Hot Spots and Pseudogaps for Hole- and Electron-Doped High-Temperature Superconductors

Using cluster perturbation theory, it is shown that the spectral weight and pseudogap observed at the Fermi energy in recent angle resolved photoemission spectroscopy of both electron- and hole-doped high-temperature superconductors find their natural explanation within the $t\mathrm{\text{−}}{t}^{\prime }\mathrm{\text{−}}{t}^{\prime \prime }\mathrm{\text{−}}U$ Hubbard model in two dimensions. The value of the interaction $U$ needed to explain the experiments for electron-doped systems at optimal doping is in the weak to intermediate coupling regime where the $t\mathrm{\text{−}}J$ model is inappropriate. At strong coupling, short-range correlations suffice to create a pseudogap, but at weak-coupling long correlation lengths associated with the antiferromagnetic wave vector are necessary.

Figure 1

Chemical potential calculated at various dopings using CPT, in units of $t$, the nearest neighbor hopping. For this figure only, $t^{\prime }=-0.4t$ and $t^{\prime \prime }=0$.

Figure 2

Single particle spectral weight, as a function of energy $\omega$ in units of $t$, for wave vectors along the high-symmetry directions shown in the inset. (a) CPT calculations on a $3\times 4$ cluster with ten electrons ($17\%$ hole doped). (b) the same as (a), with 14 electrons ($17\%$ electron doped). In all cases we use $t^{\prime }=-0.3t$ and $t^{\prime \prime }=0.2t$. A Lorentzian broadening $\eta =0.12t$ is used to reveal the otherwise delta peaks.

Figure 3

Top: Intensity plot of the spectral function at the Fermi level, in the first quadrant of the Brillouin zone, for a $17\%$ hole-doped system (ten electrons on a $3\times 4$ cluster). Here $t^{\prime }=-0.3t$ and $t^{\prime \prime }=0.2t$ (the gray dashed line is the noninteracting Fermi surface). Bottom: Imaginary part of the self-energy (in units of $t$) corresponding to the same parameters as the top plot. A Lorentzian broadening is used: $\eta =0.12t$ (top) and $\eta =0.4t$ (bottom).

Figure 4

Same as Fig. 3, but for an electron-doped system (14 electrons on a $3\times 4$ cluster). The white dashed line on the left panels is the AFM zone boundary, showing the coincidence of hot spots with the intersection of this line with the Fermi surface.

Figure 5

Left: Spectral function for the hole doped system illustrated in Figs. 2a, 3 plotted as a function of energy, for wave vectors along the direction $X=(\pi ,0)$ to $Z=(\pi ,\pi /2)$. At $U=2t$ (top), a depression in the spectral function is visible slightly away from $\omega =0$, while the pseudogap is fully opened at $U=8t$ (middle). Right: Spectral function for the electron-doped system illustrated in Figs. 2b, 4 plotted along the diagonal of the Brillouin zone, from $A=(0.3\pi ,0.3\pi )$ to $B=(0.7\pi ,0.7\pi )$. The results for the experimentally relevant electron underdoped system are similar.