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Surface states of a topological insulator demonstrate interesting quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the quantum magnetoelectric effect. Fermi energy tuning plays a role in inducing phase transitions and developing future device functions. Here, we report on controlling the topological phases in a dual-gate field-effect transistor of a semi-magnetic topological insulator heterostructure. The heterostructure consists of magnetized one-surface and non-magnetic other-surface. By tuning the Fermi energy to the energy gap of the magnetized surface, the Hall conductivity $\sigma_{xy}$ becomes close to the half-integer quantized Hall conductivity $e^2/2h$, exemplifying parity anomaly. The dual-gate control enables the band structure alignment to the two quantum Hall states with $\sigma_{xy} = e^2/h$ and 0 under a strong magnetic field. These states are topologically equivalent to the QAH and axion insulator states, respectively. Precise and independent control of the band alignment of the top and bottom surfaces successively induces various topological phase transitions among the QAH, axion insulator, and parity anomaly states in magnetic topological insulators., Comment: 20 pages, 4 figures

We report a current scaling study of a quantum phase transition between a quantum anomalous Hall insulator and a trivial insulator on the surface of a heterostructure film of magnetic topological insulators. The transition was observed by tilting the magnetization while measuring the Hall conductivity $\sigma_{xy}$. The transition curves of $\sigma_{xy}$ taken under various excitation currents cross each other at a single point, exemplifying a quantum critical behavior of the transition. The slopes of the transition curves follow a power law dependence of the excitation current, giving a scaling exponent. Combining with the result of the previous temperature scaling study, critical exponents $\nu$ for the localization length and $p$ for the coherence length are separately evaluated as $\nu$ = 2.8 $\pm$ 0.3 and $p$ = 3.3 $\pm$ 0.3., Comment: 6 pages, 4 figures

The quantum anomalous Hall effect (QAHE) is an exotic quantum phenomenon originating from dissipation-less chiral channels at the sample edge. While the QAHE has been observed in magnetically doped topological insulators (TIs), exploiting magnetic proximity effect on the TI surface from adjacent ferromagnet layers may provide an alternative approach to the QAHE by opening an exchange gap with less disorder than that in the doped system. Nevertheless, the engineering of a favorable heterointerface that realizes the QAHE based on the magnetic proximity effect remains to be achieved. Here, we report on the observation of the QAHE in a proximity coupled system of non-magnetic TI and ferromagnetic insulator (FMI). We have designed sandwich heterostructures of (Zn,Cr)Te/(Bi,Sb)2Te3/(Zn,Cr)Te that fulfills two prerequisites for the emergence of the QAHE; the formation of a sizable exchange gap at the TI surface state and the tuning of the Fermi energy into the exchange gap. The efficient proximity coupling in the all-telluride based heterostructure as demonstrated here will enable a realistic design of versatile tailor-made topological materials coupled with ferromagnetism, ferroelectricity, superconductivity, and so on., Comment: 18 pages, 4 figures

We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of ferromagnetic insulator Cr2Ge2Te6 and topological insulator (Bi,Sb)2Te3. Despite small magnetization in the (Bi,Sb)2Te3 layer, the anomalous Hall conductivity reaches a large value of 0.2e2/h in accord with a ferromagnetic response of the Cr2Ge2Te6. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr2Ge2Te6 layer is effective and strong enough to open the sizable exchange gap in the surface state., Comment: 33 pages, 12 figures including supplemental material, accepted by PRL

We report a continuous phase transition between quantum-anomalous-Hall and trivial-insulator phases in a magnetic topological insulator upon magnetization rotation. The Hall conductivity transits from one plateau of quantized Hall conductivity $e^2/h$ to the other plateau of zero Hall conductivity. The transition curves taken at various temperatures cross almost at a single point, exemplifying the critical behavior of the transition. The slope of the transition curves follows a power-law temperature dependence with a critical exponent of $-0.61$. This suggests a common underlying origin in the plateau transitions between the QAH and quantum Hall systems, which is a percolation of one-dimensional chiral edge channels., Comment: 3 figures

Instability of quantum anomalous Hall (QAH) effect has been studied as function of electric current and temperature in ferromagnetic topological insulator thin films. We find that a characteristic current for the breakdown of the QAH effect is roughly proportional to the Hall-bar width, indicating that Hall electric field is relevant to the breakdown. We also find that electron transport is dominated by variable range hopping (VRH) at low temperatures. Combining the current and temperature dependences of the conductivity in the VRH regime, the localization length of the QAH state is evaluated to be about 5 $\mu$m. The long localization length suggests a marginally insulating nature of the QAH state due to a large number of in-gap states., Comment: 5 pages, 4 figures, accepted for publication in PRL