Berlin 2018 – scientific programme
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MA: Fachverband Magnetismus
MA 44: Topological Insulators II (joint session TT/MA)
MA 44.13: Talk
Thursday, March 15, 2018, 12:45–13:00, A 053
Magnetization current and anomalous Hall effect for massive Dirac electrons — •Peter Silvestrov1 and Patrik Recher1,2 — 1Institute for Mathematical Physics, TU Braunschweig, 38106 Braunschweig, Germany — 2Laboratory for Emerging Nanometrology Braunschweig, 38106 Braunschweig, Germany
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, e.g. optical, 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 slowly varying electric field, we find the current density j(r) and the energy distribution of the current density jε(r). The latter turns out to be unexpectedly nonuniform, behaving like a δ-function at the border of a classically accessible area at energy ε. To demonstrate explicitly the difference between the magnetization and transport currents, we consider the transverse shift of an electron ray in an electric field.