Direct manifestation of band topology in the winding number of the Wannier-Stark ladder

Abstract

Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological insulators, topological superconductors, and topological semimetals. For topological insulators, the dissipationless transport via gapless helical edge or surface states is supposed to play a defining role, which unfortunately has proved difficult to realize in experiments due to inevitable backscattering induced in the sample boundary. Motivated by the fundamental connection between topological invariants and the Zak phase, here, we show that the non-trivial band topologies of both two and three-dimensional topological insulators, characterized by the Chern numbers and the ${\mathbb{Z}}_2$ invariants, respectively, are directly manifested in the winding numbers of the Wannier-Stark ladder (WSL) emerging under an electric field. We use the Floquet Green's function formalism to show that the winding number of the WSL is robust against interband interference as well as non-magnetic impurity scattering.

20 pages and 8 figures

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Cited by in corpus (14)

• Strong-field Phenomena in Periodic Systems
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Measuring Zak phase in room-temperature atoms
• Topological phase transitions in tilted optical lattices
• Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap
• Weyl nodes as topological defects of the Wannier-Stark ladder: From surface to bulk Fermi arcs
• Floquet Topological Semimetal with Nodal Helix
• Velocity Scanning Tomography for Room-Temperature Quantum Simulation
• A Passage to Topological Matter: Colloquium
• Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders
• Floquet-Bloch Theory for Nonperturbative Response to a Static Drive
• Anomalous transport in a topological Wannier-Stark ladder
• Optical Absorption and Emission from Wannier-Stark Spectra of Moiré Superlattices
• Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State