Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions

Abstract

In this article, we put forward a practical but generic approach towards constructing a large family of $(3+1)$ dimension lattice models which can naturally lead to a single Weyl cone in the infrared (IR) limit. Our proposal relies on spontaneous charge $U(1)$ symmetry breaking to evade the usual no-go theorem of a single Weyl cone in a 3d lattice. We have explored three concrete paths in this approach, all involving fermionic topological symmetry protected states (SPTs). Path a) is to push a gapped SPT in a 3d lattice with time-reversal symmetry (or $T$-symmetry) to a gapless topological quantum critical point (tQCP) which involves a minimum change of topologies,i.e. $\delta N_w=2$ where $\delta N_w$ is the change of winding numbers across the tQCP. Path b) is to peal off excessive degrees of freedom in the gapped SPT via applying $T$-symmetry breaking fields which naturally result in a pair of gapless nodal points of real fermions. Path c) is a hybrid of a) and b) where tQCPs, with $\delta N_w\ge 2$, are further subject to time-reversal-symmetry breaking actions. In the infrared limit, all the lattice models with single Weyl fermions studied here are isomorphic to either a tQCP in a DIII class topological superconductor with a protecting $T$-symmetry, or its dual, a $T$-symmetry breaking superconducting nodal point phase, and therefore form an equivalent class. For a generic $T$-symmetric tQCP along Path a), the conserved-charge operators span a six-dimensional linear space while for a $T$-symmetry breaking gapless state along Path b), c), charge operators typically span a two-dimensional linear space instead. Finally, we pinpoint connections between three spatial dimensional lattice chiral fermion models and gapless real fermions that can naturally appear in superfluids or superconductors studied previously.

arXiv comment25 pages, 9 figures, typos corrected. Comments are welcome

References in corpus (42)

• Topological Insulators
• Anyons in an exactly solved model and beyond
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Periodic table for topological insulators and superconductors
• Zoo of quantum-topological phases of matter
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Topological Superconductivity and Superfluidity
• The effects of interactions on the topological classification of free fermion systems
• Weyl Metals
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Topological phases and surface flat bands in superconductors without inversion symmetry
• Classification of interacting electronic topological insulators in three dimensions
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Protected boundary states in gapless topological phases
• Topological phases protected by point group symmetry
• Nodal Liquid Theory of the Pseudo-Gap Phase of High-Tc Superconductors
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Topology and edge modes in quantum critical chains
• Emergence of supersymmetry at a critical point of a lattice model
• Intrinsically Gapless Topological Phases
• Topological Blount's theorem of odd-parity superconductors
• Topologically stable gapless phases of time-reversal invariant superconductors
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Emergence of supersymmetric quantum electrodynamics
• Superconducting quantum criticality of topological surface states at three loops
• Gapless Fermions and Quantum Order
• Onsager symmetries in $U(1)$-invariant clock models
• Quantized axial charge of staggered fermions and the chiral anomaly
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States
• Cusps near Topological Phase Transitions: Signatures of Majorana fermions and interactions with fluctuations
• Topological Quantum Critical Points in Strong Coupling limits: Global Symmetries and Strongly Interacting Majorana Fermions
• A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Exact Chiral Symmetries of 3+1D Hamiltonian Lattice Fermions
• Dynamic critical exponents as an emergent property at interacting topological quantum critical points