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Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems

Veronika C. Stangier1, Daniel E. Sheehy2, and Jörg Schmalian1,3

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Phys. Rev. B 113, 085119 – Published 10 February, 2026

DOI: https://doi.org/10.1103/x7lc-ztqn

Abstract

We study two-dimensional massless Dirac fermions at neutrality, coupled to bosonic modes through a Yukawa interaction. We then examine the intriguing possibility that such a system, devoid of carriers at zero temperature, might nevertheless exhibit superconductivity. Remarkably, we find that superconductivity emerges in the vicinity of Gross-Neveu quantum criticality, provided the fermions cease to behave as well-defined quasiparticles, that is, once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined fermions do not superconduct, whereas ill-defined ones do. We analyze four symmetry-distinct bosonic modes, each capable of driving normal-state criticality and, in three of the four cases, giving rise to a distinct superconducting phase. While phase fluctuations are strong in this regime, we argue that they do not destroy the superconducting state. We further characterize the resulting pairing states for a concrete Dirac model of spin-orbit coupled systems with orbitals of different parity. Our results are obtained using the Sachdev-Ye-Kitaev (SYK)-inspired framework for Dirac systems introduced by Kim et al. [Dirac fast scramblers, Phys. Rev. B 103, L081113 (2021)], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.

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Phys. Rev. B 113, 085119– Published 10 February, 2026
  • Received 13 October 2025
  • Revised 27 November 2025
  • Accepted 15 December 2025
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