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<p>This work presents a theoretical investigation of the smearing of the 0–<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\pi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation> phase transition in a superconductor–quantum dot–superconductor system using the Keldysh Green’s function formalism within the equation of motion approach. The analysis focuses on the behavior of the Josephson current under the influence of thermal energy and on-site Coulomb interaction. Our results reveal that as thermal energy increases, the sharp 0–<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\pi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation> transition gradually smoothens, ultimately yielding a fully sinusoidal current-phase relationship.</p>

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Vanishing 0–\(\pi\) Discontinuity in Superconductor–Quantum Dot Josephson Junctions

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • Bhupendra Kumar

摘要

This work presents a theoretical investigation of the smearing of the 0– \(\pi\) π phase transition in a superconductor–quantum dot–superconductor system using the Keldysh Green’s function formalism within the equation of motion approach. The analysis focuses on the behavior of the Josephson current under the influence of thermal energy and on-site Coulomb interaction. Our results reveal that as thermal energy increases, the sharp 0– \(\pi\) π transition gradually smoothens, ultimately yielding a fully sinusoidal current-phase relationship.