Observation of fractionally quantized anomalous Hall effect
The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field 1 – 3 . This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the prese...
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| Published in | Nature (London) Vol. 622; no. 7981; pp. 74 - 79 |
|---|---|
| Main Authors | , , , , , , , , , , , , , , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Nature Publishing Group UK
05.10.2023
Nature Publishing Group |
| Subjects | |
| Online Access | Get full text |
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| Abstract | The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field
1
–
3
. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect
4
–
7
, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe
2
. At zero magnetic field, near filling factor
ν
= −1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance
R
xy
quantized to
h
/
e
2
± 0.1%, whereas the longitudinal resistance
R
xx
vanishes. Remarkably, at
ν
= −2/3 and −3/5, we see plateau features in
R
xy
at
3
2
h
/
e
2
±
1
%
and
5
3
h
/
e
2
±
3
%
, respectively, whereas
R
xx
remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers −1, −2/3 and −3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field,
R
xy
is approximately 2
h
/
e
2
near half-filling (
ν
= −1/2) and varies linearly as
ν
is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field
8
–
14
. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.
Transport measurements in twisted bilayer MoTe
2
reveal quantized Hall resistance plateaus and composite Fermi liquid-like behaviour under zero magnetic field, constituting a direct observation of integer and fractional quantum anomalous Hall effects. |
|---|---|
| AbstractList | Not provided. The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field 1 – 3 . This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect 4 – 7 , would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe 2 . At zero magnetic field, near filling factor ν = −1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance R xy quantized to h / e 2 ± 0.1%, whereas the longitudinal resistance R xx vanishes. Remarkably, at ν = −2/3 and −3/5, we see plateau features in R xy at 3 2 h / e 2 ± 1 % and 5 3 h / e 2 ± 3 % , respectively, whereas R xx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers −1, −2/3 and −3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, R xy is approximately 2 h / e 2 near half-filling ( ν = −1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field 8 – 14 . Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field. Transport measurements in twisted bilayer MoTe 2 reveal quantized Hall resistance plateaus and composite Fermi liquid-like behaviour under zero magnetic field, constituting a direct observation of integer and fractional quantum anomalous Hall effects. The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field. The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic held13. This phenomenon occurs in systems with topologically non-trivial bandsand spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic held, near filling factor v = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy to quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at v = -2/3 and -3/5, we see plateau features in Rxy at 3/2h/e2 ± 1% and 5/3 h/e2 ±3%, respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic held with slopes matchingthe corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic held, Rxy is approximately 2h/e2 near half-filling (v = -1/2) and varies linearly as v is tuned. This behaviour resemblesthat ofthe composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic held8-14. Direct observation ofthe fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic held. |
| Author | Liu, Xiaoyu Cobden, David Taniguchi, Takashi Liu, Zhaoyu Cai, Jiaqi Holtzmann, William Zhu, Jiayi Yao, Wang Xiao, Di Chu, Jiun-Haw Park, Heonjoon Wang, Chong Hu, Chaowei Fu, Liang Zhang, Yinong Watanabe, Kenji Cao, Ting Anderson, Eric Xu, Xiaodong Chang, Cui-Zu |
| Author_xml | – sequence: 1 givenname: Heonjoon surname: Park fullname: Park, Heonjoon organization: Department of Physics, University of Washington – sequence: 2 givenname: Jiaqi orcidid: 0000-0002-7829-9554 surname: Cai fullname: Cai, Jiaqi organization: Department of Physics, University of Washington – sequence: 3 givenname: Eric orcidid: 0000-0002-1357-6645 surname: Anderson fullname: Anderson, Eric organization: Department of Physics, University of Washington – sequence: 4 givenname: Yinong surname: Zhang fullname: Zhang, Yinong organization: Department of Physics, University of Washington – sequence: 5 givenname: Jiayi surname: Zhu fullname: Zhu, Jiayi organization: Department of Physics, University of Washington – sequence: 6 givenname: Xiaoyu surname: Liu fullname: Liu, Xiaoyu organization: Department of Materials Science and Engineering, University of Washington – sequence: 7 givenname: Chong orcidid: 0000-0002-8646-3529 surname: Wang fullname: Wang, Chong organization: Department of Materials Science and Engineering, University of Washington – sequence: 8 givenname: William surname: Holtzmann fullname: Holtzmann, William organization: Department of Physics, University of Washington – sequence: 9 givenname: Chaowei surname: Hu fullname: Hu, Chaowei organization: Department of Physics, University of Washington – sequence: 10 givenname: Zhaoyu orcidid: 0000-0002-9894-9622 surname: Liu fullname: Liu, Zhaoyu organization: Department of Physics, University of Washington – sequence: 11 givenname: Takashi orcidid: 0000-0002-1467-3105 surname: Taniguchi fullname: Taniguchi, Takashi organization: Research Center for Materials Nanoarchitectonics, National Institute for Materials Science – sequence: 12 givenname: Kenji orcidid: 0000-0003-3701-8119 surname: Watanabe fullname: Watanabe, Kenji organization: Research Center for Electronic and Optical Materials, National Institute for Materials Science – sequence: 13 givenname: Jiun-Haw orcidid: 0000-0001-6222-1210 surname: Chu fullname: Chu, Jiun-Haw organization: Department of Physics, University of Washington – sequence: 14 givenname: Ting orcidid: 0000-0003-1300-6084 surname: Cao fullname: Cao, Ting organization: Department of Materials Science and Engineering, University of Washington – sequence: 15 givenname: Liang orcidid: 0000-0002-8803-1017 surname: Fu fullname: Fu, Liang organization: Department of Physics, Massachusetts Institute of Technology – sequence: 16 givenname: Wang orcidid: 0000-0003-2883-4528 surname: Yao fullname: Yao, Wang organization: Department of Physics, University of Hong Kong, HKU-UCAS Joint Institute of Theoretical and Computational Physics, University of Hong Kong – sequence: 17 givenname: Cui-Zu orcidid: 0000-0003-3515-2955 surname: Chang fullname: Chang, Cui-Zu organization: Department of Physics, The Pennsylvania State University – sequence: 18 givenname: David orcidid: 0000-0002-7254-2728 surname: Cobden fullname: Cobden, David organization: Department of Physics, University of Washington – sequence: 19 givenname: Di orcidid: 0000-0003-0165-6848 surname: Xiao fullname: Xiao, Di organization: Department of Physics, University of Washington, Department of Materials Science and Engineering, University of Washington – sequence: 20 givenname: Xiaodong orcidid: 0000-0003-0348-2095 surname: Xu fullname: Xu, Xiaodong email: xuxd@uw.edu organization: Department of Physics, University of Washington, Department of Materials Science and Engineering, University of Washington |
| BackLink | https://www.osti.gov/biblio/2578130$$D View this record in Osti.gov |
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| Snippet | The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field
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. This phenomenon occurs in... The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic held13. This phenomenon occurs in systems... The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems... Not provided. |
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| SubjectTerms | 140/125 142/126 639/766/119/2792/4128 639/766/119/2793 639/766/119/2794 639/766/119/2795 Broken symmetry Coagulation factors Condensed matter physics Electric fields Electrical measurement Electromagnetism Electron gas Electrons Factor V Fermi liquids Hall effect Humanities and Social Sciences Integers Magnetic fields multidisciplinary Phase transitions Quantum Hall effect Science Science & Technology - Other Topics Science (multidisciplinary) Symmetry Unit cell |
| Title | Observation of fractionally quantized anomalous Hall effect |
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