Topological quantum phase transitions driven by external electric fields in Sb ₂Te ₃ thin films

Using first-principles calculations, we show that topological quantum phase transitions are driven by external electric fields in thin films of Sb ₂Te 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.