Extended Data Fig. 11: Pair density wave in monolayer Bi-2212.

a, Four representative conductance spectra (\({\rm{d}}I/{\rm{d}}V\); upper panel) and the negative of their second derivative (\(D=-{{\rm{d}}}^{3}I/{\rm{d}}{V}^{3}\); lower panel) in under-doped monolayer Bi-2212 obtained from UD50. We additionally define \(H={\rm{d}}I/{\rm{d}}V(E={\varDelta }_{0})-{\rm{d}}I/{\rm{d}}V(E=0)\), which corresponds to the amount of low-energy DOS gapped out by Cooper pairing (here \({\varDelta }_{0}=15\,{\rm{m}}{\rm{e}}{\rm{V}}\)). The pair density wave can be visualized by spatially mapping either H or D (ref. ³²). b, \(H({\bf{r}})\) map on a \(40\,{\rm{nm}}\times 40\,{\rm{nm}}\) area. A chequerboard pattern is clearly resolved. c, Fourier transform of the \(H({\bf{r}})\) map in b. Peaks at \(|{\bf{q}}|=(0.25\pm 0.02)2{\rm{\pi }}/{a}_{0}\) (marked by broken circles) along the Cu–O bond directions indicate the emergence of pair density wave order³². d–h, \(D({\bf{r}})\) maps obtained on the same area in b at various energies. i–m, Fourier transform of the \(D({\bf{r}})\) maps in d–h. The \(|{\bf{q}}|=2{\rm{\pi }}/4{a}_{0}\) spatial modulations at \(E=15\,{\rm{meV}}\) (broken circles in j) again indicate the existence of pair density wave³². Red crosses mark \({\bf{q}}=(0,\pm {\rm{\pi }}/{a}_{0})\) and \((\pm {\rm{\pi }}/{a}_{0},0)\). We followed the method described in ref. ³² to obtain \(H({\bf{r}})\) and \(D({\bf{r}})\) maps. First, a set of conductance (dI/dV) spectra was taken on a 160 × 160 grid over the 40 nm × 40 nm area. Here we used a set-point bias voltage of −300 mV, which is far beyond the energy scale of the charge-ordered state, to eliminate possible set-point effects. We then fitted each dI/dV spectrum with a second-order polynomial, and took the second derivative of the polynomial to obtain the D spectrum. The \(H({\bf{r}})\) map is directly obtained from the dI/dV spectra grid.