Atomic-scale Visualization of Electronic Fluid Flow

The most essential characteristic of any fluid is the velocity field v(r) and this is particularly true for macroscopic quantum fluids. Although rapid advances have occurred in quantum fluid v(r) imaging, the velocity field of a charged superfluid - a superconductor - has never been visualized. Here we use superconductive-tip scanning tunneling microscopy to image the electron-pair density r{ho}_S(r) and velocity v_S(r) fields of the flowing electron-pair fluid in superconducting NbSe2. Imaging v_S(r) surrounding a quantized vortex finds speeds reaching 10,000 km/hr. Together with independent imaging of r{ho}_S(r) via Josephson tunneling, we visualize the supercurrent density j_S(r)=r{ho}_S(r)v_S(r), which peaks above 3 x 10^7 A/cm^2. The spatial patterns in electronic fluid flow and magneto-hydrodynamics reveal hexagonal structures co-aligned to the crystal lattice and quasiparticle bound states, as long anticipated. These novel techniques pave the way for electronic fluid flow visualization in many other quantum fluids.

Severe Dirac Mass Gap Suppression in Sb_2Te_3-based Quantum Anomalous Hall Materials

Quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTI) when a Dirac mass gap opens in the spectrum of the topological surface states (SS). Unaccountably, although the mean mass gap can exceed 28 meV (or ~320 K), the QAH effect is frequently only detectable at temperatures below 1 K. Using atomic-resolution Landau level spectroscopic imaging, we compare the electronic structure of the archetypal FMTI Cr_0.08(Bi_0.1Sb_0.9)_1.92Te_3 to that of its non-magnetic parent (Bi_0.1Sb_0.9)_2Te_3, to explore the cause. In (Bi_0.1Sb_0.9)_2Te_3, we find spatially random variations of the Dirac energy. Statistically equivalent Dirac energy variations are detected in Cr_0.08(Bi_0.1Sb_0.9)_1.92Te_3 with concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS electronic disorder conspire to drastically suppress the minimum mass gap to below 100 {mu}eV for nanoscale regions separated by <1 {mu}m. This fundamentally limits the fully quantized anomalous Hall effect in Sb_2Te_3-based FMTI materials to very low temperatures.

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 (TMD) we use high-speed atomic-resolution scanned Josephson-tunneling microscopy (SJTM). We detect a PDW state whose electron-pair density and energy-gap modulate spatially at the wavevectors of the preexisting charge density wave (CDW) state. The PDW couples linearly to both the s-wave superconductor and to the CDW, and exhibits commensurate domains with discommensuration phase-slips at the boundaries, conforming to those of the lattice-locked commensurate CDW. Nevertheless, we find a global $deltaPhi sim pm2pi/3$ phase difference between the PDW and CDW states, possibly owing to the Cooper-pair wavefunction orbital content. Our findings presage pervasive PDW physics in the many other TMDs that sustain both CDW and superconducting states.

Multi-Atom Quasiparticle Scattering Interference for Superconductor Energy-Gap Symmetry Determination

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $Delta_mathbf{k}^alpha$, for all momenta $mathbf{k}$ on the Fermi surface of every band $alpha$. While there are a variety of techniques for determining $|Delta_mathbf{k}^alpha|$, no general method existed to measure the signed values of $Delta_mathbf{k}^alpha$. Recently, however, a new technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where $Delta_mathbf{k}^alpha$ has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the $Delta_mathbf{k}^alpha$ it generates to the $Delta_mathbf{k}^alpha$ determined from single-atom scattering in FeSe where $s_{pm}$ energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for $Delta_mathbf{k}^alpha$ of opposite sign.

Deep-Learning continuous gravitational waves

We present a first proof-of-principle study for using deep neural networks (DNNs) as a novel search method for continuous gravitational waves (CWs) from unknown spinning neutron stars. The sensitivity of current wide-parameter-space CW searches is limited by the available computing power, which makes neural networks an interesting alternative to investigate, as they are extremely fast once trained and have recently been shown to rival the sensitivity of matched filtering for black-hole merger signals. We train a convolutional neural network with residual (short-cut) connections and compare its detection power to that of a fully-coherent matched-filtering search using the WEAVE pipeline. As test benchmarks we consider two types of all-sky searches over the frequency range from $20,mathrm{Hz}$ to $1000,mathrm{Hz}$: an `easy search using $T=10^5,mathrm{s}$ of data, and a `harder search using $T=10^6,mathrm{s}$. Detection probability $p_mathrm{det}$ is measured on a signal population for which matched filtering achieves $p_mathrm{det}=90%$ in Gaussian noise. In the easiest test case ($T=10^5,mathrm{s}$ at $20,mathrm{Hz}$) the DNN achieves $p_mathrm{det}sim88%$, corresponding to a loss in sensitivity depth of $sim5%$ versus coherent matched filtering. However, at higher-frequencies and longer observation time the DNN detection power decreases, until $p_mathrm{det}sim13%$ and a loss of $sim 66%$ in sensitivity depth in the hardest case ($T=10^6,mathrm{s}$ at $1000,mathrm{Hz}$). We study the DNN generalization ability by testing on signals of different frequencies, spindowns and signal strengths than they were trained on. We observe excellent generalization: only five networks, each trained at a different frequency, would be able to cover the whole frequency range of the search.

Evidence for a Vestigial Nematic State in the Cuprate Pseudogap Phase

The CuO$_2$ antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E|<$Delta^*$, where $Delta^*$ is the pseudogap energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite Q density-wave (DW) state and a Q=0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken symmetry states to be visualized simultaneously. Using this approach, we show that, even though their reported ordering temperatures T$_{DW}$ and T$_{NE}$ are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the pseudogap energy $Delta^*$. Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi-surface), while the observed pseudogap opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries can be understood as the natural consequence of a vestigial nematic state , within the pseudogap phase of Bi$_2$Sr$_2$CaCu$_2$O$_8$.