  Here, we propose quantum spin Hall-like phononic states in van der Waals
bilayer systems with antiferromagnetic ordering. Antiferromagnetic ordering in
bilayer systems with small interlayer interaction makes the total Chern number
zero, where the Chern numbers for each layer are opposite to each other. In
bilayer CrI3 where antiferromagnetic ordering has been experimentally
demonstrated, we show that the quantum spin Hall-like states appear with
spatially separated chiral edge modes.
