No existence of the geometric potential for a Dirac fermion on a two-dimensional curved surface of revolution

•Dynamical quantum conditions are proposed.•Spin-connection on curved surface is equivalent to a gauge field.•No curvature-induced quantum potential for a relativistic Dirac fermion on a 2D surface. For a free particle that moves non-relativistically on a curved surface, there are curvature-induced...

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Bibliographic Details
Published in:Physics letters. A 2020-09, Vol.384 (25), p.126604, Article 126604
Main Authors: Yang, Z.Q., Zhou, X.Y., Li, Z., Du, W.K., Liu, Q.H.
Format: Article
Language:English
Subjects:
Canonical quantization
Curved surface
Momentum
Relativistic wave equations
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Summary:•Dynamical quantum conditions are proposed.•Spin-connection on curved surface is equivalent to a gauge field.•No curvature-induced quantum potential for a relativistic Dirac fermion on a 2D surface. For a free particle that moves non-relativistically on a curved surface, there are curvature-induced quantum potentials that significantly influence the surface quantum states. However, the experimental results in topological insulators, whether curved or not, indicate no evidence of such a potential for the relativistic particles constrained on the curved surface. Within the framework of Dirac quantization scheme, we demonstrate a general result that for a Dirac fermion on a two-dimensional curved surface of revolution, no curvature-induced quantum potential is permissible.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2020.126604