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 \(\mid\Delta\mid\), 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 \(\sim\mid\Delta\mid\) 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 \(\mid\Delta\mid 2\). 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.