Topological Axion States in the Magnetic Insulator 
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 with the Quantized Magnetoelectric Effect

Zhang, Dongqin; Shi, Mingyi; Zhu, Tongshuai; Xing, D. Y.; Zhang, Haijun; Wang, Jing

doi:10.1103/physrevlett.122.206401

Cited by 749 publications

(607 citation statements)

References 61 publications

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“…As a consequence, the ground state of EuCd 2 As 2 becomes a novel axion insulator state which is not studied in previous theoretical paper 14. This ground state is similar to that reported recently in the MnBi 2 Te 4 family 17,18. But for EuCd 2 As 2 , massless Dirac surface states appear on some specifically oriented surfaces which are protected by the mirror or

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symmetries.…”

Section: The Number Of Occupied Bands With Even and Odd Parity At Thesupporting

confidence: 79%

“…Furthermore, it was shown that for other surfaces, there are gaped surface states contributing to half‐quantized anomalous Hall conductivity. This class of AFM materials was coined as AFM TIs, and as a possible candidate for an axion insulator, as reported recently for MnBi 2 Te 4 17–21. However, the topological nature of the surface of MnBi 2 Te 4 remains puzzling due to disagreements between experimental results and theoretical predictions 19–21.…”

Section: The Number Of Occupied Bands With Even and Odd Parity At Thementioning

confidence: 95%

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Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Wang

Nie

et al. 2020

Advanced Materials

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Parity‐time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle‐resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd2As2. As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time‐reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from the c‐axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.

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symmetries.…”

Section: The Number Of Occupied Bands With Even and Odd Parity At Thesupporting

confidence: 79%

Section: The Number Of Occupied Bands With Even and Odd Parity At Thementioning

confidence: 95%

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Wang

Nie

et al. 2020

Advanced Materials

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“…To date the closest to a physical realization seems to the antiferromagnetic topological insulator 28 MnBi 2 Te 4 , which has been the subject of much recent interest. [29][30][31][32][33][34] Other symmetry operations also reverse the sign of θ, and thus support an axion Z 2 classification. These include simple mirrors and glide mirrors, rotoinversions, and time-reversed rotations and screws.…”

Section: Introductionmentioning

confidence: 75%

Axion coupling in the hybrid Wannier representation

2020

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Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those that do not ("axion-even" or "trivial"). For time-reversal or inversion symmetries, the resulting topological state is usually denoted as a "strong topological insulator" or an "axion insulator" respectively, but many other symmetries can also protect this "axion Z2" index. Topological states are often insightfully characterized by choosing one crystallographic direction of interest, and inspecting the hybrid Wannier (or equivalently, the non-Abelian Wilson-loop) band structure, considered as a function of the two-dimensional Brillouin zone in the orthogonal directions. Here, we systematically classify the axion-quantizing symmetries, and explore the implications of such symmetries on the Wannier band structure. Conversely, we clarify the conditions under which the axion Z2 index can be deduced from the Wannier band structure. In particular, we identify cases in which a counting of Dirac touchings between Wannier bands, or a calculation of the Chern number of certain Wannier bands, or both, allows for a direct determination of the axion Z2 index. We also discuss when such symmetries impose a "flow" on the Wannier bands, such that they are always glued to higher and lower bands by degeneracies somewhere in the projected Brillouin zone, and the related question of when the corresponding surfaces can remain gapped, thus exhibiting a half-quantized surface anomalous Hall conductivity. Our formal arguments are confirmed and illustrated in the context of tight-binding models for several paradigmatic axion-odd symmetries including time reversal, inversion, simple mirror, and glide mirror symmetries.

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“…Generally, after sample cleavage, the new surface of bulk MnBi 2 Te 4 is divided into two parts (layers) according to the depth from the topmost layer (see schematic in Fig. 4D): (i) the top layer with the thickness of few nanometers, which hosts an embedded Dirac cone structure due to the unclear magnetic order (26,27,38); (ii) the deep layer with the predicted out-of-plane antiferromagnetic order (18,19). Depending on the detection depths of different techniques, the top layer is detectable to surface sensitive techniques, such as STM and ARPES, while the deep intrinsic layer is detectable to bulk sensitive techniques such as transport measurements.…”

Section: Figurementioning

confidence: 99%

“…For example, the observations of magnetism-induced gap opening at the Dirac point are either too large or too small (absent) (17)(18)(19)(23)(24)(25)(26)(27)(28) and the assignment of the topological surface states are still controversial (26)(27)(28). Here we employ scanning tunneling microscopy (STM) to systematically study the electronic structure of MnBi 2 Te 4 in both real and momentum spaces, and the complementary information helps us to have a better understanding of the material.…”

Section: Introductionmentioning

confidence: 99%

Electronic States and Magnetic Response of MnBi₂Te₄ by Scanning Tunneling Microscopy and Spectroscopy

Yuan

Wang

et al. 2020

Nano Lett.

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Exotic quantum phenomena have been demonstrated in recently discovered intrinsic magnetic topological insulator MnBi 2 Te 4 . At its two-dimensional limit, quantum anomalous Hall (QAH) effect and axion insulator state are observed in odd and even layers of MnBi 2 Te 4 , respectively. The measured band structures exhibit intriguing and complex properties. Here we employ low-temperature scanning tunneling microscopy to study its surface states and magnetic response. The quasiparticle interference patterns indicate that the electronic structures on the topmost layer of MnBi 2 Te 4 is different from that of the expected out-of-plane A-type antiferromagnetic phase. The topological surface states may be embedded in deeper layers beneath the topmost surface. Such novel electronic structure presumably related to the modification of crystalline structure during sample cleaving and re-orientation of magnetic moment of Mn atoms near the surface. Mn dopants substituted at the Bi site on the second atomic layer are observed. The ratio of Mn/Bi substitutions is 5%. The electronic structures are fluctuating at atomic scale on the surface, which can affect the magnetism of MnBi 2 Te 4 . Our findings shed new lights on the magnetic property of MnBi 2 Te 4 and thus the design of magnetic topological insulators.

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Topological Axion States in the Magnetic Insulator MnBi2Te4 with the Quantized Magnetoelectric Effect

Cited by 749 publications

References 61 publications

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Axion coupling in the hybrid Wannier representation

Electronic States and Magnetic Response of MnBi₂Te₄ by Scanning Tunneling Microscopy and Spectroscopy

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Topological Axion States in the Magnetic Insulator MnBi2Te4 with the Quantized Magnetoelectric Effect

Cited by 749 publications

References 61 publications

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd2As2

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd2As2

Axion coupling in the hybrid Wannier representation

Electronic States and Magnetic Response of MnBi2Te4 by Scanning Tunneling Microscopy and Spectroscopy

Contact Info

Product

Resources

About

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Electronic States and Magnetic Response of MnBi₂Te₄ by Scanning Tunneling Microscopy and Spectroscopy