Non-linear ballistic response of quantum spin-Hall edge states

Abstract

Topological edge states exhibit dissipationless transport and electrically-driven topological phase transitions, making them ideal for next-generation transistors that are not constrained by Moore's law. Nevertheless, their dispersion has never been probed and is often assumed to be simply linear, without any rigorous justification. Here we determine the non-linear electrical response of topological edge states in the ballistic regime and demonstrate the way this response ascertains the presence of symmetry breaking terms in the edge dispersion, such as deviations from non-linearity and tilted spin quantization axes. The non-linear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of topological materials and discuss experimental measurement.

8 pages, 4 figures

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• Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Quantum spin Hall effect protected by spin U(1) quasisymmetry
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Second Harmonic Helicity and Faraday Rotation in Gated Single-Layer 1T${}^{\prime }$-WTe${}_2$
• Light-induced Nonlinear Spin Hall Current in Single-layer WTe${}_2$
• Nonlinear edge transport in a quantum Hall system