Edge states and the integer quantum Hall effect of spin-chiral ferromagnetic kagome lattice with a general spin coupling

TL;DR

This paper investigates how spin anisotropies and Hund's coupling influence chiral edge states and quantized Hall conductance in a kagome lattice, revealing their dependence on coupling strength and spin chirality.

Contribution

It provides a detailed analysis of the effects of Hund's coupling and spin chirality on edge states and Hall conductance in a kagome lattice, including a topological expression for the quantized Hall conductance.

Findings

Hund's coupling and spin chirality significantly affect edge states.

The quantized Hall conductance depends on the winding number of edge states.

Topological bulk and edge theories are consistent in describing QHC.

Abstract

The chiral edge states and the quantized Hall conductance (QHC) in the two-dimensional kagom\'{e} lattice with spin anisotropies included in a general Hund's coupling region are studied. This kagom\'{e} lattice system is periodic in the $x$ direction but has two edges in the $y$ direction. Numerical results show that the strength of the Hund's coupling, as well as the spin chirality, affects the edge states and the corresponding QHC. Within the topological edge theory, we give the expression of the QHC with the winding number of the chiral edge states on the Riemman surface. This expression is also compaired with that within the topological bulk theory and they are found to keep consistent with each other.