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arXiv 2012.11777cond-mat.supr-concond-mat.str-el
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金属中动力学相互作用的配对

Pairing by a dynamical interaction in a metal

Andrey V Chubukov, Artem Abanov

备注：
22 pages, 5 figures. For special issue of JETP devoted to the 90th birthday of I.E. Dzyaloshinskii. arXiv admin note: text overlap with arXiv:2004.13220
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摘要：

我们考虑金属中的巡游费米子在量子临界点（QCP）附近对某种形式的粒子-空穴序（自旋波、自旋密度波、电荷密度波等）的配对。在QCP中，费米子之间的主要相互作用来自交换临界序参量的无质量涨落。在低能量下，这种物理可以用一个有效的模型来描述，该模型具有动态电子-电子相互作用$V(Ω_m) \propto 1/|Ω_m|^γ$，直到某个上限截止值$Λ$。$γ=0$情形对应于BCS理论，可以通过求和Cooper矩阵的几何级数来求解。我们表明，对于有限的$γ$，配对问题仍然是边缘的（即，微扰级数是对数的），但是需要超越对数近似来找到配对不稳定性。我们详细讨论了$γ>0$的配对细节，并分析了边缘情况$γ= 0+$，当$V(Ω_m) = λ\log{(Λ/|Ω_m|)}$。我们表明，在这种情况下，库珀谱的总和产生配对不稳定性在$λ\log^2{(Λ/T_c)} = O(1)$，但对数级数不是几何。我们重新制定的配对问题的重整化群（RG）流的耦合，并表明RG方程是不同的情况下$γ=0$，$γ= 0+$，和$γ>0$。

英文摘要：

We consider pairing of itinerant fermions in a metal near a quantum-critical point (QCP) towards some form of particle-hole order (nematic, spin-density-wave, charge-density-wave, etc). At a QCP, the dominant interaction between fermions comes from exchanging massless fluctuations of a critical order parameter. At low energies, this physics can be described by an effective model with the dynamical electron-electron interaction $V(Ω_m) \propto 1/|Ω_m|^γ$, up to some upper cutoff $Λ$. The case $γ=0$ corresponds to BCS theory, and can be solved by summing up geometric series of Cooper logarithms. We show that for a finite $γ$, the pairing problem is still marginal (i.e., perturbation series are logarithmic), but one needs to go beyond logarithmic approximation to find the pairing instability. We discuss specifics of the pairing at $γ>0$ in some detail and also analyze the marginal case $γ= 0+$, when $V(Ω_m) = λ\log{(Λ/|Ω_m|)}$. We show that in this case the summation of Cooper logarithms does yield the pairing instability at $λ\log^2{(Λ/T_c)} = O(1)$, but the logarithmic series are not geometrical. We reformulate the pairing problem in terms of a renormalization group (RG) flow of the coupling, and show that the RG equation is different in the cases $γ=0$, $γ= 0+$, and $γ>0$.

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