arXiv 1902.045882019-02-12cond-mat.supr-concond-mat.quant-gas

超导体的动力学性质：BCS和BEC体系中的Anderson-Bogoliubov模和Berry相

Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in BCS and BEC regimes

Dmitry Mozyrsky, Andrey V. Chubukov

发表信息：: Phys. Rev. B 99, 174510 (2019)
DOI：: 10.1103/PhysRevB.99.174510

摘要：

我们分析了BCS和BEC制度之间的中性s波超导体的动力学的演变。我们考虑2d的情况下，当BCS-BEC交叉已经发生在弱耦合作为两个尺度的比值的函数-费米能量$E_F$和两个费米子在真空中的束缚态能量，$E_0$。BCS和BEC限值分别对应于$E_F \gg E_0$和$E_F \ll E_0$。化学势$μ= E_F-E_0$改变了两种状态之间的符号。我们发展了一种方法来获得在空间和时间导数的缓变超导序参量$Δ(r, τ)$的有效作用的扩展的主导项，并表示在$Δ(r, τ) = Δe^{iϕ(r, τ)}$的相位$ϕ(r,τ)$的导数方面的作用。在长波长范围内，第二梯度$(\nabla ϕ)^2$和${\dot ϕ}^2$描述了Bogoliubov-Anderson模式，正如我们发现的那样，Bogoliubov-Anderson模式不会通过BCS-BEC交叉而改变。有效作用还包含一阶梯度项$i πA {\dot ϕ}$，其仅在$ϕ$包含拓扑缺陷（例如涡流）时才有意义。我们应用我们的方法来评估系数$A$为一个移动的旋涡。我们发现$A_{vort}$有两个贡献，$A_{vort}= A_{vort,1} - A_{vort,2}$。一个来自远离涡核的态，具有$A_{vort,1} = n/2$，其中$n$是费米子密度。另一个来自涡核内部的电子态，具有$A_{vort,2} = -n_0/2$，其中$n_0$是涡核处的费米子密度。我们解释这个术语作为正常电子的反作用力的涡旋位移的极限时，能级之间的间距设置为零。$(n-n_0)/2$的差异通过BEC-BCS交叉而改变，因为$n_0$几乎补偿BCS体系中的$n$，但在BEC体系中消失。

英文摘要：

We analyze the evolution of the dynamics of a neutral s-wave superconductor between BCS and BEC regimes. We consider 2d case, when BCS-BEC crossover occurs already at weak coupling as a function of the ratio of the two scales -- the Fermi energy $E_F$ and the bound state energy for two fermions in a vacuum, $E_0$. BCS and BEC limits correspond to $E_F \gg E_0$ and $E_F \ll E_0$, respectively. The chemical potential $μ= E_F-E_0$ changes the sign between the two regimes. We develop an approach to derive the leading terms in the expansion of the effective action in the spatial and time derivative of the slowly varying superconducting order parameter $Δ(r, τ)$, and express the action in terms of derivatives of the phase $ϕ(r,τ)$ of $Δ(r, τ) = Δe^{iϕ(r, τ)}$. In the long wavelength limit the second gradients $(\nabla ϕ)^2$ and ${\dot ϕ}^2$, describe Bogoliubov-Anderson mode, which, as we find, does not change through BCS-BEC crossover. The effective action also contains first order gradient term, $i πA {\dot ϕ}$, which is meaningful only if $ϕ$ contains topological defects, such as vortices. We apply our approach to evaluate coefficient $A$ for a moving vortex. We find that $A_{vort}$ has two contributions, $A_{vort}= A_{vort,1} - A_{vort,2}$. One comes from the states away from the vortex core and has $A_{vort,1} = n/2$, where $n$ is the fermion density. The other comes from electronic states inside the vortex core and has $A_{vort,2} = -n_0/2$, where $n_0$ is the fermion density at the vortex core. We interpret this term as the reaction force of normal electrons to the vortex displacement in the limit when the spacing between energy levels is set to zero. The difference $(n-n_0)/2$ changes through the BEC-BCS crossover as $n_0$ nearly compensates $n$ in the BCS regime, but vanishes in the BEC regime.

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英文摘要：

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