Abstract
Adiabatic charge pumping is one of the most salient features of topological phases of matter1,2,3. Laughlin’s charge pumping in a quantum Hall system is the prototypical example4. In analogy, three-dimensional topological insulators have been predicted to support charge pumping through their magnetically gapped surface states5,6,7,8,9,10. But despite its importance as a direct probe of surface Hall conductivity, charge pumping has not been demonstrated in topological-insulator-based systems. Here we report the observation of charge pumping in a thin-film magnetic heterostructure of topological insulators in a geometry that prohibits edge transport. We find that charge pumping occurs between the inner and outer electrodes in response to alternating magnetic fields when the sample is in the quantum anomalous Hall insulator phase. The amount of pumped charge is accounted for by the surface Hall conductivity of half the quantum conductance for each surface, from a comparison with the axion insulator phase that shows no charge pumping. Because charge pumping is closely related to the theoretically predicted topological magnetoelectric effect5,6,7,8,9,10, our observation may provide clues to its direct observation.
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The data that support the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
References
Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983).
Lohse, M., Schweizer, C., Zilberberg, O., Aidelsburger, M. & Bloch, I. A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice. Nat. Phys. 12, 350–354 (2016).
Nakajima, S. et al. Topological Thouless pumping of ultracold fermions. Nat. Phys. 12, 296–300 (2016).
Laughlin, R. B. Quantized Hall conductivity in two dimensions. Phys. Rev. B 23, 5632–5633 (1981).
Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).
Essin, A. M., Moore, J. E. & Vnderbilt, D. Magnetoelectric polarizability and axion electrodynamics in crystalline insulators. Phys. Rev. Lett. 102, 146805 (2009).
Essin, A. M., Turner, A. M., Moore, J. E. & Vanderbilt, D. Orbital magnetoelectric coupling in band insulators. Phys. Rev. B 81, 205104 (2010).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Sekine, A. & Nomura, K. Axion electrodynamics in topological materials. J. Appl. Phys. 129, 141101 (2021).
Yu, R. et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 61–64 (2010).
Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).
Checkelsky, J. G. et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014).
Mogi, M. et al. Magnetic modulation dopoing in topological insulators toward higher-temperature quantum anomalous Hall effect. Appl. Phys. Lett. 107, 182401 (2015).
Tokura, Y., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat. Rev. Phys. 1, 126–143 (2019).
Kou, X. et al. Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit. Phys. Rev. Lett. 113, 137201 (2014).
Yasuda, K. et al. Quantized chiral edge conduction on domain walls of a magnetic topological insulator. Science 358, 1311–1314 (2017).
Allen, M. et al. Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states. Proc. Natl Acad. Sci. USA 116, 14511–14515 (2019).
Pertsova, A., Canali, C. M. & MacDonald, A. H. Quantum Hall edge states in topological insulator nanoribbons. Phys. Rev. B 94, 121409 (2016).
Lee, D.-H. Surface states of topological insulators: the Dirac fermion in curved two-dimensional spaces. Phys. Rev. Lett. 103, 196804 (2009).
Vafek, O. Quantum Hall effect in a singly and doubly connected three-dimensional topological insulator. Phys. Rev. B 84, 245417 (2011).
König, E. J. et al. Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface. Phys. Rev. B 90, 165435 (2014).
Dolgopolov, V. T., Shashkin, A. A., Zhitenev, N. B., Dorozhkin, S. I. & vonKlitzing, K. Quantum Hall effect in the absence of edge currents. Phys. Rev. B 46, 12560–12567 (1992).
Jeanneret, B. et al. Observation of the integer quantum Hall effect by magnetic coupling to a Corbino ring. Phys. Rev. B 51, 9752–9756 (1995).
Mogi, M. et al. Tailoring tricolor structure of magnetic topological insulator for robust axion insulator. Sci. Adv. 3, eaao1669 (2017).
Mogi, M. et al. A magnetic heterostructure of topological insulators as a candidate for an axion insulator. Nat. Mater. 16, 516–521 (2017).
Lachman, E. O. et al. Observation of superparamagnetism in coexistence with quantum anomalous Hall C = ±1 and C = 0 Chern states. npj Quant. Mater. 2, 70 (2017).
Xiao, D. et al. Realization of the axion insulator state in quantum anomalous Hall sandwich heterostructures. Phys. Rev. Lett. 120, 056801 (2018).
Fontein, P. F., Lagemaat, J. M., Wolter, J. & André, J. P. Magnetic field modulation—a method for measuring the Hall conductance with a Corbino disc. Semicond. Sci. Technol. 3, 915–918 (1998).
Morimoto, T., Furusaki, A. & Nagaosa, N. Topological magnetoelectric effects in thin films of topological insulators. Phys. Rev. B 92, 085113 (2015).
Wang, J., Lian, B., Qi, X.-L. & Zhang, S.-C. Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state. Phys. Rev. B 92, 081107 (2015).
Okada, K. N. et al. Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state. Nat. Commun. 7, 12245 (2016).
Wu, L. et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator. Science 354, 1124–1127 (2016).
Dziom, V. et al. Observation of the universal magnetoelectric effect in a 3D topological insulator. Nat. Commun. 8, 15197 (2017).
Acknowledgements
We thank H. Akimoto and H. Ikegami for experimental support and I. Belopolski for critical reading of the manuscript. This research project was partly supported by JSPS/MEXT Grant-in-Aid for Scientific Research nos. 18H03676 (N.N.), 18H01155 (M. Kawamura) and 22H04958 (M. Kawasaki); JST CREST nos. JPMJCR16F1 (M. Kawasaki), JPMJCR1874 (N.N. and Y.T.), JPMJCR19T3 (T.M.) and JPMJCR20T2 (M. Kawamura); and JST PRESTO no. JPMJPR19L9 (T.M.)
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Y.T. conceived and supervised the project. M.M. and R.Y. fabricated the samples with the help of A.T., K.S.T. and M. Kawasaki. M. Kawamura and R.Y. performed the measurements and analysed the data. T.M. and N.N. contributed to the theoretical discussions. M. Kawamura, T.M., N.N. and Y.T. wrote the manuscript with inputs from all the other authors.
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Kawamura, M., Mogi, M., Yoshimi, R. et al. Laughlin charge pumping in a quantum anomalous Hall insulator. Nat. Phys. 19, 333–337 (2023). https://doi.org/10.1038/s41567-022-01888-2
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DOI: https://doi.org/10.1038/s41567-022-01888-2
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