Using first-principles calculations, we show that topological quantum phase transitions are driven by external electric fields in thin films of Sb 2 Te 3 . The film, as the applied electric field normal to its surface increases, is transformed from a normal insulator to a topological insulator or vice versa depending on the film thickness. We identify the band topology by directly calculating the Z 2 invariant from electronic wave functions. The dispersion of edge states is also found to be consistent with the bulk band topology in view of the bulk-boundary correspondence. We present possible applications of the topological phase transition as an on/off switch of the topologically protected edge states in nano-scale devices.density functional theory | topological edge state T he concept of the topological order in condensed matter physics has provided a new perspective to the understanding of the origin of different phases and the exact quantization of Hall conductance in the quantum Hall effect (1, 2). Recently, nontrivial topological orders have been predicted theoretically and confirmed experimentally in both two-dimensional (2D) and threedimensional (3D) systems with the time-reversal invariance (3-11). These topologically nontrivial systems, called topological insulators (TIs), have intriguing properties that they develop robust conducting edge or surface states on the boundary with normal insulators (NIs) or vacuum following the bulk-boundary correspondence rule (12). These characteristic boundary states have a topological origin and are potentially useful for the design of nano-scale devices in spintronics or quantum computations.Manifestation of the nontrivial topology of occupied bands in a TI is attributed to the band inversion between occupied and unoccupied bands by large enough spin-orbit coupling (13). If the strength of the spin-orbit coupling should be reduced, the band topology would recover a trivial configuration via gap closing (14). Thus, modifying the spin-orbit strength can be a method to control the topology and induce a quantum phase transition between TI and NI phases. The band topology of a physical system may also be changed, for example, by adjusting lattice constants or internal atomic positions (15, 16). Based on this mechanism, a strain-induced topological phase transition can be driven if the original system is close to the phase boundary. In the case of 2D TIs (i.e., quantum spin Hall systems), still another factor affecting the band topology is an electrostatic scalar potential or an external electric field as an effective continuous model predicts that potential difference between upper and lower surfaces can transform topologically nontrivial thin films of Bi 2 Se 3 into topologically trivial ones (17,18). Actually, a model calculation shows that external electric fields can drive the quantum phase transition between TIs and NIs in HgTe quantum wells (19). It has been predicted that thin films of tetradymite semiconductors recently found to be 3D strong topological insulators...