Properties of high-$T_C$ copper oxides from the nearly-free-electron model

The generic band structure of high-$T_C$ copper oxides is simulated by the nearly-free-electron model in two dimensions with parameters from ab-initio linear muffin-tin orbital calculations. Interaction between phonons and spin waves will cause potential modulations, and pseudogaps and the strength of the modulations, the wavelengths, and the doping are all related. A Fermi-surface “arc” is found for dynamic spin and phonon waves. The confinement of superconductivity between two limiting dopings can be a result of competition with the pseudogap at low doping and weak coupling at high doping.

Figure 1

(Color online) Calculated 2D NFE Fermi surface for a strong dynamic spin-phonon fluctuation with $\vec{q}=(0.85,0.90)$.

Figure 2

Calculated DOS for $x=0.02$ (thin line), $x=0.16$ (dotted line), and $x=0.26$ (heavy line). The latter case is for nonequivalent modulations along $\widehat{x}$ and $\widehat{y}$, and a secondary dip below $E_F$ is seen.

Figure 3

The relation between doping $x$ and $q$ vectors of the modulation. The $q$ vectors along $\widehat{x}$ and $\widehat{y}$ are equal for doping below $\sim 0.18$. The modulation along one direction remains fixed ($8a_0$ for the spin part) for larger doping, with a weaker modulation of longer periodicity in the perpendicular direction.

Figure 4

The DOS at $E_F$ and $T^{*}$ as function of doping $x$. The DOS is at the minimum of the pseudogap, and $T^{*}$ is $1∕4\text{th}$ of $V_Q^{sf}$.