Signatures of lattice geometry in quantum and topological Hall effect

Abstract

The topological Hall effect (THE) of electrons in skyrmion crystals is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the skyrmion crystal (THE) or of the corresponding Landau levels (QHE). Striking features in the energy dependence of the Hall conductivities are traced back to the band structure without magnetic field whose properties are dictated by the lattice geometry. Based on these findings, we derive an approximation that allows us to determine the energy dependence of the topological Hall conductivity on any twodimensional lattice. The validity of this approximation is proven for the honeycomb lattice. We conclude that skyrmion crystals lend themselves for experiments to validate our findings for the THE and - indirectly - the QHE.

17 pages, 12 figures

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
• Interface-driven topological Hall effect in SrRuO${}_3$-SrIrO${}_3$ bilayer
• Robust formation of skyrmions and topological Hall effect in epitaxial thin films of MnSi
• Thermally Driven Ratchet Motion of Skyrmion Microcrystal and Topological Magnon Hall Effect
• Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
• Real-Space Berry Phases - Skyrmion Soccer
• Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice
• Skyrmions at the edge: Confinement effects in Fe/Ir(111)

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