Origin of the anomalous Hall effect in the overdoped $n$-type superconductor ${\text{Pr}}_{2-x}{\text{Ce}}_x{\text{Cuo}}_4$: Current-vertex corrections due to antiferromagnetic fluctuations

The anomalous magnetotransport properties in electron doped ($n$-type) cuprates were investigated using Hall measurements at THz frequencies. The complex Hall angle was measured in overdoped ${\text{Pr}}_{2-x}{\text{Ce}}_x{\text{CuO}}_4$ samples ($x=0.17$ and 0.18) as a continuous function of temperature above $T_c$ at excitation energies 5.24 and 10.5 meV. The results, extrapolated to low temperatures, show that inelastic scattering introduces electronlike contributions to the Hall response. First-principle calculations of the Hall angle that include current-vertex corrections (CVC) induced by electron interactions mediated by magnetic fluctuations in the Hall conductivity reproduce the temperature, frequency, and doping dependence of the experimental data. These results show that Fermi-liquid CVC effects are the source of the anomalous Hall transport properties in overdoped $n$-type cuprates.

Figure 1

(Color online) The real and imaginary parts of the Hall angle measured at dc, 5.24 and 10.5 meV. The negative value at finite temperature in both the real and imaginary parts of the Hall angle signify strong electronlike contributions which dominate the ${\sigma }_{\text{xy}}$ response, a clear deviation from the simple holelike Fermi surface observed by ARPES. The brackets at low temperature are the zero-temperature extrapolations of the data as described in the text. Depicted in gray with each data set are error bars derived from the juxtaposition of uncertainties in thickness, ${\sigma }_{\text{xx}}$, and ${\theta }_{\text{F}}$. The included dc Hall data is taken from Ref. 5.

Figure 2

(Color online) Prediction of the real and imaginary part of the Hall angle by incorporating CVCs induced by magnon scattering. The Hall angle calculated in the FLEX approximation without including CVCs is shown in the insets.

Figure 3

(Color online) Electron scattering process $\mathbf{k}\to \mathbf{k}+\mathbf{Q}$ due to AF fluctuations $\mathbf{Q}\approx \left(\pm \pi ,\pm \pi \right)$. The total current ${\mathbf{J}}_{\mathbf{k}}$ is composed of quasiparticle velocities at $\mathbf{k}$ and $\mathbf{k}+\mathbf{Q}$.