2014/11/14 by Kelly Ann Pawlak, James M. Murray, Oskar Vafek
Materials Science · Mathematics · Physics and Astronomy · #Bilayer graphene #Condensed matter physics #Electron #Fermion #Graphene #Graphene research and applications #Hamiltonian (control theory) #Instability #Mathematics #Physics #Quadratic equation #Quantum and electron transport phenomena #Quantum mechanics #Scattering #Superconductivity #Topological Materials and Phenomena #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.91.134509
published as Phys. Rev. B 91, 134509 (2015) · 7+3 Pages, 9 Figures
arxiv created 2014/11/14 · openalex publication_date 2015/04/20 · arxiv updated 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
For two-dimensional single-valley quadratic band crossing systems with weak repulsive electron-electron interactions, we show that upon introducing a chemical potential, particle-hole order is suppressed and superconductivity becomes the leading instability. In contrast to the two-valley case realized in bilayer graphene, the single-valley quadratic band touching is protected by crystal symmetries, and the different symmetries and number of fermion flavors can lead to distinct phase instabilities. Our results are obtained using a weak-coupling Wilsonian renormalization group procedure on a low-energy effective Hamiltonian relevant for describing electrons on checkerboard or kagome lattices. In fourfold-symmetric systems, we find that d- and s-wave superconductivity are realized for short-ranged (Hubbard) and longer-ranged (forward scattering) interactions, respectively. In the sixfold-symmetric case, we find either s-wave superconductivity or no superconducting instability.