Opposite sigma and pi hopping signs in a p-orbital chain
= Opposite sigma and pi hopping signs in a p-orbital chain
For a chain along $x$, translated $p_z$ orbitals form a side-on bonding combination at $k=0$, whereas translated $p_x$ orbitals form an end-on bonding combination at $k=\pi/a$. With $E=\epsilon+2t\cos ka$ and identically translated orbitals, these correspond to $t_\pi<0$ and $t_\sigma>0$. Changing the sign convention of the hopping Hamiltonian changes the parameter signs, not the physical band extrema.