is the cutoff frequency. In the last line of Eq. 23, we take the limit of 𝑘 m ‖ → ∞ when evaluating the integral, which gives a finite value despite the singularity in 𝑔 1D (𝜔 k ) because only the contribution from 𝜔 k = 𝜔 c survives. At the same time,