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Science 11 April 2008:
Vol. 320. no. 5873, pp. 196 - 201
DOI: 10.1126/science.1154700
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Research Articles

Electronic Origin of the Inhomogeneous Pairing Interaction in the High-Tc Superconductor Bi2Sr2CaCu2O8+{delta}

Abhay N. Pasupathy1*, Aakash Pushp1,2*, Kenjiro K. Gomes1,2*, Colin V. Parker1, Jinsheng Wen3, Zhijun Xu3, Genda Gu3, Shimpei Ono4, Yoichi Ando5 and Ali Yazdani1{dagger}

1 Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08544, USA.
2 Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
3 Condensed Matter Physics and Materials Science, Brookhaven National Laboratory (BNL), Upton, NY 11973, USA.
4 Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan.
5 Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan.


Figure 1 Fig. 1. (A and B) Spectra taken at two different atomic locations on an overdoped Bi2Sr2CaCu2O8+{delta} sample (Tc = 68 K, OV68) at various temperatures. The gaps in the spectra close at different temperatures, leading to a temperature-independent background conductance at high temperature. (C) Histogram of pairing gap values measured in the OV68 sample. (Inset) A typical pairing gap map (300 Å) obtained for an OV68 sample at 30 K. (D and E) Spectra taken at two different atomic locations on an optimally doped sample (Tc = 93 K, OPT) at various temperatures. The background continues to be temperature dependent well above Tc. (F) Histogram of gap values observed in the OPT sample. (Inset) A typical pairing gap map (300 Å) obtained for an OPT sample at 40 K. [View Larger Version of this Image (32K GIF file)]
 

Figure 2 Fig. 2. (A and B) The conductance ratio R =[dI/dV(V,T)]/[dI/dV(V,T>>Tc)] (circles) obtained by dividing the raw spectra in Fig. 1, A and B, by the high-temperature background spectrum. Fits to the conductance ratio with the use of a thermally broadened d-wave BCS model are depicted as lines. In general, the fits work well at low V where the slope of the conductance ratio is inversely proportional to the gap. (C) Extracted values of the pairing gap for several different locations plotted as a function of temperature. The resistive Tc is indicated by the gray line. (D) Extracted lifetime broadening at different temperatures plotted as a function of the corresponding low-temperature gap. (Inset) The average lifetime broadening as a function of temperature. Error bars in (C) and (D) indicate the SD of the fits. [View Larger Version of this Image (41K GIF file)]
 

Figure 3 Fig. 3. (A) The low-temperature (T = 30 K) conductance ratio plotted for several different gaps. The conductance ratios deviate systematically from the d-wave model (Eq. 1, thin lines) and go below unity over a range of voltages (50 to 80 mV), indicating the strong coupling to bosonic modes. (B) The positive-bias conductance ratios are referenced to the local gap at different locations, showing that the magnitude of the dip-hump feature is similar at all locations. The line is the average of all the locations. (Inset) Gap-referenced conductance ratios for negative bias. (C) The RMSD of the conductance ratios from the d-wave model for positive (blue circles) and negative (red circles) bias over the energy range 20 to 120 mV. No correlation is seen between the magnitude of the deviations and the size of the gap. [View Larger Version of this Image (33K GIF file)]
 

Figure 4 Fig. 4. (A) Spectra obtained at evenly spaced locations along a 250 Å line in the normal state (T = 93 K) of an OV62 sample. Less than 1% of the sample shows a remnant of a gap at this temperature. (B) Differential conductance map at the Fermi energy obtained at 93 K. (C) Low-temperature (50 K) gap map obtained on the same area as in (B). (D to I) Spatial maps of the conductance at different energies obtained in the normal state. The junction is stabilized at 1 V and 40 pA where there is minimum topographic disorder. Whereas conductance maps at high energies show mostly structural features (b-axis supermodulation), the low-energy spectra are inhomogeneous on the ~15 Å length scale. [View Larger Version of this Image (82K GIF file)]
 

Figure 5 Fig. 5. (A) Angle-averaged autocorrelation of the low-temperature gap map in Fig. 4C (blue line), autocorrelation of the conductance map in Fig. 4B (green line), and cross correlation between the two images (red line). All the correlation lengths are similar (~15 Å), and there is a strong anticorrelation between the normal-state Fermi level conductance and the low-temperature gap map. (B) Average normal-state (T = 93 K) spectra measured in different regions that show distinct low-temperature superconducting gaps {Delta}0. Systematic changes are seen in the shape and position of the hump feature seen for the hole-like excitations. (Inset) Differential conductance of the normal state at the Fermi energy as a function of {Delta}0. (C) The energy corresponding to the hump feature in the spectra as a function of {Delta}0. [View Larger Version of this Image (14K GIF file)]
 

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