The origin of the linear-in-temperature ($T$-linear) resistivity in cuprate superconductors remains a profound mystery in condensed matter physics. Here, we investigate the dependence of the $T$-linear resistivity coefficient on doping, i.e., $A_1\left(p\right)$, for three typical regions in the temperature versus doping phase diagram of hole-doped cuprates, from which the doping dependence of the scattering rate, i.e., ${\alpha }_1\left(p\right)$, is further derived. It is found that for region I ($p<p^{*}$ and $T>T^{*}$), ${\alpha }_1\left(p\right)$ is almost a constant; for region II ($p>p^{*}$ and $T>T_{\mathrm{coh}}$), ${\alpha }_1\left(p\right)\propto p$; for region III ($p>p^{*}$ and $T<T_{\mathrm{coh}}$), ${\alpha }_1\left(p\right)\propto p(p_c-p)$, where $T^{*}$ is the onset temperature of the pseudogap phase, $p^{*}$ indicates the doping at which $T^{*}$ goes to zero, $T_{\mathrm{coh}}$ marks the onset of antinodal quasiparticle coherence, and $p_{\mathrm{c}}$ is the doping where the low-temperature linear behavior in the overdoped regime vanishes. Moreover, the deduced ${\alpha }_1\left(p\right)$ relations are verified with the experimental data from previous reports. The discovered scattering rate versus doping relationship will shed light on the scattering mechanism underlying the $T$-linear resistivity in cuprate superconductors.

• Received 8 January 2024
• Accepted 30 April 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.023194

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Published by the American Physical Society