Square-root topological semimetals

TL;DR

This paper introduces square-root topological semimetals, a new class of materials with topological band touchings at finite energies, inheriting protection from their squared Hamiltonians, and demonstrates their properties through models and physical realizations.

Contribution

It proposes the concept of square-root topological semimetals, revealing their topological features and boundary modes, and provides models and a spring-mass system realization.

Findings

Finite-energy Dirac cones and nodal lines identified.

Topological protection inherited from squared Hamiltonian.

Robustness of finite-energy Dirac points demonstrated in spring-mass model.

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.