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A recent discovery of the pair density wave (PDW) order creates a stir inunderstanding an underlying physics in the pseudogap states of the cuprate hightemperature superconductors. We have performed a Spectroscopic Imaging ScanningTunneling Microscopy (SI-STM) measurements onBi$_2$Sr$_2$CaCu$_2$O$_8$+$\delta$ and identified that spatially uniform d-wavesuperconductivity (DSC), d-symmetry charge density wave (CDW), and the PDW playimportant roles in an intertwined fashion. In this review, we show how thesedifferent electronic degrees of freedom emerges in electronic structures of thecuprate and discuss how they are related to each other.

Atomic-Scale Visualization of the Cuprate Pair Density Wave State