Traveling edge states in massive Dirac equations along slowly varying edges
Pipi Hu, Peng Xie, Yi Zhu
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Source: Crossref
Published: Apr 21, 2023
DOI: 10.1093/imamat/hxad015
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Abstract Topologically protected wave motion has attracted considerable research interest due to its chirality and potential applications in many applied fields. We construct quasi-traveling wave solutions to the 2D Dirac equation with a domain wall mass in this work. It is known that the system admits exact and explicit traveling wave solutions, which are termed edge states if the interface is a straight line. By modifying such explicit solutions, we construct quasi-traveling-wave solutions if the interface is nearly straight. The approximate solutions in two scenarios are given. One is the circular edge with a large radius, and the second is a straight line edge with the slowly varying along the perpendicular direction. We show the quasi-traveling wave solutions are valid in a long lifespan by energy estimates. Numerical simulations are provided to support our analysis both qualitatively and quantitatively.
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