Detection of a Pair Density Wave State in UTe₂

The properties of superconducting materials, their perfectly dissipationless electronics, perfect diamagnetism, and macroscopic quantum mechanical dynamics are all the products of the formation of a macroscopic quantum fluid of electron pairs. To better understand this, we have developed the first scanned Josephson/Andreev tunneling microscopes (SJTM/SATM) which provide direct access to the macroscopic quantum electron pair condensate.
Since the 1960s the possibility of a crystalline superconducting phase within the overall fluid has been discussed with great interest in the superconducting community. Such a state should manifest itself as a spatially periodic electron-pair crystal; we call this state a Pair Density Wave (PDW). For years the superconducting community had suggested that such a PDW state might exist in the high-temperature superconductor Bi₂Sr₂CaCu₂O_8+x. In 2016 our group developed our first SJTM system and subsequently detected this long predicted PDW state. Since then we have discovered PDWs in several other materials including in the transition metal dichalcogenide superconductor NbSe₂.
Recently our focus of study has been the spin-triplet topological superconductor UTe₂. This class of superconductor should exhibit many unprecedented electronic properties including fractionalized electronic states relevant to quantum information processing. In UTe₂ we searched for a PDW state, by visualizing the pairing energy-gap with μeV-scale energy-resolution made possible by a superconducting SATM tip. We discovered three PDWs at incommensurate wavevectors P_i = 1,2,3 that are indistinguishable from the wavevectors Q_i = 1,2,3 of the prevenient CDW. From these observations and given UTe₂ as a spin-triplet superconductor, this PDW state appears to be the first known spin-triplet pair density wave.

Published Article - Nature 618, 921 - June 2023

Identification of a Nematic Pair Density Wave State in Bi₂Sr₂CaCu₂O_8+x

Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here, we use SJTM to visualize the interplay of PDW and DSC states in Bi₂Sr₂CaCu₂O_8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi₂Sr₂CaCu₂O_8+x is a vestigial nematic pair density wave [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

Published Article - Proc. Nat'l Acad. Sci. 119, 2206481119 - July 2022

Discovery of a Cooper-Pair Density Wave State in a Transition-Metal Dichalcogenide

Pair density wave (PDW) states are defined by a spatially modulating superconductive order parameter. To search for such states in transition-metal dichalcogenides (TMDs), we used high-speed atomic- resolution scanned Josephson-tunneling microscopy. We detected a PDW state whose electron-pair density and energy gap modulate spatially at the wave vectors of the preexisting charge density wave (CDW) state. The PDW couples linearly to both the s-wave superconductor and the CDW and exhibits commensurate domains with discommensuration phase slips at the boundaries, conforming those of the lattice-locked commensurate CDW. Nevertheless, we found a global δΦ ≈ ±2π/3 phase difference between the PDW and CDW states, possibly owing to the Cooper-pair wave function orbital content. Our findings presage pervasive PDW physics in the many other TMDs that sustain both CDW and superconducting states.

Published Article - Science 372, 1447 - June 2021

Imaging the Energy Gap Modulations of the Cuprate Pair Density Wave State

The defining characteristic of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in high temperature superconducting cuprates (ARCMP 11, 231 (2020) ). Although the existence of a PDW in cuprates was discovered by using Cooper-pair tunneling (Nature 532, 343 (2016) ), its signature in single-electron tunneling of periodic Δ(r) modulations, proved elusive. Now, by using a new approach, we detect strong Δ(r) modulations in Bi₂Sr₂CaCu₂O_8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ 2π/a₀ (1/8,0); 2π/a₀ (0,1/8). Simultaneous imaging of the local-density-of-states N(r,E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated for a coexisting superconductor and PDW. Overall, this provides strong confirmation that a PDW state coexists with superconductivity in the canonical cuprate Bi₂Sr₂CaCu₂O_8+δ.

Published Article - Nature 580, 65-70 - April 2020

Magnetic-Field Induced Pair Density Wave State in the Cuprate Vortex Halo

Superconductivity occurs when electrons form pairs of opposite spin and opposite momentum, and these "Cooper pairs" condense into a homogeneous electronic fluid. However, theorists have recently realized that these electron pairs might also crystallize into a “pair density wave” (PDW) state where the density of pairs modulates periodically in space. Intense theoretical interest has emerged in whether such a PDW is the competing phase in cuprates. To search for evidence of such a PDW state we suppress the homogeneous superconductivity using high magnetic field and visualize the electronic structure of the new phase which appears. Under these circumstances we discovered modulations in the density of electronic states containing multiple signatures of a PDW state. The phenomena are in detailed and excellent agreement with theoretical predictions for a field-induced primary PDW state. These data indicate that it is a PDW state which competes with superconductivity in cuprates and that it dominates in the high-field regime.

Published Article - Science 364, 976 - June 2019