Comment to "Topological insulators and superconductors" by Xiao-Liang Qi and Shou-Cheng Zhang Reviews of Modern Physics 83, 1057 (2011)

TL;DR

This paper critiques a proposed topological surface state solution, demonstrating that the exponential decay is unphysical due to negative kinetic energy, thus challenging prior assumptions in topological insulator models.

Contribution

It provides a critical analysis of a specific topological surface state solution, highlighting its physical inconsistency and clarifying the conditions for valid surface states.

Findings

The exponential surface state results from an energy outside the allowed range.

The kinetic energy of the state is negative, indicating an unphysical solution.

The proposed state does not represent a physically correct topological surface state.

Abstract

The paper reports on the solution in the semi-space corresponding to topological surface state. It was shown that the exponential surface state results from selection of the energy outside the allowed energy range. In the result, the kinetic energy of the state is negative proving that the proposed state is not physically correct solution.