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)

TL;DR

This paper critically examines a prior claim about the quantum spin Hall effect in HgTe quantum wells, arguing that the identified surface state is physically incorrect due to negative kinetic energy, impacting topological state theory.

Contribution

It provides a physical critique of the previous identification of surface states in HgTe quantum wells, challenging their validity for topological state analysis.

Findings

The identified surface state has negative kinetic energy.

The state is not a proper eigenfunction in Hilbert space.

The critique influences the interpretation of topological states in HgTe.

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.