Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals

TL;DR

This study investigates how attractive fermion interactions induce Cooper instability and potential superconductivity in two-dimensional semi-Dirac semimetals, revealing conditions under which the Cooper theorem is violated or restored.

Contribution

It demonstrates that Cooper instability depends on interaction strength, chemical potential, and impurities, providing new insights into unconventional superconductivity in semi-Dirac semimetals.

Findings

Cooper instability occurs only if interaction exceeds a critical value at zero chemical potential.

Introducing finite chemical potential restores the Cooper theorem and induces phase transition.

Impurities can both harm and enhance Cooper instability depending on conditions.

Abstract

Cooper instability associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion-fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead Cooper instability can be generated only if the absolute strength of fermion-fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the Cooper instability at zero chemical potential, which in principle are harmful to Cooper instability although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the Cooper instability is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.