Bands, spin fluctuations, and traces of Fermi surfaces in angle-resolved photoemission intensities for high-$T_c$ cuprates

The band structures of pure and hole doped La${}_2$CuO${}_4$ with antiferromagnetic (AFM) spin fluctuations are calculated and compared to spectral weights of angle-resolved photoemission spectroscopy (ARPES). It is shown that observations of coexisting Fermi-surface (FS) arcs and closed FS pockets are consistent with modulated AFM spin fluctuations of varying wavelengths. Large variations of strong spin fluctuations make the outer part of the FS break diffuse at low doping. This part of the FS is suppressed at high doping when spin fluctuations are weak. The resulting superimposed spectral weight has features both from FS arcs and closed pockets. A connection between results of ARPES, neutron scattering, and band results for the modulated AFM spin-wave state suggests that spin-phonon coupling is an important mechanism for the properties of the cuprates.

Figure 1

The band structure (nonmagnetic) of La${}_2$CuO${}_4$ for $k_z=0$. AFM order will fold the Brillouin zone, so that the $X-M$ bands are mirrored back on $X-\Gamma$. The bands from $M$ to $\Gamma$ will be folded at the new zone limit $M^{\prime \prime }$ ($\pi /2a_0,\pi /2a_0$), indicated by the downward arrow. When AFM is modulated into stripes the folding moves closer toward $\Gamma$ (indicated by the upward arrow) and the zone limit at $X$ is reduced correspondingly.

Figure 2

The band structure of nonmagnetic (broken lines) and AFM (full lines) La${}_4$Cu${}_2$O${}_8$ in the AFM brillouin zone for $k_z=0$. The AFM configuration is obtained by having a staggered magnetic field on Cu ($\pm$7 mRy). The moments are $\pm$0.19${\mu }_B$/Cu.

Figure 3

The evolution of the AFM FS for increased exchange splitting ($h=0,5$, 10 mRy) are shown by green “$\times$,” blue “+,” and black “$•$”, respectively. The original “unfolded” FS for $h=0$ has only one circular FS centered around the $M$ point ($\pi /a_0,\pi /a_0$). Two disconnected FSs are formed when $h$ increases. One at $X$, which is diffuse and disappears at high doping, and one at $M^{\prime \prime }$ with clear FS breaks toward $\Gamma$ and $M$. This piece of FS is displaced toward $\Gamma$ when AFM is $q$ modulated into stripes (red “$\circ$”).

Figure 4

A schematic closeup of the bands near the $M^{\prime \prime }$ point. The non-spin-polarized band is reflected at the zone boundary at $M^{\prime \prime }$ to create the band structure for weak AFM (full lines). An exchange energy $\xi$ will split the bands (heavy broken lines) and displace the FS breaks closer to $M^{\prime \prime }$. The bands from three striped AFM waves, modulated with three different $q$ vectors ($q_1,q_2$, and $q_3$), will be reflected by the three new zone limits indicated by the short vertical lines, as described in the text. These bands (thin broken lines) make FS crossings at different positions (*) on the part outside the zone limits, while they are all superimposed on one FS crossing (+) on the inside part, i.e., the part closest to $\Gamma$.

Figure 5

An intensity plot (the occurrence of having the bands within 2 mRy of $E_F$ for each $k_x,k_y$ bin) for the folded FS of LCO with $E_F$ shifted to be close to optimal doping. The exchange is 10–15 mRy with $q$ from 0.04 to 0.012.

Figure 6

As in Fig. 5, but for 3 mRy lower $E_F$, with $\xi$ 8–12 mRy and $q$ 0.08–0.03.

Figure 7

Approximate ranges of the exchange splitting $\xi$ as a function of modulation vector $q$ used for Figs. 5 and 6.