Phonon-mediated superconductivity in low carrier-density systems
Phonon-mediated superconductivity in low carrier-density systems
复制标题
低载流子密度系统中的声子介导的超导
DOI：
10.1103/physrevb.99.094524
复制
发表时间：
2019
影响因子：
3.7
通讯作者：
R. Fernandes
中科院分区：
文献类型：
--
作者：
M. Gastiasoro;A. Chubukov;R. Fernandes
出于观察的超导性SrTiO 3 $和Bi，我们分析声子介导的超导性在低载流子密度的三维系统中，当化学势$\mu$（等于费米能量在$T=0$）是可比的，甚至小于特征声子频率$\omega_L$。我们考虑Bardeen-Pines对相互作用的吸引部分，其中依赖于频率的电子-声子相互作用由库仑势修饰。这种修饰赋予了对相互作用动量依赖性。我们认为，传统的Migdal-Eliashberg（ME）近似变得无效时，$\mu \leq \omega_L$主要是因为占主导地位的贡献配对来自电子态远离费米面。我们得到的配对起始温度，这是等于$T_c$在没有相位波动，作为$\mu/\omega_L$的函数。我们发现无论是分析和数值，$T_c$增加的比率$\mu/\omega_L$变得更小。特别是，在稀态，$\mu \rightarrow 0$，它认为$T_c\propto\omega_L\left（\frac{Ry}{\omega_L}\right）^\eta$，其中$\text{Ry}$是里德伯常数，$\eta \sim 0.2$。
Motivated by the observation of superconductivity in SrTiO$_3$ and Bi, we analyze phonon-mediated superconductivity in three-dimensional systems at low carrier density, when the chemical potential $\mu$ (equal to Fermi energy at $T=0$) is comparable to or even smaller than the characteristic phonon frequency $\omega_L$. 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 $\mu \leq \omega_L$ 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 $\mu/\omega_L$. We find both analytically and numerically that $T_c$ increases as the ratio $\mu/\omega_L$ becomes smaller. In particular, in the dilute regime, $\mu \rightarrow 0$, it holds that $T_c\propto\omega_L\left(\frac{Ry}{\omega_L}\right)^\eta$, where $\text{Ry}$ is the Rydberg constant and $\eta \sim 0.2$.