# Quantum anomalous Hall effect in intrinsic magnetic topological insulator

Nontrivial band topology can combine with magnetic order in a magnetic topological insulator to produce exotic states of matter such as quantum anomalous Hall (QAH) insulators and axion insulators. An aim of condensed matter physics is to find new materials with useful properties and apply quantum mechanics to study them. The field has allowed physicists to better understand the uses of magnets for hard disk data storage, computer displays and other technologies. The recent discovery of topological insulators have attracted broad interest and researchers predict that the interplay between ferromagnetism and the topological insulator state can realize a range of exotic quantum magnetic phenomena of interest in fundamental physics and device applications.

In a new report, Yujun Deng and a research team at the departments of physics and quantum matter physics in China, probed quantum transport in a thin flake MnBi_{2}Te_{4 }topological insulator, with intrinsic magnetic order. The ferromagnetic layers coupled anti-parallelly to each other in the atomically thin MnBi_{2}Te_{4 }layered van der Waals crystal. However, the sample became ferromagnetic when it contained an odd number of septuple layers. The research team observed the zero-field QAH effect in a five-septuple-layer specimen at 1.4 Kelvin. The results established MnBi_{2}Te_{4 }as an ideal platform to explore exotic topological phenomena with spontaneously broken time-reversal symmetry. The work is now published on *Science*.

Topological materials distinctly contain topologically protected quantum states that are robust against local distresses. For instance, in a topological insulator (TI) such as bismuth telluride (Bi_{2}Te_{3}), the bulk band topology can guarantee the existence of two-dimensional (2-D) surface states with gapless Dirac dispersion. By introducing magnetism into the initially time-reversal invariant topological insulators (TIs), scientists can induce profound changes in their electronic structure. For example, to experimentally observe the QAH effect in chromium-doped (Bi, Sb)_{2}Te_{3}, physicists had to precisely control the ratio of multiple elements in a non-stoichiometric material. Fine-tuning the material required reconciling conflicting demands and therefore, researchers had to precisely quantize the anomalous Hall effect only at temperatures up to T = 2 K, far below the Curie temperature and exchange gap in the material. To further explore the rich topological phenomena and their potential applications, researchers must use intrinsic magnetic TIs (topological insulators) with an innate magnetic order to study their topological effects in pristine crystals.

In this work, Deng et al. probed quantum transport in atomically thin flakes of intrinsic magnetic topological insulator MnBi_{2}Te_{4. }The material contained a layered ternary tetradymite compound containing septuple layers (Te-Bi-Te-Mn-Te-Bi-Te). The resulting MnBi_{2}Te_{4 }crystal was intrinsically magnetic and the magnetism originated from Mn^{2+} ions in the crystal. They studied thin flakes of MnBi_{2}Te_{4.}to minimize parallel bulk conduction and focused on MnBi_{2}Te_{4 }flakes containing an odd number of layers.

The team started with high quality MnBi_{2}Te_{4 }crystals grown using a flux method to obtain atomically thin MnBi_{2}Te_{4 }via Al_{2}O_{3}-assisted exfoliation. To accomplish this, they thermally evaporated Al_{2}O_{3 }thin film onto a freshly prepared surface of the bulk crystal, lifted the bulk using a thermal release tape then released the combined Al_{2}O_{3}/MnBi_{2}Te_{4} stack on to a piece of transparent polydimethylsiloxane (PDMS) for microscopic inspection. Thereafter, they stamped the thin flakes onto a silicon wafer covered with SiO_{2}, followed by deposition of Cr/Au contacts for transport measurements. The team completed the process in an airtight box to prevent sample exposure to oxygen (O_{2}) and water (H_{2}O) to mitigate sample degradation. They then extensively studied the rich set of magnetic states for the few-layered samples.

Deng et al. observed a well-developed QAH effect at zero magnetic field in a five-layer MnBi_{2}Te_{4} of much improved sample quality. They noted that an external magnetic field further improved the quantization by aligning the ferromagnetic layers. The ferromagnetic alignment also improved the robustness of the QAH effect against thermal fluctuations. At zero magnetic field, they obtained an energy gap that exceeded the value in magnetically doped Ti thin films, although still much smaller than the exchange gap expected for MnBi_{2}Te_{4}.

The energy gap did not directly measure the bandgap of the surface states in the crystal, but characterized the minimum energy required to excite an electron from the valence to the conduction band. For instance, a large difference between the energy gap and the predicted bandgap implied various disorders in the sample. As a result, there is much room to further increase the energy scale of the QAH effect in pristine, high-quality MnBi_{2}Te_{4 }samples.

After the applied external magnetic field fully polarized the five-layer sample, the energy gap diminished with increasing magnetic field. The QAH states gradually evolved in the experimental setup providing a peek into the electronic structure of the surface bands outside the bandgap. Deng et al. understood all states observed in the study from a unified view. The Hall measurements near zero magnetic field yield a gate efficiency of 5 x 10^{10} cm^{-2}/V, which agreed well with the efficiency estimated from the device geometry. Since MnBi_{2}Te_{4 }is a layered material, the team expect the techniques developed for 2-D materials to be applicable to MnBi_{2}Te_{4}. In this way, Yujun Deng and colleagues anticipate that van der Waals heterostructures integrating MnBi_{2}Te_{4 }with other magnetic/superconducting 2-D materials will provide fertile ground to further explore exotic topological quantum phenomena.

**More information:** Yujun Deng et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi_{2}Te_{4}, *Science* (2020). DOI: 10.1126/science.aax8156

Haijun Zhang et al. Topological insulators in Bi2Se3, Bi_{2}Te_{3} and Sb_{2}Te_{3} with a single Dirac cone on the surface, *Nature Physics* (2009). DOI: 10.1038/nphys1270

Yoshinori Tokura et al. Magnetic topological insulators, *Nature Reviews Physics* (2019). DOI: 10.1038/s42254-018-0011-5

**Journal information:**
Science
,
Nature Physics

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