Three-Dimensional Fermi Surface of Overdoped La-Based Cuprates

We present a soft x-ray angle-resolved photoemission spectroscopy study of overdoped high-temperature superconductors. In-plane and out-of-plane components of the Fermi surface are mapped by varying the photoemission angle and the incident photon energy. No $k_z$ dispersion is observed along the nodal direction, whereas a significant antinodal $k_z$ dispersion is identified for La-based cuprates. Based on a tight-binding parametrization, we discuss the implications for the density of states near the van Hove singularity. Our results suggest that the large electronic specific heat found in overdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ cannot be assigned to the van Hove singularity alone. We therefore propose quantum criticality induced by a collapsing pseudogap phase as a plausible explanation for observed enhancement of electronic specific heat.

Figure 1

In-plane FSs of LSCO ($x=0.22$) (a), (b) and Eu-LSCO ($x=0.21$) (c), (d) measured at $T=12\mathrm{K}$ using SX-ARPES. Photoelectron intensities have been integrated $\pm 20\mathrm{meV}$ around $E_F$. Corresponding $k_z$ value at $(k_x,k_y)=(0,0)$ is indicated on the right top of each panel along with the associated incident photon energies. (e) Sketch of the Brillouin zone and location of the in-plane cuts in the 3D momentum space at $h\nu =400$ and 447 eV.

Figure 2

Out-of-plane FS dispersions. (a)–(d) Out-of-plane FS maps recorded along nodal ($\pi$, $\pi$) and the antinodal ($\pi$, 0) directions—as indicated in (g)—for LSCO ($x=0.22$) and Eu-LSCO ($x=0.21$). (e),(f) $k_z$ dependence of nodal and off-nodal [see (g) and (h)] $k_F^{\prime }s$ on the FS of Tl2201. A zoom on the off-nodal $k_z$ dispersion is provided in (f). Nodal out-of-plane maps and data in panels (b) and (f) are symmetrized around $k_{||}=0$. FSs reproduced by the three-dimensional tight-binding model (see text) are overlaid as white dashed curves. Photoelectron intensities are integrated $\pm 20\mathrm{meV}$ around $E_F$. Black lines in panels (b) and (d) represent Brillouin zone boundaries. (g) Sketch of the three-dimensional Brillouin zone and location of the cuts. (h) In-plane FS map of Tl2201 with nodal ($\pi$, $\pi$) and off-nodal cuts indicated.

Figure 3

Comparison of calculated DOS with experimentally extracted Sommerfeld constant $\gamma$. (a) Doping dependence of DOS at $E_F$ calculated for LSCO and Eu-LSCO from a tight-binding model (see text and Table 1) with $t_z=0.07t$ (3D) and 0 (2D). The diverging peak in two dimensions is replaced by a plateau in the three-dimensional model. The right axis indicates the electronic specific heat coefficient $\gamma =({\pi }^2/3)k_B^2\times \mathrm{DOS}(E_F)$. (b) Doping dependence of $\gamma$ reported on Zn-LSCO [13], LSCO ($x=0.33$) [48], Eu-LSCO, and Nd-LSCO [14] plotted on the same scale as in (a). (c) $\gamma$ values calculated from the 3D tight-binding model for LSCO with quasiparticle scattering rates as indicated.