The experimental observation of the long-sought quantum anomalous Hall effect was recently reported in magnetically doped topological insulator thin films [Chang et al., Science 340, 167 (2013)]. An intriguing observation is a rapid decrease from the quantized plateau in the Hall conductance, accompanied by a peak in the longitudinal conductance as a function of the gate voltage. Here, we present a quantum transport theory with an effective model for magnetic topological insulator thin films. The good agreement between theory and experiment reveals that the measured transport originates from a topologically nontrivial conduction band which, near its band edge, has concentrated Berry curvature and a local maximum in group velocity. The indispensable roles of the broken structure inversion and particle-hole symmetries are also revealed. The results are instructive for future experiments and transport studies based on first-principles calculations.PACS numbers: 73.50.-h, 73.63.-b, 85.70.-w In some metallic ferromagnets, a transverse current can be induced by a longitudinal electric field, known as the anomalous Hall effect [1,2]. The phenomenon does not need an external magnetic field, thus it is distinct from the ordinary Hall effect. It has been perceived that in some insulating ferromagnets the anomalous Hall conductance could be quantized in units of the conductance quantum e 2 /h, meanwhile, the longitudinal conductance vanishes [3], leading to the quantum anomalous Hall effect, the last and long-sought family member of the Hall effects. In the quantum anomalous Hall system, the nontrivial topology of the bulk states and broken timereversal symmetry give rise to chiral edge states in the energy gap. The dissipationless transport of the topologically protected edge states gives the quantized conductances, and is believed to have promising applications in quantum electronic devices with low power consumption. Solutions and mechanisms to realize the quantum anomalous Hall effect have attracted tremendous efforts in past decades [4][5][6][7][8][9][10][11][12]. One of the most promising schemes [5] is based on the magnetically doped topological insulators [13][14][15], where the interplay of strong spin-orbit coupling and magnetic exchange interaction gives rise to the band inversion required by the quantum anomalous Hall effect.Recently, the experimental observation on the quantum anomalous Hall effect was reported in Cr-doped (Bi,Sb) 2 Te 3 ultra thin films [16]. The measured Hall conductance exhibits a quantized plateau while the longitudinal conductance decreases drastically at lower temperatures. A more subtle behavior appeared on the positive gate voltage side of the quantized plateau: the Hall conductance shows a sudden drop, accompanied by a peak in the longitudinal conductance (the inset of Fig.1). Understanding the mechanisms beneath the subtle behavior is crucial because they are closely related to the topological origin of the quantized plateau. In this Letter, we present a quantum transport theory, ...
We proposed a theory of quantum anomalous Hall effect in a flat band ferromagnet on a two-dimensional decorated lattice with spin-orbit coupling. Free electrons on the lattice have dispersionless flat bands, and the ground state is highly degenerate when each lattice site is occupied averagely by one electron, i.e., the system is at half filling. The onsite Coulomb interaction can remove the degeneracy and give rise to the ferrimagnetism, which is the coexistence of the ferromagnetic and antiferromagnetic long-range orders. On the other hand, the spin-orbit coupling makes the band structure topologically nontrivial, and produces the quantum spin Hall effect with a pair of helical edge states around the system boundary. Based on the rigorous results for the Hubbard model, we found that the Coulomb interaction can provide an effective staggered potential and turn the quantum spin Hall phase into a quantum anomalous Hall phase.
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