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arXiv 1910.04579cond-mat.supr-con
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声子超导体中Tc的Kohn-Luttinger修正

Kohn-Luttinger Correction to Tc in a Phonon Superconductor

Dan Phan, Andrey V Chubukov

备注：
20 pages, 6 figures, submitted to PRB, refs added, grant number corrected
发表信息：
Phys. Rev. B 101, 024503 (2020)
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摘要：

弱耦合理论预言声子超导体的临界温度为$T_c = 1.13 e^{-3/2} ω_D e^{-{1/λ}}$，其中$ω_D$是德拜频率，$λ$是无量纲的电子-声子耦合常数，因子$e^{-3/2}$来自费米子自能和相互作用的频率依赖性。其它修正在$ω_D/E_F$中、通过Migdal定理或在$λ$中都很小。然而，该公式假设$ω_D \ll E_F$，其中$E_F$是费米能。当费米能级小于$ω_D$时，我们得到了稀态的$T_c$.我们认为，在这种情况下，Migdal的定理不再有效，和Kohn-Luttinger型的配对相互作用的修正必须包括获得正确的前因子$T_c$。

英文摘要：

Weak coupling theory predicts the critical temperature of a phonon superconductor to be $T_c = 1.13 e^{-3/2} ω_D e^{-{1/λ}}$, where $ω_D$ is the Debye frequency, $λ$ is the dimensionless electron-phonon coupling constant, and the factor $e^{-3/2}$ comes from fermionic self-energy and frequency dependence of the interaction. Other corrections are small either in $ω_D/E_F$, by Migdal's theorem, or in $λ$. However, this formula assumes that $ω_D \ll E_F$, where $E_F$ is the Fermi energy. We obtain $T_c$ in the dilute regime, when the Fermi energy is smaller than $ω_D$. We argue that in this situation Migdal's theorem is no longer valid, and Kohn-Luttinger-type corrections to the pairing interaction must be included to obtain the correct prefactor for $T_c$.

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