Detection of a Pair Density Wave State in UTe$_2$

TL;DR

This study visualizes and confirms the existence of a spin-triplet pair density wave in UTe$_2$, revealing spatial modulations of the superconducting order parameter and its relation to charge density waves, a novel finding in superconductors.

Contribution

First direct visualization of a spin-triplet pair density wave in a heavy fermion superconductor UTe$_2$, linking it to charge density wave structures.

Findings

Detection of three pair density waves with ~10 μeV gap modulations

PDWs share wavevectors with charge density waves and have a phase difference of approximately π

Establishment of a spin-triplet PDW state as unprecedented in superconductors

Abstract

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties including fractionalized electronic states relevant to quantum information processing. Although UTe$_2$ may embody such bulk topological superconductivity, its superconductive order-parameter $\Delta(\mathbf{k})$ remains unknown. Many diverse forms for $\Delta(\mathbf{k})$ are physically possible in such heavy fermion materials. Moreover, intertwined density waves of spin (SDW), charge (CDW) and pairs (PDW) may interpose, with the latter state exhibiting spatially modulating superconductive order-parameter $\Delta(\mathbf{r})$, electron pair density and pairing energy-gap. Hence, the newly discovered CDW state in UTe$_2$ motivates the prospect that a PDW state may exist in this material. To search for it, we visualize the pairing energy-gap with $\mu$$eV$-scale energy-resolution using superconductive STM tips. We detect three PDWs, each with peak-peak gap modulations circa 10 $\mu$$eV$ and at incommensurate wavevectors $\mathbf{P}_{i=1,2,3}$ that are indistinguishable from the wavevectors $\mathbf{Q}_{i=1,2,3}$ of the prevenient CDW. Concurrent visualization of the UTe$_2$ superconductive PDWs and the non-superconductive CDWs reveals that every $\mathbf{P}_i$ : $\mathbf{Q}_i$ pair exhibits a relative phase $\delta\phi \approx \pi$. From these observations, and given UTe$_2$ as a spin-triplet superconductor, this PDW state should be a spin-triplet pair density wave. While such states do exist in superfluid $^{3}$He, for superconductors they are unprecedented.