Three-dimensional $\mathbb{Z}$ topological insulators without reflection symmetry

Abstract

In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been expanded by considering additional crystalline symmetries. Nevertheless, realizing a three-dimensional (3D), time-reversal symmetric (class AII) topological insulator (TI) in the absence of reflection symmetries, with a classification beyond the ${\mathbb{Z}}_2$ paradigm remains an open problem. In this work we present a general procedure for constructing such systems within the framework of projected topological branes (PTBs). In particular, a 3D projected brane from a "parent" four-dimensional topological insulator exhibits a $\mathbb{Z}$ topological classification, corroborated through its response to the inserted bulk monopole loop. More generally, PTBs have been demonstrated to be an effective route to performing dimensional reduction and embedding the topology of a $(d+1)$-dimensional "parent" Hamiltonian in $d$ dimensions, yielding lower-dimensional topological phases beyond the AZ classification without additional symmetries. Our findings should be relevant for the metamaterial platforms, such as photonic and phonic crystals, topolectric circuits, and designer systems.

arXiv comment5 pages, 4 figures, published version

References in corpus (29)

• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Imaging topological edge states in silicon photonics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological mechanics of gyroscopic metamaterials
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• A Four Dimensional Generalization of the Quantum Hall Effect
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Time Reversal Invariant Topologically Insulating Circuits
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Topological classification with additional symmetries from Clifford algebras
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Topological surface states in three-dimensional magnetic insulators
• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• Witten effect in a crystalline topological insulator
• Spin-charge Separated Solitons in a Topological Band Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• Multicellularity of delicate topological insulators
• $N$-band Hopf insulator
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Quantum spin Hall effect and spin-charge separation in a kagome lattice

Cited by in corpus (2)

• Topological insulators on fractal lattices: A general principle of construction
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases