Time-reversal operation and transport phenomena in topological insulators

TL;DR

This paper demonstrates that electric current measurements inherently break time reversal symmetry in quantum systems and reveals that topological insulator surface states involve unique energy level crossings unrelated to Kramers degeneracy, explaining transport phenomena.

Contribution

It introduces a novel perspective on surface state crossings in topological insulators and links them to transport properties without relying on TRS-induced degeneracy.

Findings

Electric current measurements violate TRS in quantum systems.

Surface states involve special energy level crossings not due to Kramers degeneracy.

Derived scattering rates explain resistivity and carrier transitions in topological insulators.

Abstract

We prove that any forms of electric current measurements within a gapped or gapless quantum system necessarily violate the time reversal symmetry (TRS). We then use the ionization energy theory to unequivocally show that the metallic surface states of a topological insulator consist of some special energy level crossings, not due to TRS induced Kramers degeneracy because there is a finite energy gap due to different wavefunctions. We use this special crossings and derive the electron-ion scattering rate required to explain the resistivity and carrier-type transition in (Bi1-xSbx)2Te3 and Pb1-xSnxSe topological insulators.