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arXiv · 2509.25318

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

Veronika C. Stangier·Daniel E. Sheehy·Jörg Schmalian
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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 SYK-inspired framework for Dirac systems introduced by Kim et al.[1], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.

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Veronika C. Stangier, Daniel E. Sheehy, Jörg Schmalian. 2025-09-29. Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems. https://doi.org/10.1103/x7lc-ztqn

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