  Recently, the niobium (Nb)-doped topological insulator Bi_2Se_3, in which the
finite magnetic moments of the Nb atoms are intercalated in the van der Waals
gap between the Bi_2Se_3 layers, has been shown to exhibit both
superconductivity with T_c = 3 K and topological surface states. Here we report
on muon spin rotation experiments probing the temperature-dependent of
effective magnetic penetration depth Lambda_eff(T) in the layered topological
superconductor candidate Nb_0.25Bi_2Se_3. The exponential temperature
dependence of lambda_(eff)^(-2)(T) at low temperatures suggests a fully gapped
superconducting state in the bulk with the superconducting transition
temperature T_c = 2.9 K and the gap to T_c ratio 2Delta/k_BT_c = 3.95(19). We
also revealed that the ratio T_c/lambda_(eff)^(-2) is comparable to those of
unconventional superconductors, which hints at an unconventional pairing
mechanism. Furthermore, time reversal symmetry breaking was excluded in the
superconducting state with sensitive zero-field muSR experiments. We hope the
present results will stimulate theoretical investigations to obtain a
microscopic understanding of the relation between superconductivity and the
topologically non-trivial electronic structure of Nb_0.25Bi_2Se_3.
