Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Scaling of the Anomalous Hall Effect in the Insulating Regime   We develop a theoretical approach to study the scaling of anomalous Hall
effect (AHE) in the insulating regime, which is observed to be
$\sigma_{xy}^{AH}\propto\sigma_{xx}^{1.40\sim1.75}$ in experiments over a large
range of materials. This scaling is qualitatively different from the ones
observed in metals. Basing our theory on the phonon-assisted hopping mechanism
and percolation theory, we derive a general formula for the anomalous Hall
conductivity, and show that it scales with the longitudinal conductivity as
$\sigma_{xy}^{AH}\sim\sigma_{xx}^{\gamma}$ with $\gamma$ predicted to be
$1.38\leq\gamma\leq1.76$, quantitatively in agreement with the experimental
observations. Our result provides a clearer understanding of the AHE in the
insulating regime and completes the scaling phase diagram of the AHE.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con