AI 中文总结
该研究从Keldysh非线性σ模型推导无序非中心对称超导体的广义含时Ginzburg-Landau理论，揭示动力学利夫希茨不变量及非互易涨落动力学，调和磁电耦合矛盾并计算超导二极管效率与磁手性各向异性。
AI 中文摘要
我们采用具有Rashba自旋轨道耦合和面内塞曼场的二维电子气作为最小模型，从Keldysh非线性σ模型出发，推导了无序非中心对称超导体的广义含时Ginzburg-Landau理论。在热力学方面，我们构建了自由能的利夫希茨不变量、线性和三次梯度项以及四次顶点的动量奇性部分，并追踪它们对无序的依赖关系。这些耦合由一个闭式核控制，该核由Dyakonov-Perel自旋弛豫率与温度的比值决定，在弱弛豫 regime（此时不变量被抑制）和弛豫主导 regime（此时序参数的螺旋调制饱和于与无序无关的普适值）之间插值。这种交叉调和了关于脏Rashba超导体的磁电耦合的矛盾结果。由于该理论建立在Keldysh轮廓上，它还确定了耗散动力学：具有对动量q的涨落的弛豫率，因此根据涨落-耗散定理，朗之万噪声功率获得了q奇性且磁场奇性的项。该动力学利夫希茨不变量的结构由Onsager倒易性决定：摩擦和噪声同步重正化，使得等时涨落保持吉布斯分布，而动力学是非互易的。作为应用，我们计算了T_c附近的超导二极管效率，其中三次不变量与四次顶点以及由螺旋位移导致的奇性更高梯度项竞争，反转了二极管系数的符号；还计算了T_c以上的涨落诱导磁手性各向异性，其中电流分辨的非互易电阻在高斯区域形成平台。
英文摘要
We derive the generalized time-dependent Ginzburg-Landau theory of a disordered noncentrosymmetric superconductor from the Keldysh nonlinear sigma model, using a two-dimensional electron gas with Rashba spin-orbit coupling and an in-plane Zeeman field as a minimal model. On the thermodynamic side we construct the Lifshitz invariants of the free energy, the linear and cubic gradient terms and the momentum-odd part of the quartic vertex, and trace their dependence on disorder. These couplings are governed by a single closed-form kernel controlled by the ratio of the Dyakonov-Perel spin-relaxation rate to temperature, interpolating between the weak-relaxation regime, where the invariants are suppressed, and the relaxation-dominated regime, where the helical modulation of the order parameter saturates at a universal, disorder-independent value. This crossover reconciles conflicting results for the magnetoelectric couplings of dirty Rashba superconductors. Because the theory is formulated on the Keldysh contour, it also determines the dissipative dynamics: the relaxation rate of a fluctuation with pair momentum $\mathbf{q}$, and hence, by the fluctuation-dissipation theorem, the Langevin noise power, acquires a term odd in $\mathbf{q}$ and odd in the magnetic field. The structure of this kinetic Lifshitz invariant is dictated by Onsager reciprocity: friction and noise renormalize in lockstep, so equal-time fluctuations remain Gibbsian while the dynamics are nonreciprocal. As applications we compute the superconducting diode efficiency near $T_c$, where the cubic invariant competes with the quartic vertex and with even higher-gradient terms rendered odd by the helical shift, reversing the sign of the diode coefficient, and the fluctuation-induced magnetochiral anisotropy above $T_c$, where the current-resolved nonreciprocal resistance forms a plateau across the Gaussian regime.
Comments33 pages, 2 figures
