Fig. 2: Visualizing CuO2 charge transfer energy variations δε(r).
a, Topograph of the BiO surface of Bi2Sr2CaCu2O8+x (VS = –750 mV:IS =25 pA). The bulk-crystal supermodulation, a quasi-periodic modulation along the (1, 1) direction, is clearly evident. It is at 45° to—and therefore is the mirror plane between—the x and y axes, as always26. Any distinctions between the states of oxygen orbitals along the x and y axes are not influenced by supermodulation for this symmetry reason, as empirically demonstrated in Methodsand Extended Data Fig. 9. Therefore, supermodulation has no discernable influence on the intra-unit-cell symmetry breaking of δε(r). b, High-voltage differential conductance spectra g(r, V) are shown as a solid black curve, whereas the spatially averaged spectrum \(\overline{g\left(V\right)}\) is shown as a dashed curve. The example spectrum is measured at a location (yellow dot) in a. Such high junction resistances of 85 GΩ or large tip–sample distances preclude the effects of the tip–sample electric field on g(V). The separation between the lower and upper bands is clearly visible for the example spectrum (blue arrows) as well as for the average spectrum (red double-headed arrow). Setpoint VS = –600 mV:IS = 7 pA. c, Visualization of charge transfer energy variations δε(r) from a. d, Histogram of charge transfer energy variations δε in c. e, PSD Fourier transform T(q) of the topograph measured simultaneously as c. The QSM peaks (orange arrow) signify the supermodulation. f, Linecuts from q = (0, 0) to (1, 0)2π/a0 and from q = (0, 0) to (0, 1)2π/a0 in T(q). The values at Qx = (1, 0)2π/a0 and Qy = (0, 1)2π/a0 are indistinguishable; thus, the PSD T(q) does not break C4 symmetry at its Bragg peaks. g, PSD Fourier transform δε(q) of charge transfer energy map from c. The QSM peaks are removed in δε(q). h, Linecuts from q = (0, 0) to (1, 0)2π/a0 and from q = (0, 0) to (0, 1)2π/a0 in δε(q) from g. The δε(q) breaks C4 symmetry at its Bragg peaks as the plots of δε(q) are distinct at Qx = (1, 0)2π/a0 and Qy = (0, 1)2π/a0. This is direct evidence of intra-unit-cell rotational symmetry breaking at the charge transfer energy in cuprates.
