Band energy spectrum Bloch band 1 Bloch waves 1 Bosons 1 Chemical analysis 1 Edge localization 1 Eigenstates 1 Energy 1 Energy conversion 1 Gages 1 Gauge fields 1 Greens' function method 1 Ground state 1 Hamiltonians 1 Hermitians 1 Infinite boundary 1 Ladders 1 Linear response 1 Non-linear response 1 Nondegenerate 1 Performance efficiency 1 Power 1 Property 1 Self-healing 1 Self-healing materials 1 Spectroscopy 1 Topology 1 Two bands 1 Unique features 1