Phase Dynamics in 3D Superconductors: Analysis Using the Sine-Gordon

Kiran Khadka; Saddam Husain Dhobi; Kishori Yadav

doi:10.21009/SPEKTRA.093.02

Authors

Kiran Khadka Department of Physics, Mahendra Morang Adarsh Multiple Campus, Biratnagar 56613, Nepal
Saddam Husain Dhobi Central Department of Physics, Tribhuvan University, Kirtipur 44618, Kathmandu, Nepal
Kishori Yadav Department of Physics, Patan Multiple Campus, Tribhuvan University, Patandhoka, Lalitpur 44700, Nepal

DOI:

https://doi.org/10.21009/SPEKTRA.093.02

Keywords:

phase dynamics, superconducting states, London penetration depth, coherence length, quantum confinement, 3D superconductors, phase behavior, waveforms

Abstract

This study investigates the phase dynamics of superconducting states in 3D superconductors using the sine-Gordon equation, with a focus on the interplay between the London penetration depth (LPD) and coherence length ( ). The research employs a combination of analytical modeling and simulation techniques to explore how variations in LPD influence phase behavior across different coherence lengths in the developed model. At a critical coherence length of = 2 Å, the LPD decreases from 150 nm to 120 nm as the nanoparticle spacing increases from 5 nm to 10 nm, attributed to reduced interactions between superconducting states. Conversely, at = 1 Å, quantum confinement effects lead to non-linear LPD behavior, with an initial decrease from 180 nm to 160 nm followed by an increase to 200 nm as nanoparticle spacing changes. In 3D superconductors, phase evolution is characterized by distinct waveforms—square, rectangular, and mixed—corresponding to LPD values between 100 nm and 200 nm, with phase shifts ranging from 1° to 20°. Smaller phase shifts (1°) produce higher-frequency oscillations with amplitudes up to 0.2, while larger shifts (20°) generate broader, less intense waveforms. These findings underscore the critical role of LPD in determining superconducting properties, offering valuable insights for the design and optimization of superconducting devices to enhance performance and efficiency.

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