Chern Vector Protected Three-dimensional Quantized Hall Effect

TL;DR

This paper introduces a new type of three-dimensional quantized Hall effect protected by a specific Chern vector configuration, revealing dimension-dependent topological transport properties and proposing experimental candidates.

Contribution

It proposes the hern vector =(0,m,n)-protected quantized Hall effect in 3D systems, expanding understanding of topological responses and their dependence on sample dimensions.

Findings

Topologically protected two-terminal response proportional to (mL_y + nL_z)

Quantized Hall conductances G_{xy} and G_{xz} depend on sample dimensions

Potential experimental realizations are suggested

Abstract

Recently, Chern vector with arbitrary formula $\textbf{C}\!=\!(\mathcal{C}_{yz},\mathcal{C}_{xz},\mathcal{C}_{xy})$ in three-dimensional systems has been experimentally realized [\B{Nature 609, 925 (2022)}]. Motivated by these progresses, we propose the Chern vector $\textbf{C}\!=\!(0,m,n)$-protected quantized Hall effect in three-dimensional systems. By examining samples with Chern vector $\textbf{C}\!=\!(0,m,n)$ and dimensions $L_y$ and $L_z$ along the $y$- and $z$-directions, we demonstrate a topologically protected two-terminal response. This response can be reformulated as the sum of the transmission coefficients along the $x$- and $y$-directions, given by $(mL_y\!+\!nL_z)$. When applied to Hall bar setups, this topological mechanism gives rise to quantized Hall conductances, such as \(G_{xy}\) and \(G_{xz}\), which are expressed by $\pm(mL_y\!+\!nL_z)$. These Hall conductances exhibit a clear dependency on sample dimensions, illuminating the intrinsic three-dimensional nature. Finally, we propse potential candidates for experimental realization. Our findings not only deepen the understanding of the topological nature of Chern vectors but also enlighten the exploration of their transport properties.