Hidden Fermi Liquid: Self-Consistent Theory for the Normal State of High-$T_c$ Superconductors

Hidden Fermi liquid theory explicitly accounts for the effects of Gutzwiller projection in the $t\mathrm{\text{−}}J$ Hamiltonian, widely believed to contain the essential physics of the high-$T_c$ superconductors. We derive expressions for the entire “strange metal,” normal state relating angle-resolved photoemission, resistivity, Hall angle, and by generalizing the formalism to include the Fermi surface topology—angle-dependent magnetoresistance. We show this theory to be the first self-consistent description for the normal state of the cuprates based on transparent, fundamental assumptions. Our well-defined formalism also serves as a guide for further experimental confirmation.

Figure 1

Self-consistent HFL fits (black) of $\rho$ versus $T$ and inverse Hall angle versus $T^2$. The sample is OD ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CuO}}_{6+\delta }$ ($x=0.26$). The resistivity is given by Eq. (6) (prefactor is a free parameter) with $W_{\mathrm{HFL}}=800\mathrm{K}$. This linear best fit for $\cot {\theta }_H$ was used to determine $\alpha$ for Eq. (7), resulting in $W_{\mathrm{HFL}}=800\mathrm{K}$. Data for the inverse Hall angle (red) and resistivity (blue) were extracted from Ref. 29.

Figure 2

ADMR $({\omega }_c{\tau }_{\mathrm{tr}}{)}^{-1}$ versus $T$ showing excellent agreement with HFL using no free parameters (solid lines) and the data of Ref. 9 for OD ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CuO}}_{6+\delta }$ ($x=0.26$). Shown are the isotropic contribution [Eq. (S1), blue] and the anisotropic term [Eq. (S2), red] that vanishes at the node. $W_{\mathrm{HFL}}=800\mathrm{K}$ was used for the HFL bandwidth along ($\pi$, $\pi$), determined independently from both $\rho (T)$ and $\cot {\theta }_H$, as discussed. To evaluate the prefactor of Eqs. (S1, S2), we determined the nodal ${\omega }_c$ from $({\omega }_c{\tau }_H{)}^{-1}$ in Fig. 1 with ${\tau }_H^{-1}=T^2/W_{\mathrm{HFL}}$. We account for the anisotropic $k_F$ with $k_F(\pi ,0)/k_F(\pi ,\pi )=9/10$ (Ref. 28) and anisotropic $v_F$ with $v_F(\pi ,0)/v_F(\pi ,\pi )=1/2$ (Refs. 8, 28). The $T=0$, impurity offset in the dark (blue) curve is arbitrary as it is sample specific.