Topological Fermiology of gate-tunable Rashba electron gases.

By introducing first-order quantum phases as topological invariants, recent symmetry analysis-based theories have reinvigorated magnetic quantum oscillations as a versatile quantum probe for unfolding the Fermi surface topology along with the geometry information, i.e., topo-Fermiology. Here, we demonstrate the comprehensive topo-Fermiology of high-mobility Rashba two-dimensional electron gases with ultragate tunability of spin-orbit coupling parameter in few-layer black arsenic. The remarkable consistencies with the key theoretical predictions of period doubling in quantum oscillations, gate-tunable aperiodic beating patterns, and the symmetry-enforced Landau level crossing phenomena controlled by the competition between Rashba coupling and the Zeeman interaction, which ultimately manifests as all odd-filling factor integer quantum Hall effect with superb sensitivity to quantum phases, establish topo-Fermiology as an indispensable methodology for studying topological quantum matters.