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Existing investigations of the anomalous Hall effect i.e. a current flowing transverse to the electric field in the absence of an external magnetic field) are concerned with the transport current. However, for many applications one needs to know the total current, including its pure magnetization part. In this paper, we employ the two-dimensional massive Dirac equation to find the exact universal total current flowing along a potential step of arbitrary shape. For a spatially slowly varying potential we find the current density $mathbf{j}(vec r)$ and the energy distribution of the current density $mathbf{j}^varepsilon(vec r)$. The latter turns out to be unexpectedly nonuniform, behaving like a $delta$-function at the border of the classically accessible area at energy~$varepsilon$. To demonstrate explicitly the difference between the magnetization and transport currents we consider the transverse shift of an electron ray in an electric field.
Spin-Hall conductivity (SHC) of fully relativistic (4x4 matrix) Dirac electrons is studied based on the Kubo formula aiming at possible application to bismuth and bismuth-antimony alloys. It is found that there are two distinct contributions to SHC,
Dirac fermions are actively investigated, and the discovery of the quantized anomalous Hall effect of massive Dirac fermions has spurred the promise of low-energy electronics. Some materials hosting Dirac fermions are natural platforms for interlayer
Spin-Hall conductivity $sigma_{{rm s}xy}$ and orbital susceptibility $chi$ are investigated for the anisotropic Wolff Hamiltonian, which is an effective Hamiltonian common to Dirac electrons in solids. It is found that, both for $sigma_{{rm s}xy}$ an
The quantum anomalous Hall effect (QAHE) realizes dissipationless longitudinal resistivity and quantized Hall resistance without the need of an external magnetic field. However, when reducing the device dimensions or increasing the current density, a
We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electro