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

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 kagomé 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.

22 pages, 12 figures; Nulcear Physics B 966, 115371 (2021)

References in corpus (31)

• The electronic properties of graphene
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• A new magnetic field dependence of Landau levels on a graphene like structure
• Zero modes of tight binding electrons on the honeycomb lattice
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• Renormalization group theory of nematic ordering in d-wave superconductors
• Theory of the nodal nematic quantum phase transition in superconductors
• Density dependent exchange contribution to $\partial \mu /\partial n$ in extrinsic graphene
• Electronic multicriticality in bilayer graphene
• Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids
• A semi-Dirac point in the Hofstadter spectrum
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Experimental observables near a nematic quantum critical point in the pnictide and cuprate superconductors
• Stability of Quantum Critical Points in the Presence of Competing Orders
• Unexpected impact of magnetic disorder on multiband superconductivity
• Spontaneous quantum Hall effect via thermally induced quadratic Fermi point
• Superconductivity of disordered Dirac fermions in graphene
• Charge density waves in Weyl semimetals
• The fate of interaction-driven topological insulators under disorder
• Anomalous Scaling of the Penetration Depth in Nodal Superconductors
• Disorder effects in correlated topological insulators
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Velocity renormalization of nodal quasiparticles in d-wave superconductors
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Possible instabilities in quadratic and cubic nodal line fermion systems with correlated interactions
• Unconventional non-Fermi liquid state caused by nematic criticality in cuprates
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems

Cited by in corpus (5)

• Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Renormalization group study of systems with quadratic band touching
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals