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We report the observation of quantum Hall effect (QHE) in a Bi$_2$Se$_3$single crystal having carrier concentration ($n$)$\sim1.13\times10^{19}$cm$^{-3}$, three dimensional Fermi surface and bulktransport characteristics. The plateaus in Hall resistivity coincide withminima of Shubnikov de Haas oscillations in resistivity. Our resultsdemonstrate that the presence of perfect two dimensional transport is not anessential condition for QHE in Bi$_2$Se$_3$. The results of high resolutionx-ray diffraction (HRXRD), energy-dispersive x-ray spectroscopy (EDX), andresidual resistivity measurements show the presence of enhanced crystallinedefects and microstrain. We propose that the formation of localized state atthe edge of each Landau level due to resonance between the bulk and defect bandof Bi$_2$Se$_3$ causes the quantum Hall effect.

Observation of quantum Hall effect in a microstrained Bi$_2$Se$_3$ single crystal