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Electronic spectrum of spherical fullerene molecules in the presence of generalized magnetic fields

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Abstract

We consider a spherical fullerene molecule under magnetic fields perpendicular to the surface. The aim is to find out the general forms of magnetic field profiles for which the exact electronic spectrum can be found. Starting with a magnetic field profile for which the electronic spectrum is exactly known, we use a technique based on supersymmetry to construct very general magnetic field profiles which produce nearly the same spectrum as the original problem. Some examples have been investigated in detail using the method mentioned above.

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Notes

  1. 1.

    As mentioned before, such magnetic field may be produced experimentally by combination of various sources including strain-induced one. To use strain engineering, purely magnetic field without an associated electric field is generated by the strain \(\vec {u} = - 2^{-1} \left( u_\theta (\theta ) \cot \theta + \partial _{\theta } u_\theta (\theta ) \right) \vec {e}_r + u_\theta (\theta ) \vec {e}_\theta \). The vector potential induced from this strain is \(A_{\varphi } (\theta ) = \beta t b^{-1} \left( u_{\theta } (\theta ) \cot \theta - \partial _{\theta } u_{\theta } (\theta ) \right) \), where tb and \(\beta \approx 2\) are hoping energy, lattice constant and Grüneisen parameter, respectively [3, 33]. Hence, if we want to create the vector potential \(A_{\varphi } (\theta )\), we solely need the deformation corresponding to \(u_{\theta } (\theta ) = b \beta ^{-1} t^{-1} \sin \theta \int A _{\varphi } (\theta ) \csc \theta d \theta \).

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Acknowledgements

The authors thank the anonymous reviewers for their recommendations that help improve our manuscript. One of the authors (Anh-Luan Phan) was supported by the Domestic Master/PhD Scholarship Programme of Vingroup Innovation Foundation.

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Correspondence to Anh-Luan Phan.

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Phan, A., Le, D., Le, V. et al. Electronic spectrum of spherical fullerene molecules in the presence of generalized magnetic fields. Eur. Phys. J. Plus 135, 6 (2020). https://doi.org/10.1140/epjp/s13360-019-00009-y

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