  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.
