Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene

TL;DR

This paper investigates how short-range fermion interactions influence phase transitions in rhombohedral trilayer graphene, identifying fixed points and dominant states like various superconducting and pair-density-wave phases through renormalization group analysis.

Contribution

It introduces a comprehensive renormalization group framework accounting for all one-loop corrections to analyze interaction-driven phase transitions in the material.

Findings

Identification of four fixed points dictating low-energy phases.

Dominant states include spin-singlet and triplet superconductivity.

Interactions lead to specific symmetry-breaking instabilities.

Abstract

The effects of short-range fermion-fermion interactions on the low-energy properties of rhombohedral trilayer graphene are comprehensively investigated using the momentum-shell renormalization group method. We take into account all one-loop corrections and establish the energy-dependent coupled evolutions of independent fermionic couplings that carry the physical information stemming from the interplay of various fermion-fermion interactions. With detailed numerical analysis, we observe that the ferocious competition among all fermion-fermion interactions can drive fermionic couplings to four distinct fixed points, dubbed $\textrm{FP}_{1}$, $\textrm{FP}_{2}$, $\textrm{FP}_{3}$, and $\textrm{FP}_{4}$, in the interaction-parameter space. These fixed points primarily dictate the fate of the system in the low-energy regime and are always associated with some instabilities characterized by specific symmetry breakings, leading to certain phase transitions. To determine the favorable states arising from the potential phase transitions, we introduce a number of fermion-bilinear source terms to characterize the underlying candidate states. By comparing their related susceptibilities, we find that the dominant states correspond to spin-singlet superconductivity, spin-triplet pair-density-waves, and spin-triplet superconductivity for fixed points $\textrm{FP}_{1,3}$, $\textrm{FP}_{2}$, and $\textrm{FP}_{4}$, respectively. These provide valuable insights into the low-energy properties of rhombohedral trilayer graphene and analogous materials.