Linear Resistivity from Spatially Random Interactions and the Uniqueness of Yukawa Coupling

Recent studies have shown that a spatially random Yukawa-type interaction between a Fermi surface and critical bosons can produce linear-in-temperature resistivity, the defining signature of strange metals. In this article, we systematically classify all scalar couplings of the form $({\psi }^{†}\psi {)}^n{\phi }^m$ in arbitrary dimensions to identify possible candidates for strange-metal behaviour within this disordered framework. We find that only spatially random Yukawa-type interaction in $(2+1)$ dimensions can yield linear resistivity. This indicates that linear resistivity is not a universal property of all spatially random scalar coupling, and strange-metal property replies on both dimensions and interaction type.