- Letter
- Open Access
Laughlin charge pumping from interplay of chiral Dirac and chiral Majorana modes
Phys. Rev. Research 7, L032060 – Published 17 September, 2025
DOI: https://doi.org/10.1103/8drx-qktw
Abstract
Laughlin charge pumping has provided critical insights into the topological classification of individual materials, but remains largely unexplored in topological junctions. We explore Laughlin charge pumping in junctions composed of a chiral topological superconductor sandwiched between two quantum anomalous Hall insulators, driven by an adiabatically varying magnetic flux. Here, charge pumping can be mediated merely by chiral Dirac modes or by the interplay of chiral Dirac and chiral Majorana modes (CMMs). In the former case, a variation of one magnetic flux quantum induces the pumping of a unit charge, as the chiral Dirac mode accumulates the full flux-induced phase. In contrast, in the latter case, pumping a unit charge requires a variation of fractional magnetic flux quanta, determined by the device geometry and the parity of the number of enclosed superconducting vortices. This unique feature results from the charge-neutral and zero-momentum nature of zero-energy CMMs. Our work offers an experimentally viable pathway toward detecting CMMs and could also inspire further research into Laughlin charge or spin pumping in diverse topological junctions, which are now within experimental reach.
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References (72)
- R. B. Laughlin, Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632(R) (1981).
- V. T. Dolgopolov, A. A. Shashkin, N. B. Zhitenev, S. I. Dorozhkin, and K. von Klitzing, Quantum Hall effect in the absence of edge currents, Phys. Rev. B 46, 12560 (1992).
- B. Jeanneret, B. D. Hall, H.-J. Bühlmann, R. Houdré, M. Ilegems, B. Jeckelmann, and U. Feller, Observation of the integer quantum Hall effect by magnetic coupling to a Corbino ring, Phys. Rev. B 51, 9752 (1995).
- A. Fabre, J.-B. Bouhiron, T. Satoor, R. Lopes, and S. Nascimbene, Laughlin’s topological charge pump in an atomic Hall cylinder, Phys. Rev. Lett. 128, 173202 (2022).
- M. Kawamura, M. Mogi, R. Yoshimi, T. Morimoto, K. S. Takahashi, A. Tsukazaki, N. Nagaosa, M. Kawasaki, and Y. Tokura, Laughlin charge pumping in a quantum anomalous Hall insulator, Nat. Phys. 19, 333 (2023).
- D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
- M. Kohmoto, Topological invariant and the quantization of the Hall conductance, Ann. Phys. 160, 343 (1985).
- L. Fu and C. L. Kane, Time reversal polarization and a adiabatic spin pump, Phys. Rev. B 74, 195312 (2006).
- D. Meidan, T. Micklitz, and P. W. Brouwer, Optimal topological spin pump, Phys. Rev. B 82, 161303(R) (2010).
- D. Meidan, T. Micklitz, and P. W. Brouwer, Topological classification of adiabatic processes, Phys. Rev. B 84, 195410 (2011).
- I. C. Fulga, F. Hassler, and A. R. Akhmerov, Scattering theory of topological insulators and superconductors, Phys. Rev. B 85, 165409 (2012).
- X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Phys. Rev. B 74, 085308 (2006).
- R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science 329, 61 (2010).
- D. Ovchinnikov, J. Cai, Z. Lin, Z. Fei, Z. Liu, Y.-T. Cui, D. H. Cobden, J.-H. Chu, C.-Z. Chang, D. Xiao et al., Topological current divider in a Chern insulator junction, Nat. Commun. 13, 5967 (2022).
- Y.-F. Zhao, R. Zhang, J. Cai, D. Zhuo, L.-J. Zhou, Z.-J. Yan, M. H. Chan, X. Xu, and C.-Z. Chang, Creation of chiral interface channels for quantized transport in magnetic topological insulator multilayer heterostructures, Nat. Commun. 14, 770 (2023).
- X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
- M. Sato and Y. Ando, Topological superconductors: A review, Rep. Prog. Phys. 80, 076501 (2017).
- M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B 38, 9375 (1988).
- C.-X. Liu, S.-C. Zhang, and X.-L. Qi, The quantum anomalous Hall effect: Theory and experiment, Annu. Rev. Condens. Matter Phys. 7, 301 (2016).
- C.-Z. Chang, C.-X. Liu, and A. H. MacDonald, Colloquium: Quantum anomalous Hall effect, Rev. Mod. Phys. 95, 011002 (2023).
- C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340, 167 (2013).
- N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000).
- A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys.-Usp. 44, 131 (2001).
- C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
- S. Das Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Inf. 1, 15001 (2015).
- B. Lian, X.-Q. Sun, A. Vaezi, X.-L. Qi, and S.-C. Zhang, Topological quantum computation based on chiral Majorana fermions, Proc. Natl. Acad. Sci. USA 115, 10938 (2018).
- Y.-F. Zhou, Z. Hou, and Q.-F. Sun, Non-Abelian operation on chiral Majorana fermions by quantum dots, Phys. Rev. B 99, 195137 (2019).
- Z. Cao, S. Chen, G. Zhang, and D. E. Liu, Recent progress on Majorana in semiconductor-superconductor heterostructures—Engineering and detection, Sci. China: Phys. Mech. Astron. 66, 267003 (2023).
- T. Machida and T. Hanaguri, Searching for Majorana quasiparticles at vortex cores in iron-based superconductors, Prog. Theor. Exp. Phys. 2024, 08C103 (2024).
- Semiconductor-superconductor hybrid nanowires have long been considered a leading platform for topological quantum computation, but various disorders continue to hinder the realization of MZMs [28], limiting their advantage over alternative platforms.
- M. Kayyalha, D. Xiao, R. Zhang, J. Shin, J. Jiang, F. Wang, Y.-F. Zhao, R. Xiao, L. Zhang, K. M. Fijalkowski et al., Absence of evidence for chiral Majorana modes in quantum anomalous Hall-superconductor devices, Science 367, 64 (2020).
- Y. Huang, Y. Fu, P. Zhang, K. L. Wang, and Q. L. He, Inducing superconductivity in quantum anomalous Hall regime, J. Phys.: Condens. Matter 36, 37LT01 (2024).
- A. Uday, G. Lippertz, B. Bhujel, A. A. Taskin, and Y. Ando, Non-Majorana origin of the half-integer conductance quantization elucidated by multiterminal superconductor–quantum anomalous Hall insulator heterostructure, Phys. Rev. B 111, 035440 (2025).
- J. Wang, Q. Zhou, B. Lian, and S.-C. Zhang, Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition, Phys. Rev. B 92, 064520 (2015).
- J. Wang, Electrically tunable topological superconductivity and Majorana fermions in two dimensions, Phys. Rev. B 94, 214502 (2016).
- L. Chen, Z. Cao, K. He, X. Liu, and D. E. Liu, Electrostatic effects of -superconductor heterostructures in the chiral Majorana search, Phys. Rev. B 107, 165405 (2023).
- X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Chiral topological superconductor from the quantum Hall state, Phys. Rev. B 82, 184516 (2010).
- M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York, 1996).
- J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75, 076501 (2012).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/8drx-qktw for the details of model Hamiltonians, numerical simulations, and formula derivations, which includes Refs. [31, 32, 33, 37, 39, 46, 70, 71, 72].
- P. W. Brouwer, Scattering approach to parametric pumping, Phys. Rev. B 58, R10135 (1998).
- M. Blaauboer, Charge pumping in mesoscopic systems coupled to a superconducting lead, Phys. Rev. B 65, 235318 (2002).
- F. Taddei, M. Governale, and R. Fazio, Andreev interference in adiabatic pumping, Phys. Rev. B 70, 052510 (2004).
- M. Alos-Palop, R. P. Tiwari, and M. Blaauboer, Adiabatic quantum pumping of chiral Majorana fermions, Phys. Rev. B 89, 045307 (2014).
- W. Luo, W. Deng, and M.-X. Deng, Half-integer quantized charge pumping induced by a Majorana fermion, Phys. Rev. B 103, 125126 (2021).
- C. Mahaux and H. A. Weidenmüller, Shell-Model Approach to Nuclear Reactions (North-Holland, Amsterdam, 1969).
- M. V. Moskalets, Scattering Matrix Approach to Non-Stationary Quantum Transport (Imperial College Press, London, 2012).
- Y. Ando, Topological insulator materials, J. Phys. Soc. Jpn. 82, 102001 (2013).
- J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Cambridge University Press, Cambridge, 2017).
- L. Fu and C. L. Kane, Probing neutral Majorana fermion edge modes with charge transport, Phys. Rev. Lett. 102, 216403 (2009).
- A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Electrically detected interferometry of Majorana fermions in a topological insulator, Phys. Rev. Lett. 102, 216404 (2009).
- J. Li, G. Fleury, and M. Büttiker, Scattering theory of chiral Majorana fermion interferometry, Phys. Rev. B 85, 125440 (2012).
- C.-A. Li, J. Li, and S.-Q. Shen, Majorana-Josephson interferometer, Phys. Rev. B 99, 100504(R) (2019).
- D. A. Ivanov, Non-Abelian statistics of half-quantum vortices in -wave superconductors, Phys. Rev. Lett. 86, 268 (2001).
- M. Sato and S. Fujimoto, Majorana fermions and topology in superconductors, J. Phys. Soc. Jpn. 85, 072001 (2016).
- Caroli-de Gennes-Matricon states may emerge at vortex cores [29], but they do not induce phase winding. These localized states, when spatially isolated from the edge modes, do not influence the charge pumping resulting from the coherent propagation of edge modes.
- S. Park, J. E. Moore, and H.-S. Sim, Absence of the Aharonov-Bohm effect of chiral Majorana fermion edge states, Phys. Rev. B 89, 161408(R) (2014).
- S. B. Chung, X.-L. Qi, J. Maciejko, and S.-C. Zhang, Conductance and noise signatures of Majorana backscattering, Phys. Rev. B 83, 100512(R) (2011).
- C.-Z. Chen, J. J. He, D.-H. Xu, and K. T. Law, Effects of domain walls in quantum anomalous Hall insulator/superconductor heterostructures, Phys. Rev. B 96, 041118(R) (2017).
- W. Ji and X.-G. Wen, conductance plateau without 1D chiral Majorana fermions, Phys. Rev. Lett. 120, 107002 (2018).
- Y.-H. Li, J. Liu, H. Liu, H. Jiang, Q.-F. Sun, and X. C. Xie, Noise signatures for determining chiral Majorana fermion modes, Phys. Rev. B 98, 045141 (2018).
- L. Zhao, E. G. Arnault, A. Bondarev, A. Seredinski, T. F. Larson, A. W. Draelos, H. Li, K. Watanabe, T. Taniguchi, F. Amet et al., Interference of chiral Andreev edge states, Nat. Phys. 16, 862 (2020).
- J. Shen, J. Lyu, J. Z. Gao, Y.-M. Xie, C.-Z. Chen, C.-w. Cho, O. Atanov, Z. Chen, K. Liu, Y. J. Hu et al., Spectroscopic fingerprint of chiral Majorana modes at the edge of a quantum anomalous Hall insulator/superconductor heterostructure, Proc. Natl. Acad. Sci. USA 117, 238 (2020).
- J. Chen, W. Xu, Z. Tan, Z. Pan, P. Zhu, Z.-M. Liao, and D. Yu, Superconducting proximity in intrinsic magnetic topological insulator hybrid device modulated by Coulomb blockade effect, Nano Lett. 22, 6484 (2022).
- W.-Z. Xu, C.-G. Chu, Z.-C. Pan, J.-J. Chen, A.-Q. Wang, Z.-B. Tan, P.-F. Zhu, X.-G. Ye, D.-P. Yu, and Z.-M. Liao, Proximity-induced superconducting gap in the intrinsic magnetic topological insulator , Phys. Rev. B 105, 184515 (2022).
- P. Dong, X. Hou, J. He, Y. Zhang, Y. Ding, X. Zeng, J. Wang, Y. Wu, K. Watanabe, T. Taniguchi et al., Proximity-effect-induced superconductivity in a van der Waals heterostructure consisting of a magnetic topological insulator and a conventional superconductor, Phys. Rev. B 109, L140503 (2024).
- O. Atanov, W. T. Tai, Y.-M. Xie, Y. H. Ng, M. A. Hammond, T. S. M. Ho, T. H. Koo, H. Li, S. L. Ho, J. Lyu et al., Proximity-induced quasi-one-dimensional superconducting quantum anomalous Hall state, Cell Rep. Phys. Sci. 5, 101762 (2024).
- A. Uday, G. Lippertz, K. Moors, H. F. Legg, R. Joris, A. Bliesener, L. M. Pereira, A. Taskin, and Y. Ando, Induced superconducting correlations in a quantum anomalous Hall insulator, Nat. Phys. 20, 1589 (2024).
- Z. Cao, Unique Laughlin charge pumping from the interplay of chiral Dirac and chiral Majorana modes (version v2), Zenodo (2025), https://zenodo.org/records/14978710.
- C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: A software package for quantum transport, New J. Phys. 16, 063065 (2014).
- F. Peñaranda, R. Aguado, P. San-Jose, and E. Prada, Even-odd effect and Majorana states in full-shell nanowires, Phys. Rev. Res. 2, 023171 (2020).
- P. San-Jose, C. Payá, C. M. Marcus, S. Vaitiekėnas, and E. Prada, Theory of Caroli–de Gennes–Matricon analogs in full-Shell hybrid nanowires, Phys. Rev. B 107, 155423 (2023).