In the newly discovered magnetic topological insulator MnBi$_2$Te$_4$, both axion insulator state and quantized anomalous Hall effect (QAHE) have been observed by tuning the magnetic structure. The related (MnBi$_2$Te$_4$)$_m$(Bi$_2$Te$_3$)$_n$ heterostructures with increased tuning knobs, are predicted to be a more versatile platform for exotic topological states. Here, we report angle-resolved photoemission spectroscopy (ARPES) studies on a series of the heterostructures (MnBi$_2$Te$_4$, MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$). A universal gapless Dirac cone is observed at the MnBi$_2$Te$_4$ terminated (0001) surfaces in all systems. This is in sharp contrast to the expected gap from the original antiferromagnetic ground state, indicating an altered magnetic structure near the surface, possibly due to the surface termination. In the meantime, the electron band dispersion of the surface states, presumably dominated by the top surface, is found to be sensitive to different stackings of the underlying MnBi$_2$Te$_4$ and Bi$_2$Te$_3$ layers. Our results suggest the high tunability of both magnetic and electronic structures of the topological surface states in (MnBi$_2$Te$_4$)$_m$(Bi$_2$Te$_3$)$_n$ heterostructures, which is essential in realizing various novel topological states.
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