Visualizing the Energy-gap Modulations of the Cuprate Pair Density Wave State

Kavli Affiliate: J. C. Davis

| First 5 Authors: Zengyi Du, Hui Li, Sanghyun Joo, Elizabeth P. Donoway, Jinho Lee

| Summary:

When Cooper pairs are formed with finite center-of-mass momentum, the
defining characteristic is a spatially modulating superconducting energy gap
$Delta(r)$. Recently, this concept has been generalized to the pair density
wave (PDW) state predicted to exist in a variety of strongly correlated
electronic materials such as the cuprates. Although the signature of a cuprate
PDW has been detected in Cooper-pair tunnelling, the distinctive signature in
single-electron tunneling of a periodic $Delta(r)$ modulation has never been
observed. Here, using a new approach, we discover strong $Delta(r)$
modulations in Bi$_2$Sr$_2$CaCu$_2$O$_8$+$delta$ that have eight-unit-cell
periodicity or wavevectors $Q=2{pi}/a_0(1/8,0)$; $2{pi}/a_0(0,1/8)$. This
constitutes the first energy-resolved spectroscopic evidence for the cuprate
PDW state. An analysis of spatial arrangements of $Delta(r)$ modulations then
reveals that this PDW is predominantly unidirectional, but with an arrangement
of nanoscale domains indicative of a vestigial PDW. Simultaneous imaging of the
local-density-of-states $N(r,E)$ reveals electronic modulations with
wavevectors $Q$ and $2Q$, as anticipated when the PDW coexists with
superconductivity. Finally, by visualizing the topological defects in these
$N(r,E)$ density waves at $2Q$, we discover them to be concentrated in areas
where the PDW spatial phase changes by $pi$, as predicted by the theory of
half-vortices in a PDW state. Overall, this is a compelling demonstration, from
multiple single-electron signatures, of a PDW state coexisting with
superconductivity at zero magnetic field, in the canonical cuprate

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