Higher harmonics of quantum oscillations uncover Dirac Fermons in LaRhIn₅

Quantum oscillations are commonly used to experimentally diagnose the band topology of a semimetal. When the cyclotron orbit encloses a topological defect, it is often presumed that the nontrivial Berry phase results in a π-phase shift of the fundamental harmonic. However, this presumption neglects how spin-orbit coupling renders the Berry phase a continuously varying quantity, and ignores the Zeeman interaction with the spin-orbit-induced magnetic moment. Here, we overcome these shortcomings and demonstrate how to rigorously identify three-dimensional Dirac fermions from the higher harmonics of quantum oscillations. Applying this method to the intermetallic LaRhIn₅, we unambiguously identify the nontrivial Berry phase of a topological Fermi pocket with a small frequency ≈ 7T, despite the presence of large, trivial Fermi pockets which dominate transport by orders of magnitude. Our analysis identifies LaRhIn₅ as a 3D Dirac-point metal, revising a previous proposal of LaRhIn₅ as a nodal-line semimetal by Mikitik et. al. [Phys. Rev. Lett. 93, 106403 (2004)]. The electronic similarity of LaRhIn₅ to the prototypical heavy-fermion superconductors Ce(Co,Rh,Ir)In₅ further suggests them as prime candidates for strongly-correlated Dirac systems.