Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases

Abstract

Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of four-dimensional (4D) ${\mathbb{Z}}_2$ topological insulator (TI) protected by $\mathcal{C}\mathcal{P}$-symmetry, whose 3D boundary supports an odd number of Dirac cones. A specific perturbation splits each bulk massive Dirac cone into two valleys separated in energy-momentum space with opposite second Chern numbers, in which the 3D boundary modes become a nodal sphere or a Weyl semimetallic phase. By introducing the electromagnetic (EM) and pseudo-EM fields, exotic topological responses of our 4D system are revealed, which are found to be described by the (4+1)D mixed Chern-Simons theories in the low-energy regime. Notably, several topological phase transitions occur from a $\mathcal{C}\mathcal{P}$-broken ${\mathbb{Z}}_2$ TI to a $\mathbb{Z}$ TI when the bulk gap closes by giving rise to exotic double-nodal-line/nodal-hyper-torus gapless phases. Finally, we propose to probe experimentally these topological effects in cold atoms.

Some typos have been corrected, and the relevant references have been added

References in corpus (19)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Topological response in Weyl semimetals and the chiral anomaly
• The space group classification of topological band insulators
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• 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
• Topological Euler class as a dynamical observable in optical lattices
• Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Chiral Anomaly in Interacting Condensed Matter Systems
• Non-Abelian tensor Berry connections in multi-band topological systems
• Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling
• Chiral magnetic effect in three-dimensional optical lattices
• Non-linear ballistic response of quantum spin-Hall edge states
• Non-Hermitian chiral anomalies

Cited by in corpus (5)

• Topological Insulators with Hybrid-order Boundary States
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Second Euler number in four dimensional synthetic matter
• Synthetic spin-orbit coupling for the multispin models in optical lattices
• Eight-dimensional topological systems simulated using time-space crystalline structures