Cuprate phase diagram and the influence of nanoscale inhomogeneities

The phase diagram associated with high-$T_c$ superconductors is complicated by an array of different ground states. The parent material represents an antiferromagnetic insulator but with doping superconductivity becomes possible with transition temperatures previously thought unattainable. The underdoped region of the phase diagram is dominated by the so-called pseudogap phenomena, whereby in the normal state the system mimics superconductivity in its spectral response but does not show the complete loss of resistivity associated with the superconducting state. An understanding of this regime presents one of the great challenges for the field. In the present study we revisit the structure of the phase diagram as determined in photoemission studies. By careful analysis of the role of nanoscale inhomogeneities in the overdoped region, we are able to more carefully separate out the gaps due to the pseudogap phenomena from the gaps due to the superconducting transition. Within a mean-field description, we are thus able to link the magnitude of the doping-dependent pseudogap directly to the Heisenberg exchange interaction term, $J\sum s_i{s}_j$, contained in the $t-J$ model. This approach provides a clear indication that the pseudogap is associated with spin singlet formation.

Figure 1

Two scenarios for the hole-doped high temperature superconductivity (HTS) phase diagram. (a) $T^{*}$ merges with $T_c$ on the overdoped side. (b) $T^{*}$ crosses the superconducting dome (SC) and falls to zero at a quantum critical point (QCP). $T_N$ is the Néel temperature for the antiferromagnetic (AF) state.

Figure 2

Photoemission spectra recorded from an overdoped sample with $T_c=80\mathrm{K}$. (a) Temperature dependence of the spectra recorded at the antinodal point indicated in the schematic of the Fermi surface shown in (b). In the latter we indicate both the nodal and antinodal directions. In (a) the measured transition temperature $T_c$ is indicated by the transition from black to red curves. (c) The same spectra as in (a) symmetrized around the chemical potential. Now the color coding indicates that the gap loses a minimum in the center at approximately 90 K but does not finally disappear until approximately 120 K.

Figure 3

(a) The FWHM of the two-peak structure indicated in Fig. 2. The open circles indicate where two Lorentzians are used to fit the structure, the filled circles indicate a single Lorentzian. (b) The separation of the two Lorentzians used in the fitting procedure. $T_1^{*}$ indicates the temperature at which there is no longer a dip between the two peaks and $T_2^{*}$ indicates the temperature at which there is no longer a decrease in the overall width which then simply increases linearly with temperature.

Figure 4

Simulation of the photoemission spectra in the antinodal region. (a) The gap distributions used in the simulation as a function of doping. The transition temperature $T_c$ and region in the phase diagram is indicated. The distribution peaks at the overall $T_c$ measured for the sample as in magnetization studies. (b) The simulated overall width of the peak structure in the overdoped region as a function of doping to be compared with the experimental measurements as shown in Fig. 3, for example. (c) Simulation of the measured two-peak structure. The gray curve represents a simple two-peaked structure associated with the average $T_c$; the green curve reflects the gap structure associated with the nanoscale inhomogeneities and FWHM indicated in (b).

Figure 5

The pseudogap temperature $T^{*}$ determined in different studies of the Bi2212 system as a function of doping $x$. The different sources are indicated. The red line indicates a fit to the data recorded for doping levels below $x=0.2$. The references associated with different data points are indicated.