Computing Symmetry-Protected Band Crossings and Boundary Nodes from Random Matrix Models

Topological materials protected by symmetry, such as nodal line materials, exhibit distinct characteristics from their non-symmetric counterpart. 

Quantifying these properties, such as the band-crossings and boundary modes, can be difficult for real materials with complicated Hamiltonians. 

Here, we model them with a random matrix model proposed by Wilkinson and coauthors, 

which combined translationa symmetry with the successful description of complex systems by random matrices. 

We investigate how to incorporate other symmeties, such as crystalline mirror symmetry,  to this model, 

and show the statistics of band crossing and boundary modes, which can be computed efficiently.