Why the critical temperature of high-$T_{\rm c}$ cuprate superconductors is so low: The importance of the dynamical vertex structure

TL;DR

This paper uses the dynamical vertex approximation to study the two-dimensional Hubbard model, revealing that dynamical vertex corrections significantly suppress the critical temperature of high-$T_c$ cuprate superconductors by screening interactions and reducing pairing interactions.

Contribution

It demonstrates that dynamical vertex corrections are key factors suppressing $T_c$ in cuprates, providing insights for achieving higher critical temperatures.

Findings

Local particle-particle diagrams screen the bare interaction at low frequencies.

Dynamical vertex corrections suppress antiferromagnetic spin fluctuations.

These corrections are identified as main oppressors of $T_c$.

Abstract

To fathom the mechanism of high-temperature ($T_{\rm c}$) superconductivity, the dynamical vertex approximation (D$\Gamma$A) is evoked for the two-dimensional repulsive Hubbard model. After showing that our results well reproduce the cuprate phase diagram with a reasonable $T_{\rm c}$ and dome structure, we keep track of the scattering processes that primarily affect $T_{\rm c}$. We find that local particle-particle diagrams significantly screen the bare interaction at low frequencies, which in turn suppresses antiferromagnetic spin fluctuations and hence the pairing interaction. Thus we identify dynamical vertex corrections as one of the main oppressors of $T_{\rm c}$, which may provide a hint toward higher $T_{\rm c}$'s.