Experimental signature of the parity anomaly in a semi-magnetic topological insulator

ABSTRACT A three-dimensional (3D) topological insulator features a 2D surface state consisting of a single linearly dispersive Dirac cone1,2,3. Under broken time-reversal symmetry, the

single Dirac cone is predicted to cause half-integer quantization of Hall conductance, which is a manifestation of the parity anomaly in quantum field theory1,2,3,4,5,6,7,8,9. However,

despite various observations of quantization phenomena10,11,12,13,14,15, the half-integer quantization has not been observed because most experiments simultaneously measure a pair of

equivalent Dirac cones16 on two opposing surfaces. Here we demonstrate the half-integer quantization of Hall conductance in a synthetic heterostructure termed a semi-magnetic topological

insulator, where only one surface state is gapped by magnetic doping and the opposite one is non-magnetic and gapless. We observe half-quantized Faraday and Kerr rotations with terahertz

magneto-optical spectroscopy and half-quantized Hall conductance in transport at zero magnetic field. Our results suggest a condensed-matter realization of the parity anomaly4,5,6,7,8,9 and

open a way for studying the physics enabled by a single Dirac fermion. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution

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FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS SPECTRAL SIGNATURES OF THE SURFACE ANOMALOUS HALL EFFECT IN MAGNETIC AXION INSULATORS Article Open access 10 June 2021

\({\MATHBB{Z}}/2\) TOPOLOGICAL INVARIANTS AND THE HALF QUANTIZED HALL EFFECT Article Open access 02 January 2025 QUANTIZED SPIN HALL CONDUCTANCE IN A MAGNETICALLY DOPED TWO DIMENSIONAL

TOPOLOGICAL INSULATOR Article Open access 27 May 2021 DATA AVAILABILITY All relevant data within this paper are available from the authors upon reasonable request. Source data are provided

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We thank J. G. Checkelsky for enlightening discussions, and K. N. Okada, S. Iguchi, M. Ogino, Y. Hayashi, H. Shishikura, D. Murata and Y. D. Kato for support of the terahertz measurements.

This research project was partly supported by the JSPS/MEXT Grant-in-Aid for Scientific Research (nos. 15H05853, 15H05867, 17J03179, 18H04229 and 18H01155) and JST CREST (nos. JPMJCR16F1 and

JPMJCR1874). AUTHOR INFORMATION Author notes * M. Mogi Present address: Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA AUTHORS AND AFFILIATIONS *

Department of Applied Physics and Quantum Phase Electronics Center (QPEC), University of Tokyo, Bunkyo-ku, Tokyo, Japan M. Mogi, Y. Okamura, K. Yasuda, T. Morimoto, N. Nagaosa, M. Kawasaki, 

Y. Takahashi & Y. Tokura * RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama, Japan M. Kawamura, R. Yoshimi, K. S. Takahashi, N. Nagaosa, M. Kawasaki, Y. Takahashi & Y.

Tokura * Institute for Materials Research, Tohoku University, Sendai, Miyagi, Japan A. Tsukazaki * Tokyo College, University of Tokyo, Bunkyo-ku, Tokyo, Japan Y. Tokura * Department of

Physics, Massachusetts Institute of Technology, Cambridge, MA, USA K. Yasuda Authors * M. Mogi View author publications You can also search for this author inPubMed Google Scholar * Y.

Okamura View author publications You can also search for this author inPubMed Google Scholar * M. Kawamura View author publications You can also search for this author inPubMed Google

Scholar * R. Yoshimi View author publications You can also search for this author inPubMed Google Scholar * K. Yasuda View author publications You can also search for this author inPubMed 

Google Scholar * A. Tsukazaki View author publications You can also search for this author inPubMed Google Scholar * K. S. Takahashi View author publications You can also search for this

author inPubMed Google Scholar * T. Morimoto View author publications You can also search for this author inPubMed Google Scholar * N. Nagaosa View author publications You can also search

for this author inPubMed Google Scholar * M. Kawasaki View author publications You can also search for this author inPubMed Google Scholar * Y. Takahashi View author publications You can

also search for this author inPubMed Google Scholar * Y. Tokura View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS Y. Tokura conceived and

supervised the project. M.M., R.Y. and K.Y. fabricated the samples with help from A.T., K.S.T. and M. Kawasaki. M.M., Y.O. and Y. Takahashi performed the terahertz spectroscopy measurements

and analysed the data. M.M. and M. Kawamura performed the transport measurements and analysed the data. T.M. and N.N. contributed to the theoretical discussions. M.M., M. Kawamura, T.M.,

N.N. and Y. Tokura wrote the manuscript, with input from all the other authors. CORRESPONDING AUTHORS Correspondence to M. Mogi or Y. Tokura. ETHICS DECLARATIONS COMPETING INTERESTS The

authors declare no competing interests. PEER REVIEW PEER REVIEW INFORMATION _Nature Physics_ thanks Liuyan Zhao and the other, anonymous, reviewer(s) for their contribution to the peer

review of this work. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. EXTENDED

DATA EXTENDED DATA FIG. 1 QUANTIZED FARADAY AND KERR ROTATIONS IN A QAH STATE. A,B, _θ_F and _η_F (A) and _θ_K and _η_K (B) spectra at _T_ = 1 K for the QAH insulator film, which is partly

the same as Fig. 2c and d in the main text, with a slight variation of external magnetic fields (_μ_0_H_ = 0, 0.01, and 1 T). C, Measured fine-structure constant _α_meas which is calculated

from (A) and (B) by using a relation of \(\alpha _{{{{\mathrm{meas}}}}} = ({{{\mathrm{tan}}}}\theta _{{{\mathrm{F}}}}{{{\mathrm{tan}}}}\theta _{{{\mathrm{K}}}} - {{{\mathrm{tan}}}}^2\theta

_{{{\mathrm{F}}}})/({{{\mathrm{tan}}}}\theta _{{{\mathrm{K}}}} - 2{{{\mathrm{tan}}}}\theta _{{{\mathrm{F}}}})\) (refs. 29,30). D, E, _θ_F, _η_F (D) and _θ_K, _η_K (E) spectra at _μ_0_H_ = 0 

T and at various temperatures (_T_ = 1, 1.6, 4.2, 15.6, 32.6, and 56.7 K). F, _T_ dependence of _θ_F and _θ_K taken at _ħω_ = 2 meV, suggesting that the Curie temperature is about 50 K and

that the integer quantization subsists possibly up to 4.2 K. The inset is the magnified view of F. The error bars in a-f represent the standard error of the mean. EXTENDED DATA FIG. 2

OPTICAL MICROSCOPE IMAGE OF A TYPICAL HALL BAR DEVICE USED IN THE TRANSPORT MEASUREMENTS. The black broken lines indicate the shape of the TI film below the gate electrode, formed into the

Hall bar structure. EXTENDED DATA FIG. 3 KERR ROTATION IN THE SEMI-MAGNETIC TI UNDER MAGNETIC FIELDS. A, Representative complex Kerr rotation spectra for the semi-magnetic TI film used for

Fig. 4a in the main text. The open circles at _ħω_ = 0 meV indicate the values anticipated from the measured dc conductivity values. B, Background Kerr spectra of the InP substrate without

any TI films at 7 T. The inset shows the Faraday rotation spectra at 7 T, where an observable polarization rotation occurs at _ħω_ > 2 meV, possibly due to the magnetic resonance of

magnetic impurities involved in InP substrates. The error bars in A and B represent the standard error of the mean. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION Supplementary Sections

I–XII and Figs. 1–14. SOURCE DATA SOURCE DATA FIG. 2 Source data for Fig. 2. SOURCE DATA FIG. 3 Source data for Fig. 3. SOURCE DATA FIG. 4 Source data for Fig. 4. RIGHTS AND PERMISSIONS

Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Mogi, M., Okamura, Y., Kawamura, M. _et al._ Experimental signature of the parity anomaly in a semi-magnetic topological

insulator. _Nat. Phys._ 18, 390–394 (2022). https://doi.org/10.1038/s41567-021-01490-y Download citation * Received: 10 May 2021 * Accepted: 08 December 2021 * Published: 27 January 2022 *

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