Square-root topological semimetals

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.

Automated summary

This study introduces topological semimetals generated by the square-root operation in two and three dimensions for tight-binding models, termed square-root topological semimetals. These semimetals exhibit topological band touching at finite energies and emergence of boundary modes. The research also shows that a decorated honeycomb (decorated diamond) model in class AIII hosts finite-energy Dirac cones (nodal lines) and demonstrates the robustness of finite-energy Dirac points in a spring-mass model.