论文标题
通过在金属中的动态相互作用配对
Pairing by a dynamical interaction in a metal
论文作者
论文摘要
我们考虑将量子关键点（QCP）附近的金属中的巡回费物配对与某种形式的粒子孔（列，旋转密度波，电荷密度波等）配对。在QCP上，费米子之间的主要相互作用来自交换临界阶参数的无质量波动。在低能量下，可以通过有效的模型来描述该物理学的动态电子交互$ V（ω_m）\ propto 1/|ω_m|^γ$，最多可达某些上层截止$λ$。 $γ= 0 $的情况对应于BCS理论，可以通过总结库珀对数的几何系列来解决。我们表明，对于有限的$γ$，配对问题仍然很边缘（即扰动序列是对数），但是需要超越对数近似以找到配对的不稳定性。我们在一些细节上讨论以$γ> 0 $的详细信息，并分析边缘情况$γ= 0+$，当$ v（ω_m）=λ\ log {（λ/|ω_m|）} $时。我们表明，在这种情况下，库珀对数的求和确实在$λ\ log^2 {（λ/t_c）} = o（1）$中产生的配对不稳定性，但对数系列不是几何的。我们根据耦合的重新归一化组（RG）流重新制定了配对问题，并表明在$γ= 0 $，$γ= 0+$和$γ> 0 $的情况下，RG方程有所不同。
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 $γ>0$.
