Atomic-scale visualization of electronic fluid flow

Rotating curved spacetime signatures from a giant quantum vortex

Gravity simulators1 are laboratory systems in which small excitations such as sound2 or surface waves3,4 behave as fields propagating on a curved spacetime geometry. The analogy between gravity and fluids requires vanishing viscosity2-4, a feature naturally realized in superfluids such as liquid helium or cold atomic clouds5-8. Such systems have been successful in verifying key predictions of quantum field theory in curved spacetime7-11. In particular, quantum simulations of rotating curved spacetimes indicative of astrophysical black holes require the realization of an extensive vortex flow12 in superfluid systems. Here we demonstrate that, despite the inherent instability of multiply quantized vortices13,14, a stationary giant quantum vortex can be stabilized in superfluid 4He. Its compact core carries thousands of circulation quanta, prevailing over current limitations in other physical systems such as magnons5, atomic clouds6,7 and polaritons15,16. We introduce a minimally invasive way to characterize the vortex flow17,18 by exploiting the interaction of micrometre-scale waves on the superfluid interface with the background velocity field. Intricate wave-vortex interactions, including the detection of bound states and distinctive analogue black hole ringdown signatures, have been observed. These results open new avenues to explore quantum-to-classical vortex transitions and use superfluid helium as a finite-temperature quantum field theory simulator for rotating curved spacetimes19.

Detection of a pair density wave state in UTe2

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe₂ may embody such bulk topological superconductivity^1-11, its superconductive order parameter Δ(k) remains unknown¹². Many diverse forms for Δ(k) are physically possible¹² in such heavy fermion materials¹³. Moreover, intertwined^14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating^14,15 superconductive order parameter Δ(r), electron-pair density^16-19 and pairing energy gap^17,20-23. Hence, the newly discovered CDW state²⁴ in UTe₂ motivates the prospect that a PDW state may exist in this material^24,25. To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips^26-31. We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P_i=1,2,3 that are indistinguishable from the wavevectors Q_i=1,2,3 of the prevenient²⁴ CDW. Concurrent visualization of the UTe₂ superconductive PDWs and the non-superconductive CDWs shows that every P_i:Q_i pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe₂ as a spin-triplet superconductor¹², this PDW state should be a spin-triplet PDW^24,25. Although such states do exist³² in superfluid ³He, for superconductors, they are unprecedented.

Extreme enhancement of superconductivity in epitaxial aluminum near the monolayer limit

BCS theory has been widely successful at describing elemental bulk superconductors. Yet, as the length scales of such superconductors approach the atomic limit, dimensionality as well as the environment of the superconductor can lead to drastically different and unpredictable superconducting behavior. Here, we report a threefold enhancement of the superconducting critical temperature and gap size in ultrathin epitaxial Al films on Si(111), when approaching the 2D limit, based on high-resolution scanning tunneling microscopy/spectroscopy (STM/STS) measurements. Using spatially resolved spectroscopy, we characterize the vortex structure in the presence of a strong Zeeman field and find evidence of a paramagnetic Meissner effect originating from odd-frequency pairing contributions. These results illustrate two notable influences of reduced dimensionality on a BCS superconductor and present a platform to study BCS superconductivity in large magnetic fields.

Splashes in isotropic media

The response of a weakly absorbing isotropic medium to a sudden localized perturbation (a "splash") is explained within the framework of linear response theory. In this theory splashes result from the interference of the collective excitations of the medium, with the outcome determined by the interplay between their phase and group velocities as well as the sign of the latter. The salient features of splashes are controlled by the existence of extremal values of the phase and the group velocities: the group velocity gives the expansion rate of the locus of the points where new wave fronts nucleate or existing ones disappear, while the phase velocity determines the large-time expansion rate of a group of wave fronts. If the group velocity is negative in a spectral range and takes on a minimal value within it, then converging wave fronts will be present in the splash. These results are relevant to the studies of several experimentally viable setups, such as a splash on the surface of deep water due to a small pebble or a raindrop, a splash in the two-dimensional electron gas caused by a short voltage pulse applied with the tip of a scanning tunneling microscope, or a bulk splash in superfluid ^{4}He due to formation of an electron bubble. Specifically, the gross features of a splash in superfluid ^{4}He are determined by five extremal velocities. Additionally, due to the existence of a negative group-velocity spectral range, some of the wave fronts in the superfluid splash are converging.

Identification of a nematic pair density wave state in Bi2Sr2CaCu2O8+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 state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].