  Here, we theoretically predict that the series of Pb-based layered
chalcogenides, Pb$_n$Bi$_2$Se$_{n+3}$ and Pb$_n$Sb$_2$Te$_{n+3}$, are possible
new candidates for topological insulators. As $n$ increases, the phase
transition from a topological insulator to a band insulator is found to occur
between $n=2$ and 3 for both series. Significantly, among the new topological
insulators, we found a bulk band gap of 0.40eV in PbBi$_2$Se$_4$ which is one
of the largest gap topological insulators, and that Pb$_2$Sb$_2$Te$_5$ is
located in the immediate vicinity of the topological phase boundary, making its
topological phase easily tunable by changing external parameters such as
lattice constants. Due to the three-dimensional Dirac cone at the phase
boundary, massless Dirac fermions also may be easily accessible in
Pb$_2$Sb$_2$Te$_5$.
