Robust edge states in periodically strained graphene

A periodic pseudo-magnetic field can be achieved by depositing graphene onto a patterned substrate, making it possible to explore moiré-like physics with straintronics. Recent studies have shown that periodically strained graphene exhibits isolated flat bands [1] with opposite valley Chern numbers due to time-reversal symmetry [2]. Interestingly, despite a vanishing total Chern number, in-gap edge states are found in zigzag nanoribbon geometries. Although such edge states are not topologically protected [3], they appear surprisingly ubiquitous. This work investigates the emergence and robustness of the in-gap edge states in periodically strained graphene with various superlattice structures. In different configurations, the band structures always resemble those of a nanoribbon in an external periodic magnetic field, as long as the ribbon’s termination preserves the valley pseudospin. The edge states remain against variations of ribbon width, strain period and intensity, and disorder potentials. As an application, we show that low-energy edge states can be turned on and off by using an out-of-plane electric field and a hBN substrate. Our results prove that strained graphene superlattices are promising for building straintronics devices.

[1] V. T. Phong and E. J. Mele, PRL 128, 176406 (2022).

[2] Md. T. Mahmud, D. Zhai, and N. Sandler. Nano letters 23, 7725 (2023)

[2] J. Li, A. F. Morpurgo, M. Büttiker, and I. Martin. PRB 82, 245404 (2010).