Comment to "Quantum Spin Hall Effect and Topological Phase Transition in HGTe Quantum Wells" by B. Andrei Bernevig, Taylor L. Hughes and Shou-Cheng Zhang Science 314, 1757 (2006)

Abstract

The manuscript contains Comment to "Quantum Spin Hall Effect and Topological Phase Transitio in HGTe Quantum Wells" by B. Andrei Bernevig, Taylor L. Hughes and Shou-Cheng Zhang Science 314, 1757 (2006). The text proves that the quantum state, identified by these authors as the surface state located inside HgTe well is incorrect physically. The kinetic energy of the state is negative. The state cannot be identified as proper eigenfunction (vector) in the Hilbert space. Therefore the state could be used as a primer in the topological state theory, developed in the following publications.