High-Spin Polaron in Lightly Doped ${\mathrm{CuO}}_2$ Planes

We derive and investigate numerically a minimal yet detailed spin-polaron model that describes lightly doped ${\mathrm{CuO}}_2$ layers. The low-energy physics of a hole is studied by total-spin-resolved exact diagonalization on clusters of up to 32 ${\mathrm{CuO}}_2$ unit cells, revealing features missed by previous studies. In particular, spin-polaron states with total spin $3/2$ are the lowest eigenstates in some regions of the Brillouin zone. In these regions, and also at other points, the quasiparticle weight is identically zero indicating orthogonal states to those represented in the one electron Green’s function. This highlights the importance of the proper treatment of spin fluctuations in the many-body background.

Figure 1

(a) Two adjacent unit cells of the ${\mathrm{CuO}}_2$ plane. The orbitals kept in the three-band model of Eq. (1) are shown, with white (shaded) for positive (negative) signs. The two $ϵ$ vectors (solid arrow) and the four $\delta$ vectors (dashed arrow) are also shown. (b) Sketch of a virtual process of $T_{\mathrm{swap}}$.

Figure 2

(a) Energy shifted to align GS values. (b) Quasiparticle weight for the lowest eigenstates with $S_T=\frac{1}{2}$ and $\frac{3}{2}$ vs momentum.

Figure 3

$⟨C_x(\delta ,a)⟩$ for the lowest energy state at (a) ($\frac{\pi }{2}$, $\frac{\pi }{2}$) with $S_T=\frac{1}{2}$, and (b) at ($\pi$, $\pi$) with $S_T=\frac{3}{2}$. The darkly shaded bullet denotes the oxygen position at $l+e_x$. Each bullet shows the correlation value between the two sandwiching Cu sites. The central 12 Cu sites are shown; the correlations between the other 20 Cu spins converge fast towards the AFM value of $\sim -0.33$. $⟨C_y(\delta ,a)⟩$ is the ${\widehat{P}}_{x\leftrightarrow y}$ reflection.

Figure 4

$⟨C_{x/y}⟩$ for the $\frac{1}{2}$ state at $k=(0,\pi )$.