# Physics:Edge states

In physics, Edge states are the topologically protected electronic states that exist at the boundary of the material and cannot be removed without breaking the system's symmetry.[1][2]

## Background

Schematic for illustration of edge states in typical two-dimensional material. The conduction band (CB), edge states (ES) and valance band (VB) are characterized by positive, zero and negative energy eigenvalues.

In solid-state physics, quantum mechanics, materials science, physical chemistry and other several disciplines we study the electronic band structure of materials primarily based on the extent of the band gap, the gap between highest occupied valance bands and lowest unoccupied conduction bands. We can represent the possible energy level of the material that provides the discrete energy values of all possible states in the energy profile diagram by solving the Hamiltonian of the system. This solution provides the corresponding energy eigenvalues and eigenvectors. Based on the energy eigenvalues, conduction band are the high energy states (E>0) while valance bands are the low energy states (E<0). In some materials, for example, in graphene and zigzag graphene quantum dot, there exists the energy states having energy eigenvalues exactly equal to zero (E=0) besides the conduction and valance bands. These states are called edge states which modifies the electronic and optical properties of the materials significantly.[3][4][5][6]

## References

1. Kim, Sungmin; Schwenk, Johannes; Walkup, Daniel; Zeng, Yihang; Ghahari, Fereshte; Le, Son T.; Slot, Marlou R.; Berwanger, Julian et al. (2021-05-14). "Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy" (in en). Nature Communications 12 (1): 2852. doi:10.1038/s41467-021-22886-7. ISSN 2041-1723. PMID 33990565. Bibcode2021NatCo..12.2852K.
2. Young, A. F.; Sanchez-Yamagishi, J. D.; Hunt, B.; Choi, S. H.; Watanabe, K.; Taniguchi, T.; Ashoori, R. C.; Jarillo-Herrero, P. (2014). "Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state". Nature 505 (7484): 528–532. doi:10.1038/nature12800. PMID 24362569. Bibcode2014Natur.505..528Y.
3. Yao, Wang; Yang, Shengyuan A.; Niu, Qian (2009). "Edge States in Graphene: From Gapped Flat-Band to Gapless Chiral Modes". Physical Review Letters 102 (9): 096801. doi:10.1103/PhysRevLett.102.096801. PMID 19392547. Bibcode2009PhRvL.102i6801Y.
4. Plotnik, Yonatan; Rechtsman, Mikael C.; Song, Daohong; Heinrich, Matthias; Zeuner, Julia M.; Nolte, Stefan; Lumer, Yaakov; Malkova, Natalia et al. (2014). "Observation of unconventional edge states in 'photonic graphene'". Nature Materials 13 (1): 57–62. doi:10.1038/nmat3783. PMID 24193661. Bibcode2014NatMa..13...57P.
5. Xu, Bing-Cong; Xie, Bi-Ye; Xu, Li-Hua; Deng, Ming; Chen, Weijin; Wei, Heng; Dong, Fengliang; Wang, Jian et al. (2023). "Topological Landau–Zener nanophotonic circuits". Advanced Photonics 5 (3): 036005. doi:10.1117/1.AP.5.3.036005. Bibcode2023AdPho...5c6005X.