Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown

Abstract

Weyl semimetals (WSMs) constitute a 3D phase with linearly-dispersing Weyl excitations at low energy, which lead to unusual electrodynamic responses and open Fermi arcs on boundaries. We derive a simple criterion to identify and characterize WSMs in an interacting setting using the exact electronic Green's function at zero frequency, which defines a topological Bloch Hamiltonian. We apply this criterion by numerically analyzing, via cluster and other methods, interacting lattice models with and without time-reversal symmetry. We identify various mechanisms for how interactions move and renormalize Weyl fermions. Our methods remain valid in the presence of long-ranged Coulomb repulsion. Finally, we introduce a WSM-like phase for which our criterion breaks down due to fractionalization: the charge-carrying Weyl quasiparticles are orthogonal to the electron.

4+7 pages; 3+2 figs; v2: as published in PRL, extra clarifications, added references

References in corpus (6)

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• Simplified topological invariants for interacting insulators
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• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
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Cited by in corpus (15)

• Chiral anomaly and transport in Weyl metals
• Thermoelectric properties of Weyl and Dirac semimetals
• Correlation effects in double-Weyl semimetals
• Density wave instabilities and surface state evolution in interacting Weyl semimetals
• Weyl semimetal from spontaneous inversion symmetry breaking in pyrochlore oxides
• Magnetic-field-induced nonlinear transport in HfTe5
• Quantum Monte Carlo simulation of topological phase transitions
• Large anomalous magnetic moment in three-dimensional Dirac and Weyl semimetals
• Quasiparticle Properties under Interactions in Weyl and Nodal Line Semimetals
• Topological property of a $t_{2g}^5$ system with a honeycomb lattice structure
• Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions
• Berry curvature associated to Fermi arcs in continuum and lattice Weyl systems
• Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals
• Holographic Topological Semimetals