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Crossed Surface Flat Bands in Three-Dimensional Superconducting Altermagnets

Yuri Fukaya1, Bo Lu2, Keiji Yada3, Yukio Tanaka3, and Jorge Cayao4

  • 1Faculty of Environmental Life, Natural Science and Technology, Okayama University, 700-8530 Okayama, Japan
  • 2Center for Joint Quantum Studies, Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Physics, Tianjin University, Tianjin 300354, China
  • 3Department of Applied Physics, Nagoya University, 464-8603 Nagoya, Japan
  • 4Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden

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Phys. Rev. Lett. 136, 226001 – Published 4 June, 2026

DOI: https://doi.org/10.1103/65q6-5wxl

Abstract

Superconducting altermagnets have proven to be a promising ground for emergent phenomena, but their study has involved two-dimensional systems. In this work, we investigate three-dimensional d- and g-wave altermagnets with spin-singlet chiral d-wave superconductivity and show the formation of crossed surface flat bands due to the interplay between superconducting and altermagnetic symmetries. We find that these crossed flat bands are topologically protected, appear at zero energy in the surface along z due to the superconducting nodal lines in the xy plane, and their number of corners is determined by the crystal symmetry of altermagnets. We also show that the superconducting nodal lines give rise to Bogoliubov-Fermi surfaces, which then affect the appearance of zero-energy arcs in the surface along x. Moreover, we demonstrate that the crossed flat bands or surface arcs, and Bogoliubov-Fermi surfaces give rise to the coexistence of three distinct dependences of the charge conductance on the normal transparency, hence offering a solid way for their detection and paving the way for realizing higher-dimensional topological phases using altermagnets.

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Phys. Rev. Lett. 136, 226001– Published 4 June, 2026
  • Received 25 October 2025
  • Revised 4 February 2026
  • Accepted 14 April 2026
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