The Influence of the Inelastic Electron–Phonon Collision Time on the Resistive State of 3D Superconducting Materials

This study investigates the influence of inelastic electron–phonon collision time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mrow><mi>e</mi><mo>-</mo><mi>ph</mi></mrow></msub></semantics></math></inline-formula>) on the behavior of the resistive state of three-dimensional superconducting systems. Using the generalized time-dependent Ginzburg–Landau formalism, we model the interplay between vortex dynamics, energy dissipation, and thermal effects across varying values of the dimensionless parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mrow><mi>e</mi><mo>-</mo><mi>ph</mi></mrow></msub></semantics></math></inline-formula> and different values of the Ginzburg–Landau parameter. The results show that larger values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> enhance the superconducting state by delaying the transition to the normal state, modulating critical currents, and altering differential resistance. An exponential relationship between the upper critical current and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> is observed, indicating prolonged resistive states as the inelastic electron–phonon collision time becomes larger. Furthermore, the study investigates the maximum local peaks in the differential resistance curves, revealing their exponential decay with increasing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>.