Symmetry-protected topological photonic crystal in three dimensions

• Published in: Nature physics Vol. 12; no. 4; pp. 337 - 340
• Main Authors: Lu, Ling, Fang, Chen, Fu, Liang, Johnson, Steven G., Joannopoulos, John D., Soljačić, Marin
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.04.2016; Nature Publishing Group; Nature Publishing Group (NPG)
• Subjects: 639/624/399/1022; 639/766/119/2792; Atomic; Atoms & subatomic particles; Bosons; Classical and Continuum Physics; Complex Systems; Condensed Matter Physics; Cones; Insulators; letter; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Phases; Physics; Quantum physics; solar (photovoltaic), solar (thermal), solid state lighting, phonons, thermal conductivity, thermoelectric, defects, mechanical behavior, charge transport, spin dynamics, materials and chemistry by design, optics, synthesis (novel materials), synthesis (self-assembly), synthesis (scalable processing); Symmetry; Theoretical; Three dimensional; Topology; Two dimensional
• ISSN: 1745-2473; 1745-2481
• DOI: 10.1038/nphys3611

Crystal symmetries may protect single Dirac cones on the surface of a photonic crystal, creating a photonic analogue of a three-dimensional solid-state topological insulator. Topology of electron wavefunctions was first introduced to characterize the quantum Hall states in two dimensions discovered in 1980 (ref.  1 ). Over the past decade, it has been recognized that symmetry plays a crucial role in the classification of topological phases, leading to the broad notion of symmetry-protected topological phases 2 . As a primary example, topological insulators 3 , 4 are distinguished from normal insulators in the presence of time-reversal symmetry ( ). A three-dimensional (3D) topological insulator 3 , 4 , 5 , 6 exhibits an odd number of protected surface Dirac cones, a unique property that cannot be realized in any 2D systems. Importantly, the existence of topological insulators requires Kramers’ degeneracy in spin–orbit coupled electronic materials; this forbids any direct analogue in boson systems 7 . In this report, we discover a 3D topological photonic crystal phase hosting a single surface Dirac cone, which is protected by a crystal symmetry 8 , 9 , 10 —the nonsymmorphic glide reflection 11 , 12 , 13 rather than . Such a gapless surface state is fully robust against random disorder of any type 14 , 15 . This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D ‘generalized Dirac points’ discovered in the bulk of our crystal. The Z 2 bulk invariant is characterized through the evolution of Wannier centres 16 . Our proposal—readily realizable using ferrimagnetic materials at microwave frequencies 17 , 18 —expands the scope of 3D topological materials from fermions to bosons.