  At an interface between a topological insulator (TI) and a conventional
superconductor (SC), superconductivity has been predicted to change
dramatically and exhibit novel correlations. In particular, the induced
superconductivity by an $s$-wave SC in a TI can develop an order parameter with
a $p$-wave component. Here we present experimental evidence for an unexpected
proximity-induced novel superconducting state in a thin layer of the
prototypical TI, Bi$_2$Se$_3$, proximity coupled to Nb. From depth-resolved
magnetic field measurements below the superconducting transition temperature of
Nb, we observe a local enhancement of the magnetic field in Bi$_2$Se$_3$ that
exceeds the externally applied field, thus supporting the existence of an
intrinsic paramagnetic Meissner effect arising from an odd-frequency
superconducting state. Our experimental results are complemented by theoretical
calculations supporting the appearance of such a component at the interface
which extends into the TI. This state is topologically distinct from the
conventional Bardeen-Cooper-Schrieffer state it originates from. To the best of
our knowledge, these findings present a first observation of bulk odd-frequency
superconductivity in a TI. We thus reaffirm the potential of the TI-SC
interface as a versatile platform to produce novel superconducting states.
