Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

TL;DR

This paper investigates how fermion-fermion interactions influence the low-energy states of a 2D quadratic band crossing system on a kagome lattice, revealing competing instabilities and dominant charge density wave order.

Contribution

The study applies a renormalization group approach to analyze all fermionic interactions simultaneously, identifying fixed points, competing phases, and the dominant charge density wave instability in the system.

Findings

Fermionic interactions compete and flow towards fixed points depending on material parameters.

Charge density wave is the dominant instability among various competing phases.

Strong fluctuations suppress density of states, specific heat, and compressibility near the leading instability.

Abstract

We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-$1/2$ fermionic system on the kagom\'{e} lattice with a quadratic band crossing point. With the help of the renormalization group approach, we can treat all kinds of fermionic interactions on the the same footing and then establish the coupled energy-dependent flows of fermionic interaction parameters via collecting one-loop corrections, from which a number of interesting results are extracted in the low-energy regime. At first, various sorts of fermion-fermion interactions furiously compete with each other and are inevitably attracted by certain fixed point in the parameter space, which clusters into three qualitatively distinct regions relying heavily upon the structure parameters of materials. In addition, we notice that an instability accompanied by some symmetry breaking is triggered around different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over all other instabilities. Incidently, there exist several subleading ones including the $x$-current, bond density, and chiral plus s-wave superconductors. Finally, we realize that strong fluctuations nearby the leading instability prefer to suppress density of states and specific heat as well compressibility of quasiparticles in the lowest-energy limit.