Dynamics of order parameters near stationary states in superconductors with a charge-density wave
Dynamics of order parameters near stationary states in superconductors with a charge-density wave
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DOI：
10.1103/physrevb.90.024511
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发表时间：
2014-02
影响因子：
3.7
通讯作者：
A. Moor;P. Volkov;A. Volkov;K. Efetov
中科院分区：
文献类型：
--
作者：
A. Moor;P. Volkov;A. Volkov;K. Efetov
我们考虑一个准一维导体的简单模型，其中两个有序参数（OP）可以共存，即超导OP $\Delta$和表征电荷密度波（CDW）振幅的OP $W$。在平均场近似中，我们给出了矩阵格林函数$G_{ik}$的方程，其中$i$与两个费米片中的一个有关，$k$在Gor'kov-Nambu空间中运行。利用这些方程的解，我们找到了描述费米曲面曲率的参数$\mu$的不同值的定态，这可以通过掺杂等方式改变。建立了在$\mu_1<\mu<\mu_2$区间内自洽方程对于共存的OPs $\Delta$和$W$有一个解。然而，该解对应于能量泛函$\Phi(\Delta, W)$中的一个鞍点，即不稳定。稳定状态为：1)CDW为$\mu < \mu_{2}$的状态；2)纯超导态在$\mu_1<\mu$。在$\mu<\mu_0$处，状态1)对应于全局最小值，在$\mu_0<\mu$处，状态2)具有较低的能量，即只有超导状态存在$\mu$。我们研究了在无碰撞极限下这些状态$\delta\Delta$和$\delta W$变化的动力学。它具有两种振荡模式，即快振荡和慢振荡。快模类似于传统超导体中的阻尼振荡。慢模的频率取决于曲率$\mu$，当超导和CDW的耦合常数接近时，慢模的频率远小于$2\Delta$。所考虑的模型可以应用于高$T_c$超导体，其中费米表面靠近“热点”的部分可以被视为所考虑的两个费米片。我们还讨论了所考虑的模型与铁基化合物最简单模型的关系。
We consider a simple model of a quasi-one-dimensional conductor in which two order parameters (OP) may coexist, i.e., the superconducting OP $\Delta$ and the OP $W$ that characterizes the amplitude of a charge-density wave (CDW). In the mean field approximation we present equations for the matrix Green's functions $G_{ik}$, where $i$ relates to the one of the two Fermi sheets and $k$, operates in the Gor'kov-Nambu space. Using the solutions of these equations, we find stationary states for different values of the parameter describing the curvature of the Fermi surface, $\mu$, which can be varied, e.g., by doping. It is established that in the interval $\mu_1<\mu<\mu_2$ the self-consistency equations have a solution for coexisting OPs $\Delta$ and $W$. However, this solution corresponds to a saddle point in the energy functional $\Phi(\Delta, W)$, i.e., it is unstable. Stable states are: 1)the state with the CDW at $\mu < \mu_{2}$; and 2) the purely superconducting state at $\mu_1<\mu$. At $\mu<\mu_0$, the state 1) corresponds to a global minimum, and at $\mu_0<\mu$, the state 2) has a lower energy, i.e., only the superconducting state survives at large $\mu$. We study the dynamics of the variations $\delta\Delta$ and $\delta W$ from these states in the collisionless limit. It is characterized by two modes of oscillations, the fast and the slow one. The fast mode is analogous to damped oscillations in conventional superconductors. The frequency of slow modes depends on the curvature $\mu$ and is much smaller than $2\Delta$ if the coupling constants for superconductivity and CDW are close to each other. The considered model can be applied to high-$T_c$ superconductors where the parts of the Fermi surface near the `hot' spots may be regarded as the considered two Fermi sheets. We also discuss relation of the considered model to the simplest model for Fe-based pnictides.