Theory of resistivity upturns in metallic cuprates

We propose that the experimentally observed resistivity upturn of cuprates at low temperatures may be explained by properly accounting for the effects of disorder in a strongly correlated metallic host. Within a calculation of the dc conductivity using real-space diagonalization of a Hubbard model treated in an inhomogeneous unrestricted Hartree-Fock approximation, we find that correlations induce magnetic droplets around impurities, and give rise to additional magnetic scattering which causes the resistivity upturn. A pseudogap in the density of states is shown to enhance both the disorder-induced magnetic state and the resistivity upturns.

Figure 1

(Color online) [(a) and (b)] Real-space magnetization pattern induced by a single nonmagnetic impurity for (a) the normal state, and (b) the dSC state, both at $U=1.75$ and $B=0.01$. One sees that the dSC state has more pronounced nearest-neighbor site magnetization due to bound-state formation and has smaller homogeneous magnetization due to the opening of a gap at the Fermi surface. These effects are shown more clearly in (c) the total magnetization $S_z$ and (d) the magnetic contrast $\lambda$ versus external field.

Figure 2

(a) Magnetic contrast $\lambda$ and (b) resistivity in units of $241\mu \Omega \text{cm}$ versus $U$ at optimal doping with $T=0.03$ and 2% impurities.

Figure 3

(a) Magnetic contrast $\lambda$ and (b) change in resistivity $\Delta \rho /{\rho }_0$ versus $T$ at optimal doping with $U=1.74$ and 2% impurities.

Figure 4

(a) Magnetic contrast and (b) change in resistivity versus $B$ at optimal doping with $U=1.74$ and 2% impurities.

Figure 5

(a) Magnetic contrast $\lambda$ and change in resistivity $\Delta \rho /{\rho }_0$ versus $n_{imp}$ at optimal doping with $U=1.74$, $B=0.001$, $T=0.03$, and (b)$\lambda$ induced by the two-impurity model plotted against the separation between the two impurities $r_{12}$, collecting all relative positions up to 13th shell. Values of $r_{12}$ that correspond to average distance of impurities at $n_{imp}=3\%$, 1%, and 0.5% are indicated.

Figure 6

Comparison of DOS: the normal-state dispersion ${\xi }_k$ gives $N_1\left(\omega \right)$ (shifted), the proposed phenomenological model for the pseudogap state $E_k$ gives $N_2\left(\omega \right)$ (shifted), and the actual $N_3\left(\omega \right)$ (original scale) given by the effective hopping model after Fourier transform of $E_k$ in a $40\times 40$ system, with ${\mu }_f=0.02$ and $\Delta =0.2$.

Figure 7

Comparison of (a) $\lambda$ and (b) $\Delta \rho /{\rho }_0$ for models with (extended) and without (normal) reduction in DOS by applying extended hopping Eq. (9), both at optimal doping, with $U=1.75$, $B=0.001$ and 2% impurities. [(c) and (d)]: same quantities vs $B$ for normal and extended hopping models.