Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5\mathrm{/}2$

Under hydrostatic pressure, the ground state of a two-dimensional electron gas at $\nu =5\mathrm{/}2$ changes from a fractional quantum Hall state to the stripe phase. By measuring the energy gap of the fractional quantum Hall state and of the onset temperature of the stripe phase we mapped out a phase diagram of these competing phases in the pressure-temperature plane. Our data highlight the dichotomy of two descriptions of the half-filled Landau level near the quantum critical point: one based on electrons and another on composite fermions.