Quantum Anomalous Hall Effect in Ferromagnetic Metals

Abstract

The quantum anomalous Hall (QAH) effect holds fundamental importance in topological physics and technological promise for electronics. It is generally believed that the QAH effect can only be realized in insulators. In this Letter, we theoretically demonstrate that the QAH effect can also be realized in metallic systems, representing a phase distinct from the conventional QAH phase in insulators. This phase is characterized by the coexistence of chiral edge channels and isotropic bulk conduction channels without a bulk energy gap. Notably, in a six-terminal Hall bar, our calculations show that, the quantized Hall conductivity and nonzero longitudinal conductivity can emerge due to dephasing, despite the Hall resistivity itself never becoming quantized. Furthermore, the quantized Hall conductivity exhibits remarkable robustness against disorder. Our findings not only extend the range of materials capable of hosting the QAH effect from insulators to metals, but also provide insights that may pave the way for the experimental realization of the QAH effect at elevated temperatures.

Figures (4)

• Figure 1: (a) Schematic of the metallic QAH system under dephasing, showing coexisting isotropic (blue arrows) and chiral (red arrows) conduction channels. The dark gray regions represent the leads I-VI for measuring the QAH effect. The size of the system is $L_{x}=240$ and $L_{y}=60$. The separation between leads II (V) and III (VI) is $l=40$ (A schematic of the device geometry is shown in the Supplementary Materialsseesupplemental). (b) Band structure of the nanoribbon system, with colors indicating the average displacement of each Bloch state relative to the center, $\langle y/L_{y}-1/2\rangle$. (c) Spatial distribution of the states marked by differently colored spheres in (b).
• Figure 2: The Hall resistance $\rho_{xy}$ (a), longitudinal resistance $\rho_{xx}$ (b), Hall conductance $\sigma_{xy}$ (c), and longitudinal conductance $\sigma_{xx}$ (d) as functions of dephasing strength $\Gamma_{d}$. The curves with different colors represent different Fermi energies $E_{F}$ as shown in (c).
• Figure 3: (a) Two-terminal conductance $G$ as a function of the central region length $L_{x}$ for various $\Gamma_d$. (b– c) Spatial distribution of the potential for $\Gamma_d=0.001$ (b) and $\Gamma_d=1.5$ (c). (d) Potential distribution along the midline ($y=L_{y}/2$) of the central region for different $\Gamma_d$. $E_{F}=0$ in all calculations.
• Figure 4: (a) Histogram of the frequency distribution of $\sigma_{xy}$ for various $\Gamma_d$, obtained from 100 random configurations, with $W=0.2$. (b) The color stars represent the average $\sigma_{xy}$ over 100 random configuration sets and the gray stars correspond to $\sigma_{xy}$ when $W=0$. (c) Dependence of $\sigma_{xy}$ on increasing disorder for different dephasing strengths. The red, yellow, and blue point correspond to $\Gamma_{d}=0.3, 0.45,$ and $1.7$, respectively. The error bars in (b,c) indicate the range $\left(\bar{\sigma}_{xy}-3\alpha,\,\bar{\sigma}_{xy}+3\alpha\right)$, where $\bar{\sigma}_{xy}$ and $\alpha$ denote the mean and standard deviation of the 100 data sets, respectively. In these calculations, we set $E_{F}=0$.