Quantum critical scaling of gapped phases in nodal-line semimetals

Abstract

We study the effect of short range interactions in three dimensional nodal-line semimetals with linear band crossings. We analyze the Yukawa theories for gapped instabilities in the charge, spin and superconducting channels using the Wilsonian renormalization group framework, employing a large number of fermion flavors $N_f$ for analytical control. We obtain stable non-trivial fixed points and provide a unified description of the critical exponents for the ordering transitions in terms of the number of order parameter components $N_b$ systematically to order $1/N_f$. We show that in all cases, the dynamical exponent z = 1 in one loop, whereas $1/N_f$ corrections to various exponents follow from the anomalous dimension of the bosonic fields only.

arXiv comment7 pages, 2 figures

References in corpus (48)

• The electronic properties of graphene
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Topological nodal semimetals
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Dirac Line Nodes in Inversion Symmetric Crystals
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Weyl points and line nodes in gapless gyroid photonic crystals
• Topological Mott Insulators
• Interactions and phase transitions on graphene's honeycomb lattice
• Charge Transport in Weyl Semimetals
• Topological semi-metals with line nodes and drumhead surface states
• Merging of Dirac points in a two-dimensional crystal
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Symmetry Demanded Topological Nodal-line Materials
• Experimental discovery of nodal chains
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Long-range Coulomb interaction in nodal-ring semimetals
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Interacting Weyl fermions: Phases, phase transitions and global phase diagram
• Observation of nodal-line semimetal with ultracold fermions in an optical lattice
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
• Chiral non-Fermi Liquids
• Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Weyl and Dirac Loop Superconductors
• Stacking Faults, Bound States, and Quantum Hall Plateaus in Crystalline Graphite
• Instabilities of Weyl-loop semi-metals
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions
• Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling
• Universal phase transition and band structures for spinless nodal-line and Weyl semimetals
• Marginal Fermi liquid versus excitonic instability in 3D Dirac semimetals
• Superconducting States for Semi-Dirac Fermions at Zero and Finite Magnetic Fields
• 3D Quantum Anomalous Hall Effect in Hyperhoneycomb Lattices
• Strong Coupling Expansion in a Correlated Three-Dimensional Topological Insulator
• Hidden Charge Order of Interacting Dirac Fermions on the Honeycomb Lattice

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• Electronic interactions in a vacancy-engineered honeycomb lattice: Transition from a nodal-line semimetal to a magnetic insulator