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Triplet superconductivity supported by an X9 high-order Van Hove singularity

Chethan Sanjeevappa1,*, Anirudh Chandrasekaran1,2,†, and Joseph J. Betouras1,‡

  • *Contact author: C.Sanjeevappa@lboro.ac.uk
  • †Contact author: a.chandrasekaran@fkf.mpg.de
  • ‡Contact author: J.Betouras@lboro.ac.uk
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Phys. Rev. Research 8, 023055 – Published 16 April, 2026

DOI: https://doi.org/10.1103/jdr9-4f95

Abstract

We study a fourfold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of X9 type at the Fermi energy. First, we analyze in detail its form, type, and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature Tc on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate Sr3Ru2O7, which has been shown to exhibit this type of singularity.

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Phys. Rev. Research 8, 023055– Published 16 April, 2026
  • Received 27 December 2025
  • Accepted 18 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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