Index theorem on chiral Landau bands for topological fermions

Abstract

Topological fermions as excitations from multi-degenerate Fermi points have been attracting increasing interests in condensed matter physics. They are characterized by topological charges, and magnetic fields are usually applied in experiments for their detection. Here we present an index theorem that reveals the intrinsic connection between the topological charge of a Fermi point and the in-gap modes in the Landau band structure. The proof is based on mapping fermions under magnetic fields to a topological insulator whose topological number is exactly the topological charge of the Fermi point. Our work lays a solid foundation for the study of intriguing magneto-response effects of topological fermions.

5 pages, 2 figures, to be published in PRL

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• Chiral-phonon-induced current in helical crystals
• Topological properties of non-centrosymmetric superconductors $T$Ir${}_2$B${}_2$ ($T$=Nb, Ta)
• Encyclopedia of emergent particles in three-dimensional crystals
• Chiral separation effect for spin 3/2 fermions
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Ferroelectrically Controlled Chirality Switching of Weyl Quasiparticles
• Triply-degenerate point in three-dimensional spinless systems