# Chiral symmetry in Su-Schrieffer-Heeger (SSH) model

We know that the hamiltonian SSH model in the presence of on-site potential(V) can be written on the basis of the Pauli matrix.

$$h(k)=V\sigma_0+h_x\sigma_x+h_y\sigma_y,$$

and the term V breaks the chiral symmetry by shifting the zero energy topological edge state.

So, my question is: Does the identical matrix affect topology?