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Cu$_x$Bi$_2$Se$_3$ has drawn much attention as the leading candidate to bethe first topological superconductor and the realization of coveted Majoranaparticles in a condensed matter system. However, there has been increasingcontroversy about the nature of its superconducting phase. This study shedslight on present ambiguity in the normal state electronic state, by providing acomplete look at the quantum oscillations in magnetization inCu$_x$Bi$_2$Se$_3$ at intense high fields up to 31T. Our study focuses on theangular dependence of the quantum oscillation pattern in a low carrierconcentration. As magnetic field tilts from along the crystalline c-axis toab-plane, the change of the oscillation period follows the prediction of theellipsoidal Fermi surface. As the doping level changes, the 3D Fermi surface isfound to transform into quasi-cylindrical at high carrier density. Such atransition is potentially a Lifshitz transition of the electronic state inCu$_x$Bi$_2$Se$_3$.

Quantum Oscillations in Cu$_x$Bi$_2$Se$_3$ in High Magnetic Fields