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  • Open Access

Step-Edge Anomaly in Topological Metals

O. Schweizer1, V. Gali1, A. Y. Chaou1,2, G. Lemut1, P. W. Brouwer1, and M. Breitkreiz1,*

  • *Contact author: breitkr@physik.fu-berlin.de
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Phys. Rev. Lett. 137, 146605 – Published 30 September, 2026

DOI: https://doi.org/10.1103/3p2x-yjyd

Abstract

Bulk–boundary correspondence guarantees the presence of robust, anomalous states on the boundary of topological matter. The edges of a two-dimensional Chern insulator harbor one-dimensional chiral states, which have a conductance n  e2/h, where n is an integer that is solely determined by the bulk. In this Letter we show that step edges on the surface of three-dimensional topological metals have a robust conductance K  e2/h, where K is also fixed by the bulk and assumes noninteger values. We explain this prediction on the basis of the topology of gapless systems, exemplify it on a lattice model, and connect to recent experimental observations of enhanced density of states at step edges in topological metals.

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References (41)

  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  3. L. Trifunovic and P. W. Brouwer, Higher-order bulk-boundary correspondence for topological crystalline phases, Phys. Rev. X 9, 011012 (2019).
  4. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  5. M. J. Gilbert, Chern networks: Reconciling fundamental physics and device engineering, Nat. Commun. 16, 3904 (2025).
  6. M. T. Kiani and J. J. Cha, Shrinking interconnects beyond copper, Science 390, 572 (2025).
  7. B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5, 031013 (2015).
  8. S.-Y. Xu et al., Experimental discovery of a topological Weyl semimetal state in TaP, Sci. Adv. 1, e1501092 (2015).
  9. Y. Ran, Y. Zhang, and A. Vishwanath, One-dimensional topologically protected modes in topological insulators with lattice dislocations, Nat. Phys. 5, 298 (2009).
  10. Jeffrey C. Y. Teo and C. L. Kane, Topological defects and gapless modes in insulators and superconductors, Phys. Rev. B 82, 115120 (2010).
  11. F. de Juan, A. Rüegg, and D.-H. Lee, Bulk-defect correspondence in particle-hole symmetric insulators and semimetals, Phys. Rev. B 89, 161117(R) (2014).
  12. D. Bulmash, P. Hosur, S.-C. Zhang, and X.-L. Qi, Unified topological response theory for gapped and gapless free fermions, Phys. Rev. X 5, 021018 (2015).
  13. R. Queiroz, R. Ilan, Z. Song, B. A. Bernevig, and A. Stern, Ring states in topological materials, arXiv:2406.03529.
  14. X. Dong, M. Wang, D. Yan, X. Peng, J. Li, W. Xiao, Q. Wang, J. Han, J. Ma, Y. Shi, and Y. Yao, Observation of topological edge states at the step edges on the surface of type-II Weyl semimetal TaIrTe4, ACS Nano 13, 9571 (2019).
  15. S. Howard, L. Jiao, Z. Wang, N. Morali, R. Batabyal, P. Kumar-Nag, N. Avraham, H. Beidenkopf, P. Vir, E. Liu, C. Shekhar, C. Felser, T. Hughes, and V. Madhavan, Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co3Sn2S2, Nat. Commun. 12, 4269 (2021).
  16. P. K. Nag, N. Morali, R. Batabyal, H. T. Jahyun Koo, N. Verma, A. Mazhar, M. Geier, M. Breitkreiz, P. W. Brouwer, E. Liu, C. Felser, B. Yan, N. Avraham, R. Queiroz, and H. Beidenkopf, From ring states to Fermi arc modes in a Weyl semimetal (to be published).
  17. B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
  18. A. A. Burkov, Weyl metals, Annu. Rev. Condens. Matter Phys. 9, 359 (2018).
  19. A. A. Burkov and L. Balents, Weyl semimetal in a topological insulator multilayer, Phys. Rev. Lett. 107, 127205 (2011).
  20. T. Suzuki, R. Chisnell, A. Devarakonda, Y. T. Liu, W. Feng, D. Xiao, J. W. Lynn, and J. G. Checkelsky, Large anomalous Hall effect in a half-Heusler antiferromagnet, Nat. Phys. 12, 1119 (2016).
  21. C. Zhang, Z. Ni, J. Zhang, X. Yuan, Y. Liu, Y. Zou, Z. Liao, Y. Du, A. Narayan, H. Zhang, T. Gu, X. Zhu, L. Pi, S. Sanvito, X. Han, J. Zou, Y. Shi, X. Wan, S. Y. Savrasov, and F. Xiu, Ultrahigh conductivity in Weyl semimetal NbAs nanobelts, Nat. Mater. 18, 482 (2019).
  22. M. Breitkreiz and P. W. Brouwer, Large contribution of Fermi arcs to the conductivity of topological metals, Phys. Rev. Lett. 123, 066804 (2019).
  23. P. M. Perez-Piskunow, N. Bovenzi, A. R. Akhmerov, and M. Breitkreiz, Chiral anomaly trapped in Weyl metals: Nonequilibrium valley polarization at zero magnetic field, SciPost Phys. 11, 046 (2021).
  24. A. I. Khan, A. Ramdas, E. Lindgren, H.-M. Kim, B. Won, X. Wu, K. Saraswat, C.-T. Chen, Y. Suzuki, F. H. da Jornada et al., Surface conduction and reduced electrical resistivity in ultrathin noncrystalline NbP semimetal, Science 387, 62 (2025).
  25. N. A. Lanzillo, U. Bajpai, and C.-T. Chen, Topological semimetal interface resistivity scaling for vertical interconnect applications, Appl. Phys. Lett. 124, 181603 (2024).
  26. S.-W. Lien, I. Garate, U. Bajpai, C.-Y. Huang, C.-H. Hsu, Y.-H. Tu, N. A. Lanzillo, A. Bansil, T.-R. Chang, G. Liang, H. Lin, and C.-T. Chen, Unconventional resistivity scaling in topological semimetal CoSi, npj Quantum Mater. 8, 3 (2023).
  27. Y. Cheon et al., Surface-dominant transport in Weyl semimetal nbas nanowires for next-generation interconnects, Science 393, 272 (2026).

  28. Localized states at step edges with a height less than one unit cell were observed by [15]. We do not consider such states here, since they depend on the topology of a sub-monolayer at the surface and not on topology of the bulk crystal.

  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/3p2x-yjyd for the dependence of step-edge conductance on system size and energy, quantitative asymmetry of LDOS in energy for surface potential, detailed analytic derivation of step-edge conductance, and the transfer matrix lattice calculation, which includes Ref. [30].
  30. C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: A software package for quantum transport, New J. Phys. 16, 063065 (2014).
  31. J. H. Wilson, J. H. Pixley, D. A. Huse, G. Refael, and S. Das Sarma, Do the surface fermi arcs in Weyl semimetals survive disorder?, Phys. Rev. B 97, 235108 (2018).
  32. A. Avdoshkin, V. Kozii, and J. E. Moore, Interactions remove the quantization of the chiral photocurrent at Weyl points, Phys. Rev. Lett. 124, 196603 (2020).
  33. K. Sourounis and A. Manchon, Interaction-induced topological phase transition in magnetic Weyl semimetals, Phys. Rev. B 112, 125162 (2025).
  34. S. Wang and J. D. Sau, Interaction robustness of the chiral anomaly in Weyl semimetals and Luttinger liquids from a mixed anomaly approach, Phys. Rev. B 113, 075141 (2026).
  35. I. Belopolski et al., Synthesis of a semimetallic Weyl ferromagnet with point fermi surface, Nature (London) 637, 1078 (2025).
  36. J.-R. Soh, F. de Juan, M. G. Vergniory, N. B. M. Schröter, M. C. Rahn, D. Y. Yan, J. Jiang, M. Bristow, P. Reiss, J. N. Blandy, Y. F. Guo, Y. G. Shi, T. K. Kim, A. McCollam, S. H. Simon, Y. Chen, A. I. Coldea, and A. T. Boothroyd, Ideal Weyl semimetal induced by magnetic exchange, Phys. Rev. B 100, 201102(R) (2019); See Santos-Cottin et al., Phys. Rev. Lett. 131, 186704 (2023) for a conflicting interpretation [37]
  37. D. Santos-Cottin, I. Mohelský, J. Wyzula, F. Le Mardelé, I. Kapon, S. Nasrallah, N. Barišić, I. Živković, J. R. Soh, F. Guo, K. Rigaux, M. Puppin, J. H. Dil, B. Gudac, Z. Rukelj, M. Novak, A. B. Kuzmenko, C. C. Homes, T. Dietl, M. Orlita, and A. Akrap, EuCd2As2: A magnetic semiconductor, Phys. Rev. Lett. 131, 186704 (2023).
  38. K. M. Taddei, L. Yin, L. D. Sanjeewa, Y. Li, J. Xing, C. dela Cruz, D. Phelan, A. S. Sefat, and D. S. Parker, Single pair of Weyl nodes in the spin-canted structure of EuCd2As2, Phys. Rev. B 105, L140401 (2022), Santos-Cottin et al., Phys. Rev. Lett. 131, 186704 (2023) for a conflicting interpretation [37].
  39. S. H. Lee et al., Evidence for a magnetic-field-induced ideal type-II Weyl state in antiferromagnetic topological insulator Mn(Bi1−xSbx)2te4, Phys. Rev. X 11, 031032 (2021).
  40. J. Seo, C. M. Guo, C. Putzke, X. Huang, B. H. Goodge, Y. C. Wong, M. H. Fischer, T. Neupert, and P. J. W. Moll, Transport evidence for chiral surface states from three-dimensional landau bands, Nat. Phys. 22, 232 (2026).
  41. O. Schweizer, V. Gali, A. Y. Chaou, G. Lemut, P. W. Brouwer, and M. Breitkreiz, Code and data associated with the paper “Step-Edge Anomaly in Topological Metals,” Zenodo 10.5281/zenodo.19221298 (2026).

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Phys. Rev. Lett. 137, 146605– Published 30 September, 2026
  • Received 16 April 2026
  • Revised 8 July 2026
  • Accepted 16 September 2026
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