Linear-T resistivity at the pseudogap critical point of the cuprate superconductor Bi2212

We report high-field measurements of the electrical resistivity on a highly overdoped thin film of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ ($T_c = 50$~K), one of the archetypal cuprate superconductors, with a high maximal $T_c$ (90~K). Measurements up to 55 T enabled us to suppress superconductivity and track the normal-state behavior down to low temperature. We observe a linear temperature dependence of the resistivity as $T \to 0$, at a doping $p = 0.23$ just above $p^{\star} \simeq 0.22$, the critical doping where the pseudogap phase ends [1,2]. Our data on Bi2212 are in excellent agreement with previous data on cuprates with lower maximal $T_c$, namely LSCO [3] and Nd-LSCO [4]. This shows that a linear-$T$ resistivity is a universal signature of the pseudogap critical point in cuprates, reminiscent of the linear-$T$ resistivity found at the quantum critical point of heavy-fermion, pnictide and organic superconductors [5].\\~[1] I.~Vishik~{\it et al.}, PNAS~{\bf 109},~18332~(2012).\\~[2] S.~Benhabib~{\it et al.}, Phys.~Rev.~Lett.~{\bf 114},~147001~(2015).\\~[3] R.~A.~Cooper~{\it et al.}, Science~{\bf 323},~603~(2009).\\~[4] R.~Daou ~{\it et al.}, Nat.~Phys.~{\bf 5},~31~(2009).\\~[5] L.~Taillefer, Annu.~Rev.~Condens.~Matter Phys.~{\bf 1},~51~(2010)