Superconductivity near the (2+1)-Dimensional Ferromagnetic Quantum Critical Point

We utilize both analytical and numerical methods to study the superconducting transition temperature T_\rm c near a fermionic quantum critical point (QCP) using a model constructed by Xu et al. Phys. Rev. X 7, 031059 (2017) as an example. In this model, the bosonic critical fluctuation plays the role of pairing glue for the Cooper pairs, and we use a Bardeen–Cooper–Schrieffer-type mean-field theory to estimate T_\rm c. We further argue that the T_\rm c computed from the BCS theory approximates a pseudogap temperature T_\rm PG, instead of the Berezinskii–Kosterlitz–Thouless transition temperature T_\rm KT, which is confirmed by our determinant quantum Monte Carlo simulation. Moreover, due to the fact that electron density of state starts to deplete at T_\rm PG, the critical scaling of the underlying QCP is also affected below T_\rm PG. Thus, when studying the critical behavior of fermionic QCPs, we need to monitor that the temperature is above T_\rm PG instead of T_\rm KT. This was often ignored in previous studies.