Coulomb interaction at Superconductor to Mott-insulator transition

TL;DR

This paper investigates how long-range Coulomb interactions influence the superconductor to Mott-insulator transition, revealing a critical number of fields for the transition type and providing a detailed RG analysis.

Contribution

It provides a detailed one-loop RG analysis of Coulomb effects on the transition, challenging previous results and exploring behavior near two dimensions.

Findings

Second order transition for N ≥ 55.39 near d=3

First order transition for N < 55.39 near d=3

Disagreement with Fisher and Grinstein's results at d=3

Abstract

We reexamine the effects of long-range Coulomb interaction on the onset of superconductivity. We use the model of N complex scalar fields with the Coulomb interaction studied first by Fisher and Grinstein (FG). We find that near d=3 space dimension, the system undergoes second order phase transition if $N \ge 55.39$, but undergoes fluctuation driven first order transition if $N < 55.39$. We give the detailed derivation of the field theory Renormalization Group (RG) of this model to one loop. Our RG results disagree with those of FG at and near d=3. Possible scenario at d=2 is proposed.