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arXiv 1901.00344cond-mat.supr-con
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低载流子密度体系中声子介导的超导电性

Phonon mediated superconductivity in low carrier-density systems

Maria N. Gastiasoro, Andrey V. Chubukov, Rafael M. Fernandes

摘要:

受SrTiO $_3$和Bi中超导性观察的启发,我们分析了低载流子密度下三维系统中声子介导的超导性,当化学势$μ$(等于$T=0$处的费米能)与特征声子频率$ω_L$相当甚至更小时。我们考虑Bardeen-Pines对相互作用的吸引部分,其中依赖于频率的电子-声子相互作用由库仑势修饰。这种修饰赋予了对相互作用动量依赖性。我们认为,传统的Migdal-Eliashberg(ME)近似变得无效时,$μ\leq ω_L$主要是因为主要贡献的配对来自电子态远离费米面。我们得到的配对起始温度,这是等于$T_c$在相位波动的情况下,作为$μ/ω_L$的函数。我们发现无论是分析和数值,$T_c$增加的比率$μ/ω_L$变得更小。特别地,在稀释状态下,$μ\rightarrow 0$,它认为$T_c\proptoω_L\left(\frac{Ry}{ω_L}\right)^η$,其中$\text{Ry}$是里德伯常数,而$η\sim 0.2$。

英文摘要:

Motivated by the observation of superconductivity in SrTiO$_3$ and Bi, we analyze phonon-mediated superconductivity in three-dimensional systems at low carrier density, when the chemical potential $μ$ (equal to Fermi energy at $T=0$) is comparable to or even smaller than the characteristic phonon frequency $ω_L$. We consider the attractive part of the Bardeen-Pines pairing interaction, in which the frequency-dependent electron-phonon interaction is dressed by the Coulomb potential. This dressing endows the pairing interaction with momentum dependence. We argue that the conventional Migdal-Eliashberg (ME) approximation becomes invalid when $μ\leq ω_L$ chiefly because the dominant contribution to pairing comes from electronic states away from the Fermi surface. We obtain the pairing onset temperature, which is equal to $T_c$ in the absence of phase fluctuations, as a function of $μ/ω_L$. We find both analytically and numerically that $T_c$ increases as the ratio $μ/ω_L$ becomes smaller. In particular, in the dilute regime, $μ\rightarrow 0$, it holds that $T_c\proptoω_L\left(\frac{Ry}{ω_L}\right)^η$, where $\text{Ry}$ is the Rydberg constant and $η\sim 0.2$.

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