Electrodynamics of Superconductors: From Lorentz to Galilei at Zero Temperature

Year: 2024

Authors: Salasnich., L.

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, Padua QTech Ctr, Via Marzolo 8, I-35131 Padua, Italy; Ist Nazl Fis Nucl, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy; CNR, Ist Nazl Ott, Via Nello Carrara 2, I-50127 Sesto Fiorentino, Italy.

Abstract: We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit, we obtain a Galilei-invariant superconducting system, which differs with respect to the familiar Schrodinger-like one. From this point of view, there are similarities with the Pauli equation of fermions, which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrodinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D’Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu-Goldstone phase field, which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid, we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency.

Journal/Review: ENTROPY

Volume: 26 (1)      Pages from: 69-1  to: 69-14

More Information: The author thanks Andrea Bardin, Luca Dell’Anna, Koichiro Furutani, Francesco Lorenzi, Maria Pelizzo, Andrea Perali, and Dima Sorokin for useful discussions and suggestions.
KeyWords: superconductors; electrodynamics; zero temperature; zero entropy; nonrelativistic limit; penetration length; Bogoliubov spectrum; plasma frequency
DOI: 10.3390/e26010069

Citations: 2
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24
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