Evolution of Hall resistivity and spectral function with doping in the SU(2) theory of cuprates

Recent transport experiments in the cuprate superconductors linked the opening of the pseudogap to a change in electronic dispersion [S. Badoux et al., Nature (London) 531, 210 (2015)]. Transport measurements showed that the carrier density sharply changes from $x$ to $1+x$ at the pseudogap critical doping, in accordance with the change from Fermi arcs at low doping to a large hole Fermi surface at high doping. The SU(2) theory of cuprates shows that short-range antiferromagnetic correlations cause the arising of both charge and superconducting orders, which are related by an SU(2) symmetry. The fluctuations associated with this symmetry form a pseudogap phase. Here we derive the renormalized electronic propagator under the SU(2) dome, and calculate the spectral functions and transport quantities of the renormalized bands. We show that their evolution with doping matches both spectral and transport measurements.

Figure 1

Top: evolution of the spectral functions at zero frequency with doping. Note that because the renormalized bands are symmetrical with respect to zero energy, both spectral functions are equal at zero frequency. We therefore only plot one of them. Bottom: self-energy diagram for the renormalization of the fermionic propagator. The straight lines are bare electron lines, while the wiggly line is the SU(2) fluctuations line.

Figure 2

Top: evolution of the gap $B{M}_{0,k}^2$ with doping in a quarter of the Brillouin zone. The color blue is for zero, and the black line represents the Fermi surface. Bottom: gap on the Fermi surface with respect to the $d$-wave factor. A pure $d$-wave gap would be strictly linear.

Figure 3

Hall resistance in volume units with respect to temperature in K per units of $t_0$, for a range of hole dopings.

Figure 4

Hall number with respect to doping (blue). The experimental values from [23] (orange) and the low-doping and high-doping asymptotes (black) are also plotted for reference. Note that $x^{*}=0.2$.