Strange metal at the Lifshitz transition

Strange metals are ubiquitously observed in a variety of strongly correlated materials, among which high temperature cuprates\cite{Greene2020} and twisted bilayer graphenes\cite{Cao2020} are the most prominent examples. The prevailing consensus is that the strange metal emerges within a finite temperature fan, mediated by a quantum critical point(QCP) where the pseudogap phase terminates\cite{keimer2015quantum,Michon2019}. A growing number of experiments\cite{Benhabib2015,DoironLeyraud2017,Horio2018} suggests that, in most cuprates, the QCP nearly coincides with a Lifshitz transition point. However, the nature of the QCP\cite{Zhu2022} and the significance of van Hove singularity(VHS) in driving quantum critical phenomena remain largely unexplored\cite{Horio2018,Shen2022}. Here we investigate quantum critical transport at Lifshitz transition in two dimensions(2D), where the Fermi surface geometry undergoes a convex-to-concave transition. The VHS saddle points is coupled to critical bosons via spatially uniform Yukawa interactions. At zero temperature, the interplay between extra scattering channel at Lifshitz transition and the impurity scattering gives rise to a linear-in-$\omega$ optical conductivity. At finite temperatures, we demonstrate a persistant linear-in-$T$ \emph{dc} resistivity in the quantum-critical temperature range down to $T\rightarrow 0$, which gives in to the saturation in non-universal higher temperature regime. For the spatially random Yukawa interaction, we show that the linear-in-$T$ resistivity unexpectedly extends even into the non-universal high-$T$ regime.