Extremely Correlated Fermi-Liquid Description of Normal-State ARPES in Cuprates

The normal-state single particle spectral function of the high temperature superconducting cuprates, measured by the angle-resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand. Here, we report an unprecedented success of the new extremely correlated Fermi liquid theory by one of us [B. S. Shastry, Phys. Rev. Lett. 107, 056403 (2011)] to describe both laser and conventional synchrotron ARPES data (nodal cut at optimal doping) on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ and synchrotron data on ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_4$. It fits all data sets with the same physical parameter values, satisfies the particle sum rule and successfully addresses two widely discussed kink anomalies in the dispersion.

Figure 1

(a) ${\Delta }_0$ as a function of ${\omega }_0$ for various $Z_{\mathrm{FL}}$. Other primary ECFL parameter values are $n=0.85$, $T=100\mathrm{K}$, and ${\xi }_{\overrightarrow{k}}$ as described in the text. A small $\eta$ value, 0.010 eV, was used for this plot, which is used as a “lookup table” during the fit. (b),(c) Examples of the spectral function calculated with different values of the effective sample quality parameter $\eta$. See the caption of the next figure for parameter values used. The instrumental energy broadening of 10 meV (FWHM) is included.

Figure 2

Laser ARPES data (symbols, Bi2212) from Ref. 14 fit with the ECFL line shape (red lines). The free parameters of the fit were ${\omega }_0$ (0.5 eV), $\eta$ (0.032 eV), and ${\xi }_{\overrightarrow{k}}$ (shown). Fixed parameters: $n$ (0.85), $Z_{\mathrm{FL}}$ ($1/3$). Derived parameters: ${\Delta }_0$ (0.12 eV), ${\Omega }_0$ (0.14 eV). Other than $\eta$ and ${\xi }_{\overrightarrow{k}}$, the same parameters are used elsewhere in the Letter. In (a), the gray line corresponds to the theoretical curve with ${\xi }_{\overrightarrow{k}}=0.15\mathrm{eV}$.

Figure 3

Conventional ARPES data (Bi2212) fit with the ECFL line shape. The data are from Ref. [19] ($T_c=90\mathrm{K}$). (a) The data (symbols) and the fit (red lines) are shifted vertically by the same amount for ease of view. (b) An example of the raw data and the fit data is shown for $k_2$. The background (bg) spectrum (see text) was subtracted from each raw data, and the resulting data, shown in (a), are then fit. (c) The fixed ${\xi }_{\overrightarrow{k}}$ parameters used for the fit. Thus, in this figure, $\eta$ is the only fit parameter (cf. Fig. 2 caption). (d) Raw data at $k=k_F$ fit with a somewhat greater $\eta$ value. (e) The current fit compared with a fit using the CADS line shape.

Figure 4

Conventional ARPES data, including our own (a),(b), fit with the ECFL line shape. The procedure used to fit these data are identical with those of the previous figure, i.e., a fit with a single free parameter $\eta$, with (d) being a single exception. (a),(b), Optimally doped Bi2212 ($T_c=91\mathrm{K}$). (c) Optimally doped LSCO data [26, 27]. (d) A test fit up to 0.6 eV for the LSCO data with a small change to ${\omega }_0$ for the same data as in (c) but over a wider energy range. By changing ${\omega }_0$ slightly from 0.50 to 0.42 eV, we see that an excellent fit up to 0.6 eV is found. The LSCO data, as far as we are aware, is fit only by the ECFL theory, since an energy dependence rising linearly for occupied states occurs naturally and uniquely in the ECFL spectral function.

Figure 5

Image plots of the spectral function for (a) the ECFL theory ($\eta =0.17\mathrm{eV}$), and (b) that of the auxiliary FL. (c) The data of Fig. 4a before (inset) and after (main) MDC normalization, by which each MDC is scaled and shifted to have minimum 0 (green) and maxmimum 1 (red). Blue corresponds to $1/2$. (d) The near-$E_F$ part of the ECFL spectral function of (a), after MDC-normalization with MDC peak positions traced by black line. The black line in (c) is from (d). (e) The near-$E_F$ part of the AFL spectral function of (b) after MDC-normalization. The MDC peak positions are traced by gray dashed line, while the black line is from (d). The bending such as shown by the black line here is commonly referred to as the kink. (f) The temperature dependence of the peak asymmetry compared for three different theories, rising as $T^2$ for ECFL. Theory parameters for the calculation, apart from $T$, are taken from the fit of Fig. 2a for the ECFL, from the equivalent fit of Ref. 14 for the CADS, and from Ref. 25 for the MFL.