Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

Abstract

Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. In this work, we introduce a model describing a semimetal in four spatial dimensions, whose nodal points act like tensor monopoles in momentum space. This system is shown to exhibit monopole-to-monopole phase transitions, as signaled by a change in the value of the topological Dixmier-Douady invariant as well as by the associated surface states on its boundary. We use this model to reveal an intriguing "4D parity magnetic effect", which stems from a parity-type anomaly. In this effect, topological currents are induced upon time-modulating the separation between the fictitious monopoles in the presence of a magnetic perturbation. Besides its theoretical implications in both condensed matter and quantum field theory, the peculiar 4D magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.

References in corpus (13)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• The Chiral Magnetic Effect
• Topological response in Weyl semimetals and the chiral anomaly
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Topological quantum matter in synthetic dimensions
• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Torsion, Parity-odd Response and Anomalies in Topological States
• Linear optical conductivity of chiral multifold fermions
• Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementations
• Pseudospin 3/2 Fermions, Type-II Weyl Semimetals and Critical Weyl Semimetals in Tricolor Cubic Lattice

Cited by in corpus (2)

• Fermionic dualities with axial gauge fields
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric