In an idealized infinite crystal, the material properties are constrained by the symmetries of its unit cell. Naturally, the point-group symmetry is broken by the sample shape of any finite crystal, yet this is commonly unobservable in macroscopic me
tals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from anisotropic Fermi surfaces are needed. Here we show how strongly facetted Fermi surfaces and long quasiparticle mean free paths present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. Bar shaped transport devices narrower than the mean free path are carved from single crystals using focused ion beam (FIB) milling, such that the ballistic charge carriers at low temperatures frequently collide with both sidewalls defining a channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and transverse voltages appear in zero magnetic field. We robustly identify the channel direction as the source of symmetry breaking via ballistic Monte- Carlo simulations and numerical solution of the Boltzmann equation.
We have previously reported ferromagnetism evinced by a large hysteretic anomalous Hall effect in twisted bilayer graphene (tBLG). Subsequent measurements of a quantized Hall resistance and small longitudinal resistance confirmed that this magnetic s
tate is a Chern insulator. Here we report that, when tilting the sample in an external magnetic field, the ferromagnetism is highly anisotropic. Because spin-orbit coupling is negligible in graphene such anisotropy is unlikely to come from spin, but rather favors theories in which the ferromagnetism is orbital. We know of no other case in which ferromagnetism has a purely orbital origin. For an applied in-plane field larger than $5 mathrm{T}$, the out-of-plane magnetization is destroyed, suggesting a transition to a new phase.
Geometric electron optics may be implemented in solid state when transport is ballistic on the length scale of a device. Currently, this is realized mainly in 2D materials characterized by circular Fermi surfaces. Here we demonstrate that the nearly
perfectly hexagonal Fermi surface of PdCoO2 gives rise to highly directional ballistic transport. We probe this directional ballistic regime in a single crystal of PdCoO2 by use of focused ion beam (FIB) micro-machining, defining crystalline ballistic circuits with features as small as 250nm. The peculiar hexagonal Fermi surface naturally leads to electron self-focusing effects in a magnetic field, well below the geometric limit associated with a circular Fermi surface. This super-geometric focusing can be quantitatively predicted for arbitrary device geometry, based on the hexagonal cyclotron orbits appearing in this material. These results suggest a novel class of ballistic electronic devices exploiting the unique transport characteristics of strongly faceted Fermi surfaces.
When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here we present evidence that near three-quarters ($3/4$) filling of the conduc
tion miniband these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. We observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect as large as $10.4 mathrm{kOmega}$ and signs of chiral edge states in a narrow density range around an apparent insulating state at $3/4$. Surprisingly, the magnetization of the sample can be reversed by applying a small DC current. Although the AH resistance is not quantized and dissipation is significant, we suggest that the system is an incipient Chern insulator.
Ballistic electrons in solids can have mean free paths far larger than the smallest features patterned by lithography. This has allowed development and study of solid-state electron-optical devices such as beam splitters and quantum point contacts, w
hich have informed our understanding of electron flow and interactions. Recently, high-mobility graphene has emerged as an ideal two-dimensional semimetal that hosts unique chiral electron-optical effects due to its honeycomb crystalline lattice. However, this chiral transport prevents simple use of electrostatic gates to define electron-optical devices in graphene. Here, we present a method of creating highly-collimated electron beams in graphene based on collinear pairs of slits, with absorptive sidewalls between the slits. By this method, we achieve beams with angular width 18 degrees or narrower, and transmission matching semiclassical predictions.
