Recently the doping of topological insulators has attracted significant interest as a potential route towards topological superconductivity. Because many experimental techniques lack sufficient surface sensitivity, however, a definite proof of the coexistence of topological surface states and surface superconductivity is still outstanding. Here we report on highly surface sensitive scanning tunneling microscopy (STM) and spectroscopy (STS) experiments performed on Tl-doped Bi$_2$Te$_3$, a three-dimensional topological insulator which becomes superconducting in the bulk at $T_{rm C} = 2.3$,K. Landau level spectroscopy as well as quasiparticle interference mapping clearly demonstrated the presence of a topological surface state with a Dirac point energy $E_{textrm{D}} = -(118 pm 1)$,meV and a Dirac velocity $v_{textrm{D}} = (4.7 pm 0.1)cdot 10^{5}$,m/s. Tunneling spectra often show a superconducting gap, but temperature- and field-dependent measurements show that both $T_{rm C}$ and $mu_0 H_{rm C}$ strongly deviate from the corresponding bulk values. Furthermore, in spite of acritical field value which clearly points to type-II superconductivity, no Abrikosov lattice could be observed. Experiments performed on normal-metallic Ag(111) prove that the gapped spectrum is only caused by superconducting tips, probably caused by a gentle crash with the sample surface during approach. Nearly identical results were found for the intrinsically n-type compound Nb-doped Bi$_2$Se$_3$. Our results suggest that the superconductivity in superconducting-doped V-VI topological insulators does not extend to the surface where the topological surface state is located.
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