Imaging the energy gap modulations of the cuprate pair-density-wave state.

The defining characteristic1,2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)3,4. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling5, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi2Sr2CaCu2O8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8) (where a0 is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi2Sr2CaCu2O8+δ.

Discovery of orbital ordering in Bi2Sr2CaCu2O8+x.

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO2.

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

Time-reversal symmetry breaking in the Fe-chalcogenide superconductors.

Topological superconductivity has been sought in a variety of heterostructure systems, the interest being that a material displaying such a phenomenon could prove to be the ideal platform to support Majorana fermions, which in turn could be the basis for advanced qubit technologies. Recently, the high-Tc family of superconductors, FeTe1-xSex, have been shown to exhibit the property of topological superconductivity and further, evidence has been found for the presence of Majorana fermions. We have studied the interplay of topology, magnetism, and superconductivity in the FeTe1-x Se x family using high-resolution laser-based photoemission. At the bulk superconducting transition, a gap opens at the chemical potential as expected. However, a second gap is observed to open at the Dirac point in the topological surface state. The associated mass acquisition in the topological state points to time-reversal symmetry breaking, probably associated with the formation of ferromagnetism in the surface layer. The presence of intrinsic ferromagnetism combined with strong spin-orbit coupling provides an ideal platform for a range of exotic topological phenomena.

Revealing the Origin of Time-Reversal Symmetry Breaking in Fe-Chalcogenide Superconductor FeTe_{1-x}Se_{x}.

Recently, evidence has emerged in the topological superconductor Fe-chalcogenide FeTe_{1-x}Se_{x} for time-reversal symmetry breaking (TRSB), the nature of which has strong implications on the Majorana zero modes (MZM) discovered in this system. It remains unclear, however, whether the TRSB resides in the topological surface state (TSS) or in the bulk, and whether it is due to an unconventional TRSB superconducting order parameter or an intertwined order. Here, by performing in superconducting FeTe_{1-x}Se_{x} crystals both surface-magneto-optic-Kerr effect measurements using a Sagnac interferometer and bulk magnetic susceptibility measurements, we pinpoint the TRSB to the TSS, where we also detect a Dirac gap. Further, we observe surface TRSB in nonsuperconducting FeTe_{1-x}Se_{x} of nominally identical composition, indicating that TRSB arises from an intertwined surface ferromagnetic (FM) order. The observed surface FM bears striking similarities to the two-dimensional (2D) FM found in 2D van der Waals crystals, and is highly sensitive to the exact chemical composition, thereby providing a means for optimizing the conditions for Majorana particles that are useful for robust quantum computing.

Electronic properties of the bulk and surface states of Fe1+yTe1-xSex.

The idea of employing non-Abelian statistics for error-free quantum computing ignited interest in reports of topological surface superconductivity and Majorana zero modes (MZMs) in FeTe0.55Se0.45. However, the topological features and superconducting properties are not observed uniformly across the sample surface. The understanding and practical control of these electronic inhomogeneities present a prominent challenge for potential applications. Here, we combine neutron scattering, scanning angle-resolved photoemission spectroscopy, and microprobe composition and resistivity measurements to characterize the electronic state of Fe1+yTe1-xSex. We establish a phase diagram in which the superconductivity is observed only at sufficiently low Fe concentration, in association with distinct antiferromagnetic correlations, whereas the coexisting topological surface state occurs only at sufficiently high Te concentration. We find that FeTe0.55Se0.45 is located very close to both phase boundaries, which explains the inhomogeneity of superconducting and topological states. Our results demonstrate the compositional control required for use of topological MZMs in practical applications.

Fidelity Overhead for Nonlocal Measurements in Variational Quantum Algorithms.

Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli z operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary transformations to rotate the state of interest so that the measurement of a fragment's Ising form would be equivalent to the measurement of the fragment for the unrotated state. These extra rotations allow one to perform a fewer number of measurements by grouping more terms into the measurable fragments with a lower overall estimator variance. However, previous estimations of the number of measurements did not take into account nonunit fidelity of quantum gates implementing the additional transformations. Through a circuit fidelity reduction, additional transformations introduce extra uncertainty and increase the needed number of measurements. Here we consider a simple model for errors introduced by additional gates needed in schemes involving groupings of commuting Pauli products. For a set of molecular electronic Hamiltonians, we confirm that the numbers of measurements in schemes using nonlocal qubit rotations are still lower than those in their local qubit rotation counterparts, even after accounting for uncertainties introduced by additional gates.

Quantum Chemistry in the Age of Quantum Computing.

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering.

Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.

Design and Evaluation of [18F]CHDI-650 as a Positron Emission Tomography Ligand to Image Mutant Huntingtin Aggregates.

Therapeutic interventions are being developed for Huntington's disease (HD), a hallmark of which is mutant huntingtin protein (mHTT) aggregates. Following the advancement to human testing of two [11C]-PET ligands for aggregated mHTT, attributes for further optimization were identified. We replaced the pyridazinone ring of CHDI-180 with a pyrimidine ring and minimized off-target binding using brain homogenate derived from Alzheimer's disease patients. The major in vivo metabolic pathway via aldehyde oxidase was blocked with a 2-methyl group on the pyrimidine ring. A strategically placed ring-nitrogen on the benzoxazole core ensured high free fraction in the brain without introducing efflux. Replacing a methoxy pendant with a fluoro-ethoxy group and introducing deuterium atoms suppressed oxidative defluorination and accumulation of [18F]-signal in bones. The resulting PET ligand, CHDI-650, shows a rapid brain uptake and washout profile in non-human primates and is now being advanced to human testing.

Development of a ligand for in vivo imaging of mutant huntingtin in Huntington's disease.

Huntington's disease (HD) is a dominantly inherited neurodegenerative disorder caused by a CAG trinucleotide expansion in the huntingtin (HTT) gene that encodes the pathologic mutant HTT (mHTT) protein with an expanded polyglutamine (polyQ) tract. Whereas several therapeutic programs targeting mHTT expression have advanced to clinical evaluation, methods to visualize mHTT protein species in the living brain are lacking. Here, we demonstrate the development and characterization of a positron emission tomography (PET) imaging radioligand with high affinity and selectivity for mHTT aggregates. This small molecule radiolabeled with 11C ([11C]CHDI-180R) allowed noninvasive monitoring of mHTT pathology in the brain and could track region- and time-dependent suppression of mHTT in response to therapeutic interventions targeting mHTT expression in a rodent model. We further showed that in these animals, therapeutic agents that lowered mHTT in the striatum had a functional restorative effect that could be measured by preservation of striatal imaging markers, enabling a translational path to assess the functional effect of mHTT lowering.

Discovery and SAR of 2-arylbenzotriazoles and 2-arylindazoles as potential treatments for Duchenne muscular dystrophy.

Families of 2-arylbenzotriazoles and 2-arylindazoles that show positive effects in screens predictive of endogenous utrophin upregulation have been identified. Synthesis and structure-activity relationships are described leading to compounds with attractive in vitro profiles.

Exploiting differences in caspase-2 and -3 S2 subsites for selectivity: structure-based design, solid-phase synthesis and in vitro activity of novel substrate-based caspase-2 inhibitors.

Several caspases have been implicated in the pathogenesis of Huntington's disease (HD); however, existing caspase inhibitors lack the selectivity required to investigate the specific involvement of individual caspases in the neuronal cell death associated with HD. In order to explore the potential role played by caspase-2, the potent but non-selective canonical Ac-VDVAD-CHO caspase-2 inhibitor 1 was rationally modified at the P(2) residue in an attempt to decrease its activity against caspase-3. With the aid of structural information on the caspase-2, and -3 active sites and molecular modeling, a 3-(S)-substituted-l-proline along with four additional scaffold variants were selected as P(2) elements for their predicted ability to clash sterically with a residue of the caspase-3 S(2) pocket. These elements were then incorporated by solid-phase synthesis into pentapeptide aldehydes 33a-v. Proline-based compound 33h bearing a bulky 3-(S)-substituent displayed advantageous characteristics in biochemical and cellular assays with 20- to 60-fold increased selectivity for caspase-2 and ∼200-fold decreased caspase-3 potency compared to the reference inhibitor 1. Further optimization of this prototype compound may lead to the discovery of valuable pharmacological tools for the study of caspase-2 mediated cell death, particularly as it relates to HD.

Pharmacological characterization of mutant huntingtin aggregate-directed PET imaging tracer candidates.

Huntington's disease (HD) is caused by a CAG trinucleotide repeat expansion in the first exon of the huntingtin (HTT) gene coding for the huntingtin (HTT) protein. The misfolding and consequential aggregation of CAG-expanded mutant HTT (mHTT) underpin HD pathology. Our interest in the life cycle of HTT led us to consider the development of high-affinity small-molecule binders of HTT oligomerized/amyloid-containing species that could serve as either cellular and in vivo imaging tools or potential therapeutic agents. We recently reported the development of PET tracers CHDI-180 and CHDI-626 as suitable for imaging mHTT aggregates, and here we present an in-depth pharmacological investigation of their binding characteristics. We have implemented an array of in vitro and ex vivo radiometric binding assays using recombinant HTT, brain homogenate-derived HTT aggregates, and brain sections from mouse HD models and humans post-mortem to investigate binding affinities and selectivity against other pathological proteins from indications such as Alzheimer's disease and spinocerebellar ataxia 1. Radioligand binding assays and autoradiography studies using brain homogenates and tissue sections from HD mouse models showed that CHDI-180 and CHDI-626 specifically bind mHTT aggregates that accumulate with age and disease progression. Finally, we characterized CHDI-180 and CHDI-626 regarding their off-target selectivity and binding affinity to beta amyloid plaques in brain sections and homogenates from Alzheimer's disease patients.

[11C]CHDI-626, a PET Tracer Candidate for Imaging Mutant Huntingtin Aggregates with Reduced Binding to AD Pathological Proteins.

The expanded polyglutamine-containing mutant huntingtin (mHTT) protein is implicated in neuronal degeneration of medium spiny neurons in Huntington's disease (HD) for which multiple therapeutic approaches are currently being evaluated to eliminate or reduce mHTT. Development of effective and orthogonal biomarkers will ensure accurate assessment of the safety and efficacy of pharmacologic interventions. We have identified and optimized a class of ligands that bind to oligomerized/aggregated mHTT, which is a hallmark in the HD postmortem brain. These ligands are potentially useful imaging biomarkers for HD therapeutic development in both preclinical and clinical settings. We describe here the optimization of the benzo[4,5]imidazo[1,2-a]pyrimidine series that show selective binding to mHTT aggregates over Aß- and/or tau-aggregates associated with Alzheimer's disease pathology. Compound [11C]-2 was selected as a clinical candidate based on its high free fraction in the brain, specific binding in the HD mouse model, and rapid brain uptake/washout in nonhuman primate positron emission tomography imaging studies.

Imaging Mutant Huntingtin Aggregates: Development of a Potential PET Ligand.

Mutant huntingtin (mHTT) protein carrying the elongated N-terminal polyglutamine (polyQ) tract misfolds and forms protein aggregates characteristic of Huntington's disease (HD) pathology. A high-affinity ligand specific for mHTT aggregates could serve as a positron emission tomography (PET) imaging biomarker for HD therapeutic development and disease progression. To identify such compounds with binding affinity for polyQ aggregates, we embarked on systematic structural activity studies; lead optimization of aggregate-binding affinity, unbound fractions in brain, permeability, and low efflux culminated in the discovery of compound 1, which exhibited target engagement in autoradiography (ARG) studies in brain slices from HD mouse models and postmortem human HD samples. PET imaging studies with 11C-labeled 1 in both HD mice and WT nonhuman primates (NHPs) demonstrated that the right-hand-side labeled ligand [11C]-1R (CHDI-180R) is a suitable PET tracer for imaging of mHTT aggregates. [11C]-1R is now being advanced to human trials as a first-in-class HD PET radiotracer.

Nonequilibrium electron and lattice dynamics of strongly correlated Bi2Sr2CaCu2O8+δ single crystals.

The interplay between the electronic and lattice degrees of freedom in nonequilibrium states of strongly correlated systems has been debated for decades. Although progress has been made in establishing a hierarchy of electronic interactions with the use of time-resolved techniques, the role of the phonons often remains in dispute, a situation highlighting the need for tools that directly probe the lattice. We present the first combined megaelectron volt ultrafast electron diffraction and time- and angle-resolved photoemission spectroscopy study of optimally doped Bi2Sr2CaCu2O8+δ. Quantitative analysis of the lattice and electron subsystems' dynamics provides a unified picture of nonequilibrium electron-phonon interactions in the cuprates beyond the N-temperature model. The work provides new insights on the specific phonon branches involved in the nonequilibrium heat dissipation from the high-energy Cu-O bond stretching "hot" phonons to the lowest-energy acoustic phonons with correlated atomic motion along the <110> crystal directions and their characteristic time scales. It reveals a highly nonthermal phonon population during the first several picoseconds after the photoexcitation. The approach, taking advantage of the distinct nature of electrons and photons as probes, is applicable for studying energy relaxation in other strongly correlated electron systems.

Concise and enantioselective synthesis of the aminocyclitol core of hygromycin A.

[reaction: see text] Stereoselective aminohydroxylation and dihydroxylation using osmium(VIII) oxidants enabled the short and efficient synthesis of the aminocyclitol core of hygromycin A. In addition to allowing the selective introduction of the heteroatoms N and O, the use of osmium (via an osmate ester) as a protecting group for a 1,2-glycol is also reported. This tactic allowed efficient differentiation of otherwise equivalent hydroxyl groups and allowed us to complete the synthesis in short order (14 steps) and excellent overall yield (12%).

The discovery of a novel antibiotic for the treatment of Clostridium difficile infections: a story of an effective academic-industrial partnership.

Academic drug discovery is playing an increasingly important role in the identification of new therapies for a wide range of diseases. There is no one model that guarantees success. We describe here a drug discovery story where chance, the ability to capitalise on chance, and the assembling of a range of expertise, have all played important roles in the discovery and subsequent development of an antibiotic chemotype based on the bis-benzimidazole scaffold, with potency against a number of current therapeutically challenging diseases. One compound in this class, SMT19969, has recently entered Phase 2 human clinical trials for the treatment of Clostridium difficile infections.