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

TL;DR

This paper investigates how superconductivity influences the position of quantum critical points related to magnetic and nematic orders in pnictides and cuprates, revealing different shift behaviors for SDW and nematic orders.

Contribution

It provides a detailed comparison of quantum critical point shifts under superconductivity, highlighting the role of Fermi surface effects and their implications for phase diagrams.

Findings

SDW quantum critical point shifts by order |Delta| in superconductors.

Ising-nematic order shift remains of order |Delta|^2 due to Fermi surface effects.

Nematic order is linked to SDW order squared in pnictides, but not in 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.