Condition for the occurrence of phase slip centers in superconducting nanowires under applied current or voltage

Abstract

Experimental results on the phase slip process in superconducting lead nanowires are presented under two different experimental conditions: constant applied current or constant voltage. Based on these experiments we established a simple model which gives us the condition of the appearance of phase slip centers in a quasione-dimensional wire. The competition between two relaxations times ͑relaxation time of the absolute value of the order parameter ͉͉ and relaxation time of the phase of the order parameter in the phase slip center ) governs the phase slip process. Phase slips, as periodic oscillations in time of the order parameter, are only possible if the gradient of the phase grows faster than the value of the order parameter in the phase slip center, or equivalently if Ͻ ͉͉ .

Negative magnetoresistance and phase slip process in superconducting nanowires

“…Numerical analysis shows [13] that the amplitude of oscillations of |∆| in phase slip center is decreasing with the increase of γ and it is normally much smaller than |∆| eq . It allows to neglect the nonlinear term |∆| 3 in the right hand side (RHS) of the Eq.…”

“…As a result we have τ ∇φ ∼ τ GL I 0 ξ/Iλ Q (I is an applied current, I 0 = S /2eτ GL ξρ n is proportional to the depairing current (I c2 = (4/27)I 0 ), ρ n is a normal state resistivity and we take into account that −∂ϕ/∂x(x = 0) = I n (x = 0)ρ n /S ∼ Iρ n /S). When τ |∆| τ ∇φ the phase slip process is impossible as a periodic one in the time oscillating process [13] at I < I c2 . It allows us to estimate the first critical current of long L ≫ L Q wires…”

“…[13] using the extended quasi-1D time-dependent Ginzburg-Landau equations [14,15]. It has been found that there are two characteristic times which govern the dynamic of the order parameter in the phase slip center.…”

“…The second characteristic time τ ∇φ for long wires L ≫ λ Q (λ Q (γ ≫ 1) ≃ γ/uξ ≫ ξ is the decay length of the charge imbalance [7]) could be estimated by using the Ginzburg-Landau equation for dynamics of the phase of the order parameter [13] 2e…”

Dissipation in quasi-one-dimensional superconducting single-crystalSnnanowires

“…This is in contrast to the prediction of the SBT model, in which the major effect of increasing H is the decrease of the differential resistance in the plateau region of the V-I curves, together with the corresponding increase in the number of PSCs that can "fit" along the length of the wire (the q Λ was found to decrease with increasing times longer than the total length of our 40 nm sample. In order to understand the data seen in Sn and Pb nanowires, Michotte et al 32,33 extended the classical PSC model to 1d nanowires by considering two different boundary conditions (bridge (S-S) and N-S) using the generalized time-dependent Ginzburg-Landau (TDGL) equation. They considered the effect of the defects (a local variation of the critical temperature and a local variation of the cross-section of the wire) and magnetic field on the V-I characteristic.…”