Detection of a Cooper-Pair Density Wave in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$

Abstract

The quantum condensate of Cooper-pairs forming a superconductor was originally conceived to be translationally invariant. In theory, however, pairs can exist with finite momentum $Q$ and thereby generate states with spatially modulating Cooper-pair density. While never observed directly in any superconductor, such a state has been created in ultra-cold ${}^6$Li gas. It is now widely hypothesized that the cuprate pseudogap phase contains such a 'pair density wave' (PDW) state. Here we use nanometer resolution scanned Josephson tunneling microscopy (SJTM) to image Cooper-pair tunneling from a $d$-wave superconducting STM tip to the condensate of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$. Condensate visualization capabilities are demonstrated directly using the Cooper-pair density variations surrounding Zn impurity atoms and at the Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ crystal-supermodulation. Then, by using Fourier analysis of SJTM images, we discover the direct signature of a Cooper-pair density modulation at wavevectors $Q_p\approx (0.25,0)2\ddot{I}€/a_0$;$(0,0.25)2\ddot{I}€/a_0$ in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$. The amplitude of these modulations is ~5% of the homogenous condensate density and their form factor exhibits primarily $s$/$s^{\prime }$-symmetry. This phenomenology is expected within Ginzburg-Landau theory when a charge density wave with $d$-symmetry form factor and wave vector $Q_c=Q_p$ coexists with a homogeneous $d$-symmetry superconductor ; it is also encompassed by several contemporary microscopic theories for the pseudogap phase.