Quantization of Non-Abelian Berry Phase for Time-Reversal-Invariant Systems

2009/03/18 by Takahiro Fukui, T. Fukui, Takanori Fujiwara +1
Physics and Astronomy · #Atomic and Subatomic Physics Research #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1143/jpsj.78.093001

published as J.Phys.Soc.Jpn.78:093001,2009 · 5 pages

arxiv created 2009/03/18 · openalex publication_date 2009/09/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons one-form), whereas we propose that a similar integral but over five dimensional parameter space (an integral of the Chern-Simons five-form) is suitable to define a non-Abelian Berry phase. We study its global topological aspects and show that it is indeed quantized into two values. We also discuss its close relationship with the nonperturbative anomalies.

Citations

• Topological phases and the quantum spin Hall effect in three dimensions
• Observation of the Spin Hall Effect in Semiconductors
• Global aspects of current algebra
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• Quantum Spin Hall Effect in Graphene
• Topological Insulators with Inversion Symmetry
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Universal Intrinsic Spin Hall Effect
• Time Reversal Polarization and a Z₂ Adiabatic Spin Pump
• Spin-Hall Insulator
• Dissipationless Quantum Spin Current at Room Temperature
• Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
• Quantal phase factors accompanying adiabatic changes