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Bulk Fermi surface coexistence with Dirac surface state in Bi$_2$Se$_3$: a comparison of photoemission and Shubnikov-de Haas measurements

Shubnikov de Haas (SdH) oscillations and Angle Resolved PhotoEmission Spectroscopy (ARPES) are used to probe the Fermi surface of single crystals of Bi2Se3. We find that SdH and ARPES probes quantitatively agree on measurements of the effective mass and bulk band dispersion. In high carrier density samples, the two probes also agree in the exact position of the Fermi level EF, but for lower carrier density samples discrepancies emerge in the position of EF. In particular, SdH reveals a bulk three-dimensional Fermi surface for samples with carrier densities as low as 10^17cm-3. We suggest a simple mechanism to explain these differences and discuss consequences for existing and future transport studies of topological insulators.