Probing the shape of the Weyl Fermi surface of NbP using transverse electron focusing

The topology of the Fermi surface significantly influences the transport properties of a material. Firstly measured through quantum oscillation experiments, the Fermi surfaces of crystals are now commonly characterized using angle-resolved photoemission spectroscopy (ARPES), given the larger information volume it provides. In the case of Weyl semimetals, ARPES has proven remarkably successful in verifying the existence of the Weyl points and the Fermi arcs, which define a Weyl Fermi surface. However, ARPES is limited in resolution, leading to significant uncertainty when measuring relevant features such as the distance between the Weyl points. While quantum oscillation measurements offer higher resolution, they do not reveal insights into the cross-sectional shape of a Fermi surface. Moreover, both techniques lack critical information about transport, like the carriers mean free path. Here, we report measurements unveiling the distinctive peanut-shaped cross-section of the Fermi surface of Weyl fermions and accurately determine the separation between Weyl points in the Weyl semimetal NbP. To surpass the resolution of ARPES, we combine quantum oscillation measurements with transverse electron focusing (TEF) experiments, conducted on microstructured single-crystals. The TEF spectrum relates to the Fermi surface shape, while the frequency of the quantum oscillations to its area. Together, these techniques offer complementary information, enabling the reconstruction of the distinctive Weyl Fermi surface geometry. Concurrently, we extract the electrical transport properties of the bulk Weyl fermions. Our work showcases the integration of quantum oscillations and transverse electron focusing in a singular experiment, allowing for the measurements of complex Fermi surface geometries in high-mobility quantum materials.