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arXiv 1003.2709cond-mat.supr-con
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三维非简谐声子介导的强耦合超导

Strong coupling superconductivity mediated by three-dimensional anharmonic phonons

Kazumasa Hattori, Hirokazu Tsunetsugu

摘要:

本文研究了四面体对称中的三维非简谐声子以及由这些声子介导的超导性。通过求解薛定谔方程直接计算了三维非简谐声子谱,并在各向同性带隙函数的假设下,利用强耦合超导理论确定了超导转变温度。随着四面体离子势的三阶非谐性$b$的增加,我们发现在能谱中有一个量子隧穿区的交叉。我们得到强烈增强的转变温度的交叉点周围。我们还研究了非谐效应对Debye-Waller因子,声子谱函数和密度分布的影响,作为非谐度$b$和温度的函数。用超导强耦合理论中的第一激发态能量$Δ$和耦合常数$λ$讨论了在KOs_2O_6中观察到的同构一级跃迁。我们的结果表明,$λ$减少和增加$Δ$低于一级转变温度。我们指出,振荡振幅&lt;x^2&gt;的变化和<xyz>特征,这种同构的转变。讨论了$β$ -烧绿石化合物的超导转变温度、$λ$和$Δ$的化学变化趋势。

英文摘要:

We investigate three dimensional anharmonic phonons in tetrahedral symmetry and superconductivity mediated by these phonons. Three dimensional anharmonic phonon spectra are calculated directly by solving Schrödinger equation and the superconducting transition temperature is determined by using the theory of strong coupling superconductivity assuming an isotropic gap function. With increasing the third order anharmonicity $b$ of the tetrahedral ion potential, we find a crossover in the energy spectrum to a quantum tunneling regime. We obtain strongly enhanced transition temperatures around the crossover point. We also investigate the anharmonic effects on the Debye-Waller factor, the phonon spectral functions and the density profile, as a function of the anharmonicity $b$ and temperature. The isomorphic first order transition observed in KOs_2O_6 is discussed in terms of the first excited state energy $Δ$, and the coupling constant $λ$ in the strong coupling theory of superconductivity. Our results suggest the decrease of $λ$ and increase of $Δ$ below the first order transition temperature. We point out that the change in the oscillation amplitude <x^2> and <xyz> characterizes this isomorphic transition. The chemical trends of the superconducting transition temperature, $λ$, and $Δ$ in the $β$-pyrochlore compounds are also discussed.

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