Abstract
The effect of the magnetic impurities on the charge transport in a magnetic topological ultra-thin film (MTF) is analytically investigated by applying the semi-classical Boltzmann framework through a modified relaxation-time approximation. Our results for the relaxation time of electrons as well as the charge conductivity of the system exhibit two distinct regimes of transport. We show that the generated charge current in a MTF is always dissipative and anisotropic when both conduction bands are involved in the charge transport. The magnetic impurities induce a chirality selection rule for the transitions of electrons which can be altered by changing the orientation of the magnetic impurities. On the other hand, when a single conduction band participates in the charge transport, the resistivity is isotropic and can be entirely suppressed due to the corresponding chirality selection rule. Our findings propose a method to determine an onset thickness at which a crossover from a three-dimensional magnetic topological insulator to a (two-dimensional) MTF occurs.
Highlights
Topological states as a novel quantum state of matter have attracted a lot of theoretical [1,2,3,4,5] and experimental [6,7,8] attention in condensed-matter physics
We show that the generated charge current in a magnetic topological ultra-thin film (MTF) is always dissipative and anisotropic when both conduction bands are involved in the charge transport
When both of the two non-degenerate massive Dirac cones in a MTF are filled with electrons, we found that the extracted charge current is always dissipative
Summary
Topological states as a novel quantum state of matter have attracted a lot of theoretical [1,2,3,4,5] and experimental [6,7,8] attention in condensed-matter physics. We investigate the charge transport of massive Dirac fermions in an MTF in the presence of short-range and randomly placed dilute magnetic impurities. By applying the semi-classical Boltzmann formalism [43,44,45], and using a modified relaxation time scheme [46], to truly capture the effect of the present anisotropic interactions, the charge transport of a MTF is investigated. We address a chirality selection rule which is induced by the magnetic impurities and governs the transitions of electrons between the two non-degenerate massive Dirac cones in a MTF. We show in this work how a MTF can provide us with a system in which the massive Dirac fermions generate a dissipation-less charge current in the presence of the magnetic impurities. In appendix B we discuss the sensitivity of the charge current to the direction of the applied external electric field
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