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Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to quantify the confidence associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry. However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints. Here, we report the observation of the nonlinear Hall effect (NLHE) in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe2. Specifically, flowing an electrical current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I-V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of about 90 degree. We further show that the NLHE directly measures the "dipole moment" of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.

The capability to switch electrically between superconducting and insulating states of matter represents a novel paradigm in the state-of-the-art engineering of correlated electronic systems. An exciting possibility is to turn on superconductivity in a topologically non-trivial insulator, which provides a route to search for non-Abelian topological states. However, existing demonstrations of superconductor-insulator switches have involved only topologically trivial systems, and even those are rare due to the stringent requirement to tune the carrier density over a wide range. Here we report reversible, in-situ electrostatic on off switching of superconductivity in a recently established quantum spin Hall insulator, namely monolayer tungsten ditelluride (WTe2). Fabricated into a van der Waals field effect transistor, the monolayer's ground state can be continuously gate-tuned from the topological insulating to the superconducting state, with critical temperatures Tc up to ~ 1 Kelvin. The critical density for the onset of superconductivity is estimated to be ~ 5 x 10^12 cm^-2, among the lowest for two-dimensional (2D) superconductors. Our results establish monolayer WTe2 as a material platform for engineering novel superconducting nanodevices and topological phases of matter., Comment: 25 pages, including main text, figures and supplements

Recent experimental evidence for the quantum spin Hall (QSH) state in monolayer WTe$_2$ has bridged two of the most active fields of condensed matter physics, 2D materials and topological physics. This 2D topological crystal also displays unconventional spin-torque and gate-tunable superconductivity. While the realization of QSH has demonstrated the nontrivial topology of the electron wavefunctions of monolayer WTe$_2$, the geometrical properties of the wavefunction, such as the Berry curvature, remain unstudied. On the other hand, it has been increasingly recognized that the Berry curvature plays an important role in multiple areas of condensed matter physics including nonreciprocal electron transport, enantioselective optical responses, chiral polaritons and even unconventional superconductivity. Here we utilize mid-infrared optoelectronic microscopy to investigate the Berry curvature in monolayer WTe$_2$. By optically exciting electrons across the inverted QSH gap, we observe an in-plane circular photogalvanic current even under normal incidence. The application of an out-of-plane displacement field further systematically controls the direction and magnitude of the photocurrent. Our observed photocurrent reveals a novel Berry curvature dipole that arises from the nontrivial wavefunctions near the inverted gap edge. These previously unrealized Berry curvature dipole and strong electric field effect are uniquely enabled by the inverted band structure and tilted crystal lattice of monolayer WTe$_2$. Such an electrically switchable Berry curvature dipole opens the door to the observation of a wide range of quantum geometrical phenomena, such as quantum nonlinear Hall, orbital-Edelstein and chiral polaritonic effects., Comment: Originally submitted version, main text combined with part of the SI

The field of topological insulators (TI) was sparked by the prediction of the quantum spin Hall effect (QSHE) in time reversal invariant systems, such as spin-orbit coupled monolayer graphene. Ever since, a variety of monolayer crystals have been proposed as two-dimensional (2D) TIs exhibiting the QSHE, possibly even at high temperatures. However, conclusive evidence for a monolayer QSHE is still lacking, and systems based on semiconductor heterostructures operate at temperatures close to liquid helium. Here we report the observation of the QSHE in monolayer WTe2 at temperatures up to 100 Kelvin. The monolayer exhibits the hallmark quantized transport conductance, ~ e2/h per edge, in the short edge limit. Moreover, a magnetic field suppresses the conductance, and the observed Zeeman-type gap indicates the existence of a Kramers degenerate point, demonstrating the importance of time reversal symmetry for protection from elastic backscattering. Our results establish the high-temperature QSHE and open a new realm for the discovery of topological phases based on 2D crystals., Comment: 11 pages of maintext + 16 pages of supplementary materials

We report on electronic transport measurements of electrostatically gated nano-devices of the semimetal WTe\textsubscript{2}. High mobility metallic behavior is achieved in the 2D limit by encapsulating thin flakes in an inert atmosphere. At low temperatures, we find that a large magnetoresistance can be turned on and off by electrostatically doping the system between a semimetallic state and an electron-only metallic state, respectively. We confirm the nature of the two regimes by analyzing the magnetoresistance and Hall effect with a two-carrier model, as well as by analysis of Shubnikov-de Haas oscillations, both of which indicate depletion of hole carriers via the electrostatic gate. This confirms that semiclassical transport of two oppositely charged carriers accurately describes the exceptional magnetoresistance observed in this material. Finally, we also find that the magnetoresistance power law is sub-quadratic and density-independent, suggesting new physics specifically in the semimetallic regime., Comment: 6 pages, 3 figures

Strong spin-orbit coupling (SOC) can result in ground states with non-trivial topological properties. The situation is even richer in magnetic systems where the magnetic ordering can potentially have strong influence over the electronic band structure. The class of AMnBi$_2$ (A = Sr, Ca) compounds are important in this context as they are known to host massive Dirac fermions with strongly anisotropic dispersion that is believed to be due to the interplay between strong SOC and magnetic degrees of freedom. We report the optical conductivity of YbMnBi$_2$, a newly discovered member of this family and a proposed Weyl semi-metal (WSM) candidate with broken time reversal symmetry. Together with density functional theory (DFT) band structure calculations, we show how the complete conductivity can be interpreted as the sum of a intra-band Drude response and inter-band transitions. We argue that the canting of the magnetic moments that has been proposed to be essential for the realization of the WSM in an otherwise antiferromagnetically ordered system is not necessary to explain the optical conductivity. We believe our data is explained qualitatively by the uncanted magnetic structure with a small offset of the chemical potential from strict stochiometry. There is no definite evidence of bulk Weyl nodes, instead we see signatures of a gapped Dirac dispersion, common in other members of AMnBi$_2$ family or compounds with similar 2D network of Bi atoms., Comment: Submitted to Physical Review B

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. By mapping the quasiparticle interference and emerging Landau levels at high magnetic field in Dirac semimetals Cd$_3$As$_2$ and Na$_3$Bi, we observed extended Dirac-like bulk electronic bands. Quasiparticle interference imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface-projected Weyl nodes.

We report the crystal structure of a new polymorph of Ca$_3$P$_2$, and an analysis of its electronic structure. The crystal structure was determined through Rietveld refinements of powder synchrotron x-ray diffraction data. Ca$_3$P$_2$ is found to be a variant of the Mn$_5$Si$_3$ structure type, with a Ca ion deficiency compared to the ideal 5:3 stoichiometry to yield a charge-balanced compound. We also report the observation of a secondary phase, Ca$_5$P$_3$H, in which the Ca and P sites are fully occupied and the presence of interstitial hydride ions creates a closed-shell electron-precise compound. We show via electronic structure calculations of Ca$_3$P$_2$ that the compound is stabilized by a gap in the density of states compared to the hypothetical compound Ca$_5$P$_3$. Moreover, the calculated band structure of Ca$_3$P$_2$ indicates that it should be a three-dimensional Dirac semimetal with a highly unusual ring of Dirac nodes at the Fermi level. The Dirac states are protected against gap opening by a mirror plane in a manner analogous to graphene. The results suggest that further study of the electronic properties of Ca$_3$P$_2$ will be of interest.

We report a new family of ternary 111 hexagonal LnAuSb (Ln = La-Nd, Sm) compounds that, with a 19 valence electron count, has one extra electron compared to all other known LnAuZ compound. The "19th" electron is accommodated by Au-Au bonding between the layers; this Au-Au interaction drives the phases to crystallize in the YPtAs-type structure rather than the more common LiGaGe-type. This is critical, as the YPtAs structure type has the symmetry-allowed band crossing necessary for the formation of Dirac semimetals. Band structure, density of stats, and crystal orbital calculations confirm this picture, which results in a nearly complete band gap between full and empty electronic states and stable compounds; we can thus present a structural stability phase diagram for the LnAuZ (Ln = Ge, As, Sn, Sb, Pb, Bi) family of phases. Those calculations also show that LaAuSb has a bulk Dirac cone below the Fermi level. The YPtAs-type LnAuSb family reported here is an example of the uniqueness of gold chemistry applied to a rigidly closed shell system in an unconventional way., Comment: 32 pages, 8 Figures

3D Dirac semi-metals (DSMs) are materials that have massless Dirac electrons and exhibit exotic physical properties It has been suggested that structurally distorting a DSM can create a Topological Insulator (TI), but this has not yet been experimentally verified. Furthermore, quasiparticle excitations known as Majorana Fermions have been theoretically proposed to exist in materials that exhibit superconductivity and topological surface states. Here we show that the cubic Laves phase Au$_2$Pb has a bulk Dirac cone above 100 K that gaps out upon cooling at a structural phase transition to create a topologically non trivial phase that superconducts below 1.2 K. The nontrivial Z$_2$ = -1 invariant in the low temperature phase indicates that Au$_2$Pb in its superconducting state must have topological surface states. These characteristics make Au$_2$Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states.

Design principles and novel predictions of new 3D Dirac semimetals are presented, along with the context of currently known materials. Current materials include those based on a topological to trivial phase transition, such as in TlBiSe$_{2-x}$S$_x$ and Hg$_{1-x}$Cd$_x$Te, Bi$_{1-x}$Sb$_x$, Bi$_{2-x}$In$_x$Se$_3$, and Pb$_{1-x}$Sn$_x$Se. Some more recently revealed materials, Na$_3$Bi and Cd$_3$As$_2$, are 3D Dirac semimetals in their native composition. The different design principles presented each yield novel predictions for new candidates. For Case I, 3D Dirac semimetals based on charge balanced compounds, BaAgBi, SrAgBi, YbAuSb, PtBi$_2$ and SrSn$_2$As$_2$ are identified as candidates. For Case II, 3D Dirac semi-metals in analogy to graphene, BaGa$_2$ is identified as a candidate, and BaPt and Li$_2$Pt are discussed. For Case III, 3D Dirac semi-metals based on glide planes and screw axes, TlMo$_3$Te$_3$ and the AMo$_3$X$_3$ family in general (A=K, Na, In, Tl, X=Se,Te) as well as the Group IVb trihalides such as HfI$_3$ are identified as candidates. Finally we discuss conventional intermetallic compounds with Dirac cones, and identify Cr$_2$B as a potentially interesting material., Comment: submitted 10/30

Pb$_{0.77}$Sn$_{0.23}$Se is a novel alloy of two promising thermoelectric materials PbSe and SnSe that exhibits a temperature dependent band inversion below 300 K. Recent work has shown that this band inversion also coincides with a trivial to nontrivial topological phase transition. To understand how the properties critical to thermoelectric efficiency are affected by the band inversion, we measured the broadband optical response of Pb$_{0.77}$Sn$_{0.23}$Se as a function of temperature. We find clear optical evidence of the band inversion at $160\pm15$ K, and use the extended Drude model to accurately determine a $T^{3/2}$ dependence of the bulk carrier lifetime, associated with electron-acoustic phonon scattering. Due to the high bulk carrier doping level, no discriminating signatures of the topological surface states are found, although their presence cannot be excluded from our data., Comment: 11 pages, 6 figures

Condensed matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations and the possibility to manipulate them in materials for potential applications. Recently, it has been proposed that Weyl fermions, which are chiral, massless particles, can emerge in certain bulk materials or in topological insulator multilayers and can produce unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry, effectively forming a massless Dirac fermion, has been predicted to appear as low energy excitations in a number of candidate materials termed three-dimensional (3D) Dirac semimetals. Here we report scanning tunneling microscopy (STM) measurements at sub-Kelvin temperatures and high magnetic fields on one promising host material, the II-V semiconductor Cd3As2. Our study provides the first atomic scale probe of Cd3As2, showing that defects mostly influence the valence band, consistent with the observation of ultra-high mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference (QPI), we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a specific orientation of the applied magnetic field, Weyl fermions are the low-energy excitations in Cd3As2., Comment: Main Text: 17 pages, 4 figures. Supplementary Materials: 12 pages, 7 figures, Nature Materials (2014)

We report on a search for new wide halo binary stars in SDSS Stripe 82. A list of new halo wide binary candidates which satisfy common proper motion and photometric constraints is provided. The projected separations of the sample lie between 0.007-0.25pc. Although the sample is not large enough to improve constraints on dark matter in the halo, we find the wide binary angular separation function is broadly consistent with past work. We discuss the significance of the new sample for a number of astrophysical applications, including as a testbed for ideas about wide binary formation. For the subset of candidates which have radial velocity information we make use of integrals of motion to investigate one such scheme in which the origin of Galactic wide binaries is associated with the accretion/disruption of stellar systems in the Galaxy. Additional spectroscopic observations of these candidate binaries will strengthen their usefulness in many of these respects. Based on our search experience in Stripe 82 we estimate that the upcoming Pan-STARRS survey will increase the sample size of wide halo binaries by over an order of magnitude., Comment: 7 pages, 6 figure, 2 tables, to appear in MNRAS

We present radial velocity measurements of four wide halo binary candidates from the sample in Chaname & Gould (2004; CG04) which, to date, is the only sample containing a large number of such candidates. The four candidates that we have observed have projected separations >0.1 pc, and include the two widest binaries from the sample, with separations of 0.45 and 1.1 pc. We confirm that three of the four CG04 candidates are genuine, including the one with the largest separation. The fourth candidate, however, is spurious at the 5-sigma level. In the light of these measurements we re-examine the implications for MACHO models of the Galactic halo. Our analysis casts doubt on what MACHO constraints can be drawn from the existing sample of wide halo binaries., Comment: 6 Pages, 4 Figures, Accepted for MNRAS Letters

We present radial velocities for a sample of 723 planetary nebulae (PNe) in the disk and bulge of M31, measured using the WYFFOS fibre spectrograph on the William Herschel telescope. Velocities are determined using the [OIII] 5007 Angstrom emission line. Rotation and velocity dispersion are measured to a radius of 50 arcminutes (11.5 kpc), the first stellar rotation curve and velocity dispersion profile for M31 to such a radius. Our kinematics are consistent with rotational support at radii well beyond the bulge effective radius of 1.4kpc, although our data beyond a radius of 5kpc are limited. We present tentative evidence for kinematic substructure in the bulge of M31 to be studied fully in a later work. This paper is part of an ongoing project to constrain the total mass, mass distribution and velocity anisotropy of the disk, bulge and halo of M31., Comment: 27 pages, accepted for publication in MNRAS

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements., Comment: 7 pages