Fig. 3: Energy-gap Modulations from Superconductive to Pseudogap Phase.
From: Scattering interference signature of a pair density wave state in the cuprate pseudogap phase
a Measured \({\Delta }_{1}\left({{{{{\boldsymbol{r}}}}}}\right)\) within 20 nm × 20 nm FOV at T = \(0.11{T}_{{{{{{\rm{c}}}}}}}\) = 4.2K. The energy-gap is measured from the energy of the coherence peak at E > 0. The inset shows the linecuts from \({{{{{\boldsymbol{q}}}}}}\) = (0, 0) to (0.5, 0)2π/a0 and from \({{{{{\boldsymbol{q}}}}}}\) = (0, 0) to (0, 0.5)2π/a0 in the measured \({\Delta }_{1}\left({{{{{\boldsymbol{q}}}}}}\right)\). The significant disorder as q→0 in is fitted to a cylindrical gaussian and subtracted. \({{{{{\boldsymbol{q}}}}}}\approx [(\pm 1/{{{{\mathrm{8,0}}}}});(0,\pm 1/8)]2{{{{{\rm{\pi }}}}}}/{a}_{0}\) peaks are present in both directions. The white areas represent regions where it is impossible to determine the coherence peak position \({\Delta }_{1}\). b Gap modulations \({\Delta }_{1q}\left({{{{{\boldsymbol{r}}}}}}\right)\) from 3(a). These are visualized at wavevectors \({{{{{\boldsymbol{q}}}}}}\approx [(\pm 1/{{{{\mathrm{8,0}}}}});(0,\pm 1/8)]2{{{{{\rm{\pi }}}}}}/{a}_{0}\) by Fourier filtering \({\Delta }_{1}\left({{{{{\boldsymbol{r}}}}}}\right)\) at the 1/8 peaks as shown in inset of 3a. The Gaussian filter size σq = 1.45 pixels (or equivalently 0.455 nm−1) in q-space, which corresponds to 2.2 nm in r-space. c Measured \({g}\left({{{{{\boldsymbol{r}}}}}},60{mV}\right)\) at T = 0.14\({T}_{{{{{{\rm{c}}}}}}}\) = 5 K within 9.9 nm × 9.9 nm FOV. The \(g\left({{{{{\boldsymbol{r}}}}}},60{mV}\right)\) manifests unidirectional charge modulations. d Measured \(g\left({{{{{\boldsymbol{r}}}}}},60{mV}\right)\) at T = 1.5\({T}_{{{{{{\rm{c}}}}}}}\) = 55 K in the identical FOV as (c). No change has been detected in \(g\left({{{{{\boldsymbol{r}}}}}},60{mV}\right)\) at T = 55 K. e Measured \({\Delta }_{1}\left({{{{{\boldsymbol{r}}}}}}\right)\) at T = 0.14\({T}_{{{{{{\rm{c}}}}}}}\) = 5 K shows the spatial variation of the coherence peak at E > 0. f Measured\(\,{\Delta }_{1}\left({{{{{\boldsymbol{r}}}}}}\right)\) at T = 1.5\({T}_{{{{{{\rm{c}}}}}}}\) = 55 K in the identical FOV as (c), (d) and (e). The spatial variation of the coherence peak is highly similar to (e).
