AI 中文总结
研究无序超导薄膜接近临界电流时热相位滑移，推广近\(T_c\)结果，表明二维最优涨落在任意温度满足Boussinesq方程，通过梯度展开求解Usadel方程，计算不同维度激活势垒渐近形式及\(E(T)\)，薄膜理论在特定窗口有效，导线结果近似性好。
AI 中文摘要
我们发展了一种关于无序超导薄膜在接近临界电流\(I_c(T)\)时热相位滑移的理论。推广了近期在接近\(T_c\)时得到的结果，表明在二维中控制相位滑移势垒的最优涨落在任意温度\(T < T_c\)下满足精确可积的Boussinesq方程。由于最优核的横向和纵向尺寸在\(I \to I_c(T)\)时发散，可利用梯度展开微扰求解存在缓慢变化序参量时的准粒子Usadel方程。得到的复序参量场论进一步简化为单实场的Boussinesq自由能，其系数表示为\(I_c(T)\)处均匀Usadel方程解的Matsubara和。接近\(I_c\)时的激活势垒具有渐近形式\(\Delta F(T, I \to I_c) = E(T) (1 - I/I_c)^\alpha\)。我们计算了二维薄膜（\(\alpha = 3/4\)）和一维导线（\(\alpha = 5/4\)）在整个温度范围内的\(E(T)\)。对于薄膜，该理论在低于\(I_c(T)\)的狭窄\(10\%\)窗口内有效，其中鞍点构型保持无涡旋。对于导线，\(\Delta F(T, I \to I_c)\)对所有温度和电流下的激活势垒提供了良好近似。
英文摘要
We develop a theory of thermal phase slips in disordered superconducting films biased near the critical current $I_c(T)$. Generalizing recent results obtained close to $T_c$, we show that the optimal fluctuation governing the phase-slip barrier in two dimensions satisfies the exactly integrable Boussinesq equation for arbitrary temperatures $T<T_c$. Since both the transverse and longitudinal sizes of the optimal nucleus diverge as $I\to I_c(T)$, the Usadel equation for quasiparticles in the presence of a slowly varying order parameter can be solved perturbatively using a gradient expansion. The resulting field theory for a complex order parameter is further reduced to the Boussinesq free energy for a single real field, with the coefficients expressed as Matsubara sums over the solutions of the uniform Usadel equation at $I_c(T)$. The activation barrier near $I_c$ has the asymptotic form $ΔF(T,I\to I_c) = E(T) (1-I/I_c)^α$. We calculate $E(T)$ over the full temperature range for both two-dimensional films ($α=3/4$) and one-dimensional wires ($α=5/4$). For films, the theory is valid within a narrow $10\%$ window below $I_c(T)$, where the saddle-point configuration remains vortex-free. For wires, $ΔF(T,I\to I_c)$ provides a good approximation to the activation barrier for all temperatures and currents.
Comments10 pages, 3 figures
