  In this Letter we study the effect of topological zero modes on entanglement
Hamiltonians and entropy of free chiral fermion systems in (1+1)d. We show how
Riemann-Hilbert solutions combined with finite rank perturbation theory allow
us to obtain explicit expressions for entanglement Hamiltonians. We consider
both chiral Majorana and Dirac fermions, and explore the effects of boundary
conditions (periodic/anti-periodic for Majorana and generic for Dirac) and
associated zero modes on entanglement. In the periodic sector, we derive
explicitly the non-local contribution to the entanglement Hamiltonian due to
the zero mode, and show an exact expression for the change in entanglement
entropy due to the zero mode.
