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Here, we propose quantum spin Hall-like phononic states in van der Waalsbilayer systems with antiferromagnetic ordering. Antiferromagnetic ordering inbilayer systems with small interlayer interaction makes the total Chern numberzero, where the Chern numbers for each layer are opposite to each other. Inbilayer CrI3 where antiferromagnetic ordering has been experimentallydemonstrated, we show that the quantum spin Hall-like states appear withspatially separated chiral edge modes.

Quantum Spin Hall-like Phononic States in van der Waals Bilayers with Antiferromagnetic Ordering