The geometry of induced currents in two dimensional media

We present a framework that allows us to clearly identify the geometric features underlying the phenomenon of superconductivity in two dimensional materials. In particular, we show that any such medium whose response to an externally applied electromagnetic field is a geodesically flowing induced cu...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Lopez-Monsalvo, Cesar S, Vargas-Serdio, Servando, Alzate-Cardenas, Julian A, Flores-Alfonso, Daniel
Format: Article
Language:English
Subjects:
Current carriers
Differential geometry
Divergence
Electromagnetic fields
Electromagnetic properties
Helicity
Superconductivity
Two dimensional materials
Online Access:Get full text
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Summary:We present a framework that allows us to clearly identify the geometric features underlying the phenomenon of superconductivity in two dimensional materials. In particular, we show that any such medium whose response to an externally applied electromagnetic field is a geodesically flowing induced current, must be a superconductor. In this manner, we conclude that the underlying geometry of this type of media is that of a Lorentzian contact manifold. Moreover, we show that the macroscopic hallmark of their superconducting state is a purely topological condition equivalent to the geodesic nature of the induced current: the non-vanishing of its helicity.
ISSN:2331-8422
DOI:10.48550/arxiv.2308.09335