Proposal to measure the pair field correlator of a fluctuating pair density wave

I propose a method to directly measure the space and time dependence of the pair field correlator of a pair density wave. The method is based on two separate ideas. First, I adopt a recently proposed solenoid insertion method to provide the momentum in a tunnel junction. Second, I suggest the use of optimal or overdoped Bi-2201 films as a tunneling electrode with a known charge ordering wave vector which can match the expected pair density wave wave vectors I wish to study. The method is applicable to both fluctuating and ordered states. Potential applications are to the proposed stripe pair density wave order in LBCO and the possible pair density wave fluctuations at finite temperature or in high magnetic field in underdoped YBCO as well as other members of the cuprate family.

Figure 1

A drawing of the proposed scheme to measure PDW fluctuations. The sample being studied forms a tunnel junction with a probe superconductor that has long range ordered uniform or finite momentum pairing, or both. A hole is drilled in the middle and a solenoid is inserted (see Ref. [18]).

Figure 2

The differential conductance measured at zero voltage is plotted against the vector potential $\mathbf{A}$ assuming a fluctuating PDW with wave vector $P$ in the sample. Strictly speaking, the $x$ axis should be the gauge invariant gradient given by Eq. (6). Here, I assume there is no phase slip and take the London gauge. The shaded region denotes the $\mathbf{A}$ field that is accessible without destroying the probe superconductor. If the probe electrode has uniform pairing, a large $\mathbf{A}$ is required which is outside the accessible region. Nevertheless, even in this case there is a broad peak in $dI/dV$ as a function of voltage which may be observable for small $\mathbf{A}$. For this plot ${\xi }^{-1}=P/8$; i.e., the correlation length is about 1.27 times the PDW period.

Figure 3

Same as Fig. 2 except that a charge order is present in the probe superconductor at wave vector $Q_0$ which is parallel to $P$. This gives rise to an additional peak (in red) which partially overlaps the accessible region.