Abstract

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) ∝ 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) = λlog(Λ/|Ω_m|). We show that in this case the summation of Cooper logarithms does yield the pairing instability at λlog²(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.

中文翻译：

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通过金属中的动态相互作用配对

摘要

我们考虑在量子临界点 (QCP) 附近的金属中将流动费米子配对成某种形式的粒子 - 空穴顺序（向列、自旋密度波、电荷密度波等）。在 QCP 中，费米子之间的主要相互作用来自于交换关键阶参数的无质量波动。在低能量下，这种物理现象可以用动态电子-电子相互作用V (Ω _m ) ∝ 1/|Ω _m |的有效模型来描述。^γ，直到某个上限 Λ。γ= 0的情况对应于BCS理论，可以通过对Cooper对数的几何级数求和来解决。我们表明，对于有限的 γ，配对问题仍然是边缘问题（即扰动序列是对数的），但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 配对的细节，并分析了边际情况 γ = 0+，当V (Ω _m ) = λlog(Λ/|Ω _m |)。我们表明，在这种情况下，库珀对数的总和确实会在 λlog ² (Λ/ T _c ) = O处产生配对不稳定性(1)，但对数级数不是几何级数。我们根据耦合的重归一化组（RG）流程重新描述了配对问题，并表明在γ= 0，γ= 0+和γ> 0的情况下RG方程是不同的。