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

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.