key: cord-0589931-ngmlj56z
authors: Ge, Jun; Liu, Yanzhao; Li, Jiaheng; Li, Hao; Luo, Tianchuang; Wu, Yang; Xu, Yong; Wang, Jian
title: High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels
date: 2019-07-23
journal: nan
DOI: nan
sha: c8e05dedea8b0294077b1d94aca362598a799749
doc_id: 589931
cord_uid: ngmlj56z

The quantum Hall effect (QHE) with quantized Hall resistance of h/e2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels in the nine-septuple-layer MnBi2Te4 nano-device and C=1 Chern insulator state displaying nearly quantized Hall resistance plateau at record-high temperatures up to 60 K in the seven-septuple-layer nano-device. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures.

The Quantum Hall effect (QHE) with quantized Hall resistance plateaus of height h/νe 2 was firstly observed in two-dimensional (2D) electron systems in 1980 (1) . Here, h is Planck constant, ν is Landau filling factor and e is electron charge. The QHE in the 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. Subsequently, the exact quantization was explained by Laughlin based on gauge invariance and was later related to a topological invariance of the energy bands, which is characterized by Chern number C (2) (3) (4) (5) . Nonzero Chern number distinguishes the QHE systems from vacuum with C=0 (2, 3) . The discovery of QHE introduces the concept of topology into condensed matter physics and is extremely important to physical sciences and technologies. However, the rigorous conditions of ultrahigh mobility, ultralow temperature and strong external magnetic field limit the deep exploration and wide applications of QHE. The emergence of topological insulators (TIs) in which strong spin-orbit coupling (SOC) gives rise to topological band structures provides a new platform for the investigation on QHE without strong external magnetic field. The QAHE with quantized Hall conductance of e 2 /h was predicted to occur in magnetic TIs by doping transition metal elements (Cr or Fe) into time-reversal-invariant TIs Bi 2 Te 3 , Bi 2 Se 3 , and Sb 2 Te 3 (8) . In 2013, the QAHE with quantized Hall conductance of e 2 /h was experimentally observed in thin films of chromium-doped (Bi,Sb) 2 Te 3 at the temperature down to 30 mK (9) .

However, in the above mentioned QHE systems without LLs, only Hall resistance plateau with C=1 can be obtained by coupling topological surface states with magnetism. High-Chern-number QHE without LLs has never been observed experimentally. Besides, the requirement of ultralow temperatures limits the study of QHE without LLs. Efforts on high-Chern-number and high-temperature QHE without LLs are still highly desired for exploring emergent physics and low-power-consumption electronics (10).

Here we report the first experimental discovery of the high-Chern-number QHE without LLs at the temperature up to 4.5 K in the nine-layer MnBi 2 Te 4 nano-device and C=1 QHE without LLs at the temperature as high as 60 K in the seven-layer MnBi 2 Te 4 nano-device. We show that when modulated into the insulating regime by a small back gate voltage, the nine-layer MnBi 2 Te 4 nano-device can be driven to Chern insulator with C=2 at moderate perpendicular magnetic field. Quantized Hall resistance h/2e 2 accompany with vanishing longitudinal resistance at the temperature as high as 4.5 K is observed. When reducing the thickness of the nano-device down to seven-layer, nearly quantized Hall resistance plateau h/e 2 is detected at the temperature up to 60 K (Hall resistance plateau with height of 0.784 h/e 2 ), which is much higher than the Né el temperature T N ~21 K of the seven-layer nano-device. This quantized temperature is the highest record in systems showing QHE without LLs.

Our discoveries break new ground in the exploration of topological quantum states and provide a platform for potential application in related low-consumption electronics.

MnBi 2 Te 4 is a layered material which can be viewed as a layer of Bi 2 Te 3 TI intercalated with an additional Mn-Te bilayer (11) (12) (13) (14) (15) (16) (17) (18) (19) . This material exhibits ferromagnetic (FM) order within septuple layer (SL) and anti-ferromagnetic (AFM) order between neighboring SLs with an out-of-plane easy axis (11) , as displayed in (20) . In this work, the 9-SL MnBi 2 Te 4 flakes were mechanically exfoliated from high quality MnBi 2 Te 4 single crystals. These flakes were then transferred to 300 nm SiO 2 /Si substrates and the standard e-beam lithography followed by e-beam evaporation was used to fabricate electrodes. The doped Si was served as back gate and a back gate voltage applied between Si and the sample can modulate the sample into insulating regime. Figure 1B shows an optical image of the MnBi 2 Te 4 nano-device (s1) with Hall bar geometry. Atomic force microscope measurements are carried out to determine the thickness of the samples (Fig. S1 ). The line profile reveals a thickness of 12.2±0.3 nm, corresponding to 9-SL. The temperature dependence of longitudinal resistance R xx is shown in Fig. 1C , in which a sharp resistance peak gives the T N at around 20 K.

To get insight into the evolution of the topological states in the 9-SL MnBi 2 Te 4 nano-device, we carried out magneto-transport measurements at various back gate voltages V bg . Figure 1D displays the gate-dependent magneto-transport properties of s1 under perpendicular magnetic field at T=1.9 K. Two sharp transitions at around 2.5 T and 5.0 T can be clearly observed on both R xx and R yx in Fig. 1D . These two transitions may mark the beginning and ending of the spins flipping process. With further applying perpendicular magnetic field, the sample is supposed to enter the perfectly aligned FM state (19) . Figure 1E displays the longitudinal resistance at zero field as a function of V bg . The maximum value is obtained at V bg =0 V, which indicates that the Fermi level lies close to the gap at V bg =0 V. This makes our 9-SL MnBi 2 Te 4 nano-device an ideal platform to detect the topological quantum edge states.

The well quantized hall resistance plateau with height of 0.982 h/2e 2 is detected at -9 T by applying a small V bg =6.5 V, accompanying with the longitudinal resistance as small as 0.078 h/2e 2 as shown in Fig. 1D . The quantized Hall resistance plateau nearly does not change when further increasing V bg to 10 V (within the tolerance of the substrate), which can be clearly observed in Fig. 1F . Furthermore, the measurement results up to 12 T are shown in Fig. 2A and Fig. 2B . The quantized hall resistance plateau becomes more apparent under higher magnetic field and the longitudinal resistance can be as small as 0.04 h/2e 2 at 12 T. The well quantized Hall resistance plateau and nearly vanishing longitudinal resistance are characteristics of high-Chern-number QHE without LLs contributed by dissipationless chiral edge state and indicate a well-defined Chern insulator state with C=2, which is beyond previous theoretical models and has never been reported before.

In the absence of magnetic field, MnBi 2 Te 4 bulk is an AFM TI, whose side surfaces are gapless and (111) surfaces are intrinsically gapped by exchange interactions (11, 12, 20) . The gapped surface states are characterized by a quantized Berry phase of and can display the novel half-quantum Hall effect (21, 22) . (11, 20) , it gets greatly enhanced in the FM state by PT symmetry breaking, which generates relatively dispersive bands along thedirection (Fig. S2) . Remarkably, the magnetic transition results in a topological phase transition from AFM TI to a magnetic Weyl semimetal in the bulk (11, 12) , leading to a physical scenario to design Chern insulators with C > 1. Figure 1G shows the schematic FM order and electronic structure of the C=2 Chern insulator state with two chiral edge states across the band gap. However, the Hall plateau shows nearly quantized resistance even at 60 K (0.784

h/e 2 ), which reveals that the Chern insulator state exists at the temperature much higher than T N, indicating a potential way to realize QHE without LLs above liquid nitrogen temperature. The above physical picture is confirmed by the first-principles study, which gives for the bulk and shows that indeed increases by 1 for every (Fig. 4B ). Note that it is theoretically challenging to accurately predict , since the predicted depends sensitively on the exchange-correlational functional and the lattice structure. Based on the modified Becke-Johnson (mBJ) functional (23), we systematically tested the influence of lattice parameter on band structure and (Fig. S2) , and finally decided to use the experimental value . As shown in Fig. 4B , the 9-SL film is a high-Chern-number band insulator with . Compared to the AFM films studied before (11) , band structure of the FM film displays much more pronounced quantum confinement effects, as visualized by significant band splitting between quantum well states (Fig. 4C) . A quantum confinement induced gap ~5 meV is located at the point. The edge-state calculation reveals that there exist two chiral gapless edge channels within the gap ( Fig. 4D) 

After preparation of this manuscript, we became aware of a recent preprint showing signatures of C=2 Chern insulator state in trilayer graphene (24)

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We thank Pu Yang and Zeyan Yang for help in devices fabrications, and Jiawei Luo and Jiawei Zhang for helpful discussion in transport measurements. This work was financially supported by the National Key R&D Program of China (2018YFA0305600, 

The authors declare that they have no competing interests.

All data analyzed to evaluate the conclusions are available within the paper and its supplementary materials. Reasonable requests for further source data are available from the authors upon request. 16 Supplementary Materials:

Figures S1-S6References (1) (2) (3) (4) (5) (6)