Superconductivity at the onset of spin-density-wave order in a metal

Abstract

We revisit the issue of superconductivity at the quantum-critical point (QCP) between a 2D paramagnet and a spin-density-wave metal with ordering momentum (π,π). This problem is highly non-trivial because the system at criticality displays a non-Fermi liquid behavior and because the effective coupling constant λfor the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski, S. Sachdev, Phys.Rev.B 82, 075128 (2010)] has found that the renormalizations of the pairing vertex are stronger than in BCS theory and hold in powers of \log^2 (1/T), like in color superconductivity. We analyze the full gap equation and argue that, for QCP problem, summing up of the leading logarithms does not lead to a pairing instability. Yet, we show that superconductivity has no threshold and appears even if the coupling is set to be small, because subleading logarithmical renormalizations diverge and give rise to BCS-like \log(1/T_c) \propto 1/λ. We argue that the analogy with BCS is not accidental as at small coupling superconductivity at a QCP predominantly comes from fermions which retain Fermi liquid behavior at criticality. We computed T_c for the actual λ\sim 1, and found that both Fermi-liquid and non-Fermi liquid fermions contribute to the pairing. The value of T_c agrees well with the numerical results.

27 pages, 7 figures. Replaced with the published version (main text and supplementary material)

References in corpus (18)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Funtional Renormalization Group Study of the Pairing Symmetry and Pairing Mechanism of the FeAs Based High Temperature Superconductors
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Quantum Criticality
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• A Sharp Peak of the Zero-Temperature Penetration Depth at Optimal Composition in BaFe2(As1-xPx)2
• Critical fermi surfaces and non-fermi liquid metals
• Strongly Correlated Superconductivity: a plaquette Dynamical mean field theory study
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Antiferromagnetically Driven Electronic Correlation in Iron Pnictides and Cuprates
• Valley density-wave and multiband superconductivity in Fe-pnictides
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates
• A controlled expansion for certain non-Fermi liquid metals
• Extended quantum criticality of low-dimensional superconductors near a spin-density-wave instability
• Spin-liquid model of the sharp resistivity drop in $L{a}_{1.85}B{a}_{0.125}Cu{O}_4$

Cited by in corpus (36)

• Charge-density-wave order with momentum $(2Q,0)$ and $(0,2Q)$ within the spin-fermion model: continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Frustration and quantum criticality
• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
• Normal-state nodal electronic structure in underdoped high-Tc copper oxides
• Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency
• Competing Orders in a Nearly Antiferromagnetic Metal
• Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates
• Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $\gamma$-model and its phase diagram at $T=0$. The case $0<\gamma <1$
• Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene
• How many quantum phase transitions exist inside the superconducting dome of the iron pnictides?
• Normal state properties of quantum critical metals at finite temperature
• Quantum-critical pairing in electron-doped cuprates
• Enhancement of superconductivity at the onset of charge-density-wave order in a metal
• The special role of the first Matsubara frequency for superconductivity near a quantum-critical point -- the non-linear gap equation below $T_c$ and spectral properties in real frequencies
• The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal
• Quasiparticle interaction function in a 2D Fermi liquid near an antiferromagnetic critical point
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study
• Free energy and specific heat near a quantum critical point of a metal
• Order parameter fluctuation and ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}{\mathrm{K}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• Quantum criticality preempted by nematicity
• Exotic Superconductivity Through Bosons in a Dynamical Cluster Approximation
• Superconductivity out of a non-Fermi liquid. Free energy analysis
• Superconducting and charge-density-wave orders in the spin-fermion model: a comparative analysis
• Robustness of quantum critical pairing against disorder
• Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations
• Strain-induced long-range charge-density wave order in the optimally doped Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_6$ superconductor
• Strong coupling behavior of the neutron resonance mode in unconventional superconductors
• The Transformation of the Superconducting Gap to an Insulating Pseudogap at a Critical Hole Density in the Cuprates
• Odd frequency pairing in a quantum critical metal
• Enhanced Pairing of Quantum Critical Metals Near d=3+1
• Pseudogap in electron-doped cuprates: thermal precursor to magnetism