viscosity, argued to be applicable to strongly interacting fluids as diverse as the quark--gluon plasma and cold atomic gases (11). 3Hydrodynamic effects have also been postulated to be at the root of the T--linear resistivity of the high temperature superconductors (6, 7), but because momentum--relaxing scattering is strong in those materials, it is difficult to perform an analysis of the experimental data that unambiguously separates the two effects. In a pioneering experiment, unusual current--voltage relationships in a semiconductor wire were convincingly ascribed to hydrodynamic effects (3), but that avenue of research has not been widely pursued, even though the large difference between transport and electron--electron scattering rates in semiconductors was subsequently demonstrated by direct non--equilibrium measurements (12).Here we sought to identify a material in which momentum--relaxing scattering is anomalously suppressed in order to investigate whether a hydrodynamic contribution to electrical transport could be clearly separated from the more standard contributions from momentum--relaxing processes. The material that we chose was PdCoO ! , a layered metal with a series of unusual properties (13--21). Its electronic structure is deceptively simple, with one ...

The dispersion of charge carriers in a metal is distinctly different from that of free electrons due to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics 1-3 , and they can twist the quantum phase of electrons into topologically nontrivial knots -producing protected surface states with anomalous electromagnetic properties 4-9 . In contrast to conventional cyclotron orbits, this motion is driven by the transfer of chirality from one Weyl node to another, rather than momentum transfer of the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application. These effects intertwine in materials known asThe bulk electrons in topological semimetals are described by an ultra-relativistic dispersion relation, E(k)=±ħv F σ*k, resembling the Weyl equation for massless spin-1/2 particles. Here σ is a pseudo-spin-1/2 degree of freedom that is energetically locked parallel or anti-parallel to the momentum, k, of the electron, giving electrons definite chirality k ±σ. Applying electromagnetic fields to Weyl or Dirac semimetals induces a pumping of electric charge between Weyl nodes with opposite chirality, a phenomena known in high energy physics as the chiral anomaly [13][14][15] . At the surface of these materials, this anomalous chirality transfer is facilitated by topologically protected surface arcs, the so-called "Fermi arc" surface states, which act as a pipeline connecting opposite chirality Weyl points 11,16 (Fig.1) weaves together the chiral states in the bulk with the topological Fermi-arc states on opposite surfaces into a closed orbit. Its quantization produces a distinctive contribution to the quantum oscillation spectrum that provides an observable signature of the chiral and topological character of these materials. This closed orbit is strikingly different from typical electrons orbiting around a Fermi surface in a metal as the quasiparticle experiences zero Lorentz force on the chiral path segments traversing the bulk.The main result of this study is an additional quantum oscillation frequency observed in microstructures smaller than the mean-free-path that exhibits characteristics of both surface-like and bulk-like states, as naturally expected for Weyl orbits. The microstructures were prepared from Cd 3 As 2 single crystals by FIB etching (Fig.1, see Methods). Down to the smallest thickness of L=150nm, the magnetoresistance at temperatures below 100K shows pronounced Shubnikovde Haas oscillations signaling the low effective mass of the charge carriers and the high crystal quality of the devices (Fig.1b). Quantum oscillations on bulk crystals have reported one single frequency 19,26 , arising from an essentially spherical 3D Fermi surface in agreement with ARPES and STM experiments. This single bulk frequency (F B ) is also consistently observed in all of the studied parent ...