Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb

2006/11/16 by Takahiro Fukui, T. Fukui, Yasuhiro Hatsugai +1 · 1 citation
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.stat-mech

paper · pdf · doi:10.1143/jpsj.76.053702

published as J. Phys. Soc. Jpn. 76 (2007) 053702 · 5 pages, 5 figures

arxiv created 2006/11/16 · openalex publication_date 2007/04/25 · arxiv updated 2014/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We derive an efficient formula for Z₂ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.

Citations

• Observation of the Spin Hall Effect in Semiconductors
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Quantum Spin Hall Effect in Graphene
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Universal Intrinsic Spin Hall Effect
• Time Reversal Polarization and a Z₂ Adiabatic Spin Pump
• Intrinsic and Rashba spin-orbit interactions in graphene sheets
• Dissipationless Quantum Spin Current at Room Temperature
• Abelian chiral gauge theories on the lattice with exact gauge invariance

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