Enhancement of superconductivity at the onset of charge-density-wave order in a metal

TL;DR

This paper investigates how superconductivity is enhanced near the onset of charge-density-wave order in cuprates, showing that charge-fermion interactions lead to increased critical temperatures and that magnetic fields confine superconductivity to the quantum-critical point.

Contribution

It provides a semi-phenomenological model linking charge-density-wave fluctuations to superconductivity and demonstrates the enhancement of $T_c$ near CDW onset, supported by microscopic and magnetic field analyses.

Findings

Superconducting $T_c$ is proportional to charge-fermion coupling near CDW transition.

Charge-fermion coupling is comparable to spin-fermion coupling, enhancing $T_c$.

Magnetic field reduces $T_c$ and confines superconductivity to the CDW quantum-critical point.

Abstract

We analyze superconductivity in the cuprates near the onset of an incommensurate charge density wave (CDW) order with momentum ${\bf Q} = (Q,0)/(0,Q)$, as observed in the experiments. We first consider a semi-phenomenological charge-fermion model in which hot fermions, separated by ${\bf Q}$, attract each other by exchanging soft CDW fluctuations. We find that in a quantum-critical region near CDW transition, $T_c = A {\bar g}_c$, where ${\bar g}_c$ is charge-fermion coupling and $A$ is the prefactor which we explicitly compute. We then consider the particular microscopic scenario in which CDW order parameter emerges as a composite field made out of primary spin-density-wave fields. We show that charge-fermion coupling ${\bar g}_c$ is of order of spin-fermion coupling ${\bar g}_s$. As the consequence, superconducting $T_c$ is substantially enhanced near the onset of CDW order. Finally we analyze the effect of an external magnetic field $H$. We show that, as $H$ increases, optimal $T_c$ decreases and the superconducting dome becomes progressively more confined to the CDW quantum-critical point. These results are consistent with the experiments.