Bulk Fermi surface and momentum density in heavily doped La${}_{2-x}$Sr${}_x$CuO${}_4$ using high-resolution Compton scattering and positron annihilation spectroscopies

We have observed the bulk Fermi surface (FS) in an overdoped ($x=0.3$) single crystal of La${}_{2-x}$Sr${}_x$CuO${}_4$ by using Compton scattering. A two-dimensional (2D) momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory (DFT) calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. In particular the predicted FS topology is found to be in good accord with the corresponding experimental data. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and the DFT-based computations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either the theory or the experiment.

Figure 1

(a) Band structure of LSCO near the Fermi level. The CuO${}_2$ band is shown as a red dotted line. (b) Calculated ${\rho }_{x^2-y^2}^{2d}(p_x,p_y)$ is shown together with the FS sections at $(k_z=0)$ for the doping level $x=0.3$. The color scale is in units of ${\rho }^{2d}$(0,0). The grid represents Brillouin zones with a size of $2\pi /a$, where $a$ is the lattice constant.

Figure 2

Theoretical and experimental profiles ${\rho }^{1d}\left(p_x\right)$ for (a) ACAR and (b) Compton scattering along the [100] direction. All spectra are normalized to ${\rho }^{1d}$(0).

Figure 3

Theoretical and experimental $A^{1d}\left(p_x\right)$ for (a) ACAR and (b) Compton scattering.

Figure 4

Top: (left) Experimental and (right) theoretical ACAR $C_{4v}$ anisotropy. Bottom: (left) Experimental and (right) theoretical $C_{4v}$ anisotropy (Compton). The color scale is in units of ${\rho }^{2d}$(0,0).

Figure 5

Positron density for LSCO in the (010) plane. The positron wave function is normalized in the LSCO unit cell and a logarithmic density scale (with integer numbers as units) is used in order to enhance regions with low positron density. The atomic positions (La, Cu, O) set the scale for the $x$ and $y$ axes.

Figure 6

(a) Cylindrical anisotropy for theoretical Compton scattering momentum density. The white lines define the Brillouin zones, while blue squares indicate a family of zones where the FS features are particularly strong. (b) The blue squared regions are isolated from the rest of the spectra and folded back to the central region. The color scale is in units of ${\rho }^{2d}$(0,0).

Figure 7

Result of the partial folding procedure: (a) Nonconvoluted theory; (b) Theory convoluted with experimental resolution $0.07$ a.u.; (c) Theory convoluted with experimental resolution $0.13$ a.u.; (d) Experiment. The white color corresponds to a weight of unity (occupied) while the black color corresponds to zero (unoccupied).

Figure 8

Cuts of the distributions in Fig. 7 along the nodal direction. The amplitudes of theory and experiment are compared on the same scale. Curves are offset with respect to one another for clarity. From the bottom to the top, the first curve is the nonconvoluted theory, the second is the convoluted theory with a resolution $0.07$ a.u., the third is the convoluted theory with a resolution $0.13$ a.u., and the fourth curve is the experimental data.