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

Area of Science:

• Condensed Matter Physics
• High-Dimensional Topological Phases
• Quantum Materials

Background:

• Higher-dimensional topological phases are crucial for understanding lower-dimensional phenomena.
• Dimensional reduction procedures link topological phases across dimensions.
• Topological insulators (TIs) exhibit unique electronic properties protected by symmetries.

Purpose of the Study:

• To present a novel four-dimensional (4D) Z2 topological insulator (TI) model.
• To investigate topological responses and phase transitions in this 4D system.
• To explore potential experimental realization in cold atom systems.

Main Methods:

• Development of a Dirac-type model for a 4D Z2 TI with CP symmetry.
• Analysis of boundary modes and effects of perturbations.
• Introduction of electromagnetic and pseudo-electromagnetic fields to study topological responses.
• Investigation of topological phase transitions via bulk gap closure.

Main Results:

• The 4D Z2 TI model supports an odd number of Dirac cones on its 3D boundary.
• Perturbations lead to Weyl semimetallic phases or nodal spheres on the boundary.
• Exotic topological responses are described by (4+1)D mixed Chern-Simons theories.
• Topological phase transitions to Z TI phases with novel gapless structures are observed.

Conclusions:

• The proposed 4D Z2 TI model offers a platform for studying higher-dimensional topology.
• The system exhibits rich topological phenomena, including exotic boundary states and phase transitions.
• Cold atom experiments are proposed as a viable route for observing these predicted topological effects.