Quantum critical point shifts under superconductivity: the pnictides and the cuprates

Abstract

We compare the position of an ordering transition in a metal to that in a superconductor. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |Delta|, where Delta is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the ~ |Delta|^2 shift predicted by theories of competing orders which ignore Fermi surface effects. For Ising-nematic order, the shift from Fermi surface effects remains of order |Delta|^2. We discuss implications of these results for the phase diagrams of the cuprates and the pnictides. We conclude that recent observations imply that the Ising-nematic order is tied to the square of the SDW order in the pnictides, but not in the cuprates.

11 pages, 8 figures

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Cited by in corpus (10)

• Energy gaps in high-transition temperature cuprate superconductors
• Phase competition in trisected superconducting dome
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Instabilities near the onset of spin density wave order in metals
• Quantum critical properties of a metallic spin density wave transition
• Stability of Quantum Critical Points in the Presence of Competing Orders
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Quasiclassical description of a superconductor with a spin density wave
• Two-loop disorder effects on the nematic quantum criticality in $d$-wave superconductors
• Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors