Square-root topological semimetals

Abstract

We propose topological semimetals generated by the square-root operation for tight-binding models in two and three dimensions, which we call square-root topological semimetals. The square-root topological semimetals host topological band touching at finite energies, whose topological protection is inherited from the squared Hamiltonian. Such a topological character is also reflected in emergence of boundary modes with finite energies. Specifically, focusing on topological properties of squared Hamiltonian in class AIII, we reveal that a decorated honeycomb (decorated diamond) model hosts finite-energy Dirac cones (nodal lines). We also propose a realization of a square-root topological semimetal in a spring-mass model, where robustness of finite-energy Dirac points against the change of tension is elucidated.

8 pages, 6 figures

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Cited by in corpus (21)

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• Observation of pi/2 modes in an acoustic Floquet system
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• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Square-root topological phase with time-reversal and particle-hole symmetry
• Matryoshka approach to Sine-Cosine topological models
• Square-root Floquet topological phases and time crystals
• 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
• Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Multiplicative topological semimetals
• Molecular-orbital representation with random U(1) variables
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry
• Exceptionally deficient topological square-root insulators
• Exceptional horns in $n$-root graphene and Lieb photonic ring lattices
• $q$th-root non-Hermitian Floquet topological insulators