# Kitaev chaing, time reversel symmetry, particle hole symmetry

I was wondering if the Kitaev chain has time reversal symmetry.

I think it probably doesn't because by staking Kitaev chains it is possible to create a so called Chern insulator with propagating chiral edge modes. This topological phase should be very similar to the Integer Quantum Hall Effect where time reversal symmetry is also broken.

Is it indeed true that the Kitaev chain does not have time reversal symmetry?

Is there a way that you can directly see this from the Hamiltonian: $$H(k) = (-\mu - 2t \cos(k)) \tau_z + 2 \Delta \sin(k) \tau_y$$

I know that the Kitaev chain has particle hole symmetry. (That is the reason why the Majorana zero modes are protected when the Kitaev chain is in the topological phase).

Can a system in general have time reversal symmetry and particle hole symmetry at the same time. Is there a way how you can quickly see if a Hamiltonian has time reversal symmetry or particle hole symmetry?