Computation of stripes in cuprates within the $\mathrm{LDA}+U$ method

We present a computation of vertical stripes in ${\mathrm{La}}_{15∕8}{\mathrm{Sr}}_{1∕8}{\mathrm{CuO}}_4$ within the $\mathrm{LDA}+U$ method. We find that $\mathrm{Cu}$ centered stripes are unstable toward O centered stripes. The metallic core of the stripe is quite wide and shows reduced magnetic moments with suppressed antiferromagnetic (AF) interactions. The system can be pictured as alternating metallic and AF two-leg ladders the latter with strong AF interaction and a large spin gap. The Fermi surface shows warping due to interstripe hybridization. The periodicity and amplitude of the warping is in good agreement with angle resolved photoemission experiment. We discuss the connection with low-energy theories of the cuprates.

Figure 1

The hole charge and spin order within ${\mathrm{CuO}}_2$ plane. Sites with (without) arrows (indicating spin directions) are $\mathrm{Cu}\left(\mathrm{O}\right)$. The radii of circles are proportional to the hole content inside atomic spheres. The gray regions are metallic core with $\mathrm{Cu}$ of type $\mathrm{Cu}1$ and the white regions are the AF ladders with $\mathrm{Cu}$ of type $\mathrm{Cu}2$. Numbers indicate the distribution of the doped hole. Not shown are 1.2% (0.6%) of hole charge in the apical $\mathrm{O}$’s belonging to $\mathrm{Cu}1\left(\mathrm{Cu}2\right)$ and 0.3% of charge on $\mathrm{La}$. The unit cell in the ${\mathrm{CuO}}_2$ plane is shown by the dashed line.

Figure 2

Calculated band structure of ${\mathrm{La}}_{15∕8}{\mathrm{Sr}}_{1∕8}{\mathrm{CuO}}_4$ around the Fermi level $\left(E_F=0\right)$. Left (right) panel corresponds to the direction parallel (perpendicular) to the stripe. The point $B$ corresponds to momentum $[0,\pi ∕(2a\left)\right]$ in the $\mathrm{Cu}\text{−}\mathrm{O}$ plane.

Figure 3

Wannier function of the active band.

Figure 4

Angle resolved photoemission spectral weight integrated within $500\mathrm{meV}$ of the Fermi level, as a function of $k_x$ and $k_y$ (Ref. 26) together with calculated Fermi surface for 2D ${\mathrm{CuO}}_2$ plane with stripes oriented along $y$ (dashed line) (Ref. 50). Notice that the experimental Fermi surface has contributions due to stripes oriented along $y$ and along $x$ the latter producing the vertical structures at $k_x\sim 0.2\pi ∕a$.