Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals

Abstract

We present mathematical details of the construction of a topological invariant for periodically driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps, which was proposed recently by some of us. The invariant is represented by a gap-dependent ${\mathbb{Z}}_2$-valued index that is simply related to the Kane-Mele invariants of quasienergy bands but contains an extra information. As a byproduct, we prove new expressions for the two-dimensional Kane-Mele invariant relating the latter to Wess-Zumino amplitudes and the boundary gauge anomaly.

published version ; 56 pages, 15 figures

References in corpus (11)

• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological properties of linear circuit lattices
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Topological index for periodically driven time-reversal invariant 2D systems
• Manipulation of edge states in microwave artificial graphene
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
• Classification of "Quaternionic" Bloch-bundles: Topological Quantum Systems of type AII

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• Topological boundary invariants for Floquet systems and quantum walks
• Bundle gerbes and the Weyl map