# Topological Insulators and Inversion Symmetry

Goalie33
Hi,

I was curious if specific symmetries (or lack thereof) in crystal structure are necessary for the formation of topological insulators. Specifically, do we require that inversion symmetry (or inversion asymmetry) be present in the lattice in order to form the TI state?

Thanks,
Goalie33

## Answers and Replies

stone
No, the only symmetry that is required is Time reversal (I presume that by topological insulators you mean the Z2 variety). There are material realizations for both inversion symmetric and asymmetric crystals.

dipole
Inversion symmetry is convient though, because it allows for an easy way to determine if a material is a TI. (See Fu, Kane 2007)

Goalie33
Thanks,
I found that paper and it clarifies some questions. Originally, I wasn't sure if it was required or just convenient, but now I know.
Thanks!