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We show that the $\nu=8$ integer quantum Hall state can support Majorana zeromodes at domain walls between its two different stable chiral edge phaseswithout superconductivity. This is due to the existence of an edge phase thatdoes not support gapless fermionic excitations; all gapless excitations arebosonic in this edge phase. Majorana fermion zero modes occur at a domain wallbetween this edge phase and the more conventional one that does support gaplessfermions. Remarkably, due to the chirality of the system, the topologicaldegeneracy of these zero modes has exponential protection, as a function of therelevant length scales, in spite of the presence of gapless excitations,including gapless fermions. These results are compatible with chargeconservation, but do not require it. We discuss generalizations to otherinteger and fractional quantum Hall states, and classify possible mechanismsfor appearance of Majorana zero modes at domain walls.

Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States