We compute the particle–hole bubble for an Ising-nematic metal when the critical Fermi surface approaches the Brillouin zone boundary for $d=2$ dimensions. We find two qualitatively distinct contributions: (i) the standard antipodal piece, which gives ${\mathrm{\Pi }}_{\mathrm{ATP}}(\mathbf{q},i\mathrm{\Omega })\propto \mathrm{\Omega }/q$, and (ii) an additional umklapp piece from electrons near the zone boundary, which gives ${\mathrm{\Pi }}_{\mathrm{U}}(\mathbf{q},i\mathrm{\Omega })\propto {\mathrm{\Omega }}^{\alpha }$ at the minimum umklapp momentum $q\approx {\mathrm{\Delta }}_q$, with $\alpha =2/3$ or $1/2$ depending on the temperature $T$. At high $T$ when $\alpha =1/2$, the minimum $T$ for the activation of linear/quasilinear in $T$ resistivity, which is expected to be $T_U\propto {\mathrm{\Delta }}_q^3$ from $z=3$ criticality, could potentially get reduced to $T_U\propto {\mathrm{\Delta }}_q^4$ due to the $\sqrt{\mathrm{\Omega }}$ term. We discuss why due to fermion self-energy effects, we find only one hyperspecific scenario where this possibility might be realized and offer some evidence for the reduction of $T_U$ at the level of a scattering rate estimate for this case. For $d=3$ the umklapp contribution gives ${\mathrm{\Pi }}_{\mathrm{U}}\sim \mathrm{\Omega }$ irrespective of $T$; therefore $T_U$ is not modified in this case.

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• Quantum criticality
• Transport phenomena
• Strongly correlated systems
• Non-Fermi-liquid theory
• Sachdev-Ye-Kitaev model