Year: 2019
Type: article
Abstract: Electric currents flowing transverse to the electric field in the absence of magnetic fields in systems with broken time-reversal symmetry lead to the anomalous Hall effect observed in DC transport experiments. When the system is in equilibrium and there is no transport, anomalous currents still exist, inducing measurable magnetic fields or magnetic moments. In this paper, we employ the two-dimensional massive Dirac equation to find the exact current flowing along a potential step of arbitrary shape. The current is universal, i.e., it depends only on the asymptotic value of the potential drop. For a spatially slowly varying potential we find the current density $\mathbf{j}(\mathbf{r})$ and the energy distribution of the current density ${\mathbf{j}}^{\ensuremath{\varepsilon}}(\mathbf{r})$. The latter turns out to be unexpectedly nonuniform, behaving like a $\ensuremath{\delta}$ function at the border of the classically accessible area at energy $\ensuremath{\varepsilon}$. Consequently, even in a weak electric field the transverse current density cannot be described semiclassically. To demonstrate explicitly the difference between the magnetization and transport currents we consider the transverse shift of an electron ray in an electric field.
Authors: P. G. Silvestrov, P. Recher
Institution: Technische Universität Braunschweig
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G5229248572
OpenAlex ID: W2803940574