Superfluid response of an atomically thin gate-tuned van der Waals superconductor.

A growing number of two-dimensional superconductors are being discovered in the family of exfoliated van der Waals materials. Due to small sample volume, the superfluid response of these materials has not been characterized. Here, we use a local magnetic probe to directly measure this key property of the tunable, gate-induced superconducting state in MoS2. We find that the backgate changes the transition temperature non-monotonically whereas the superfluid stiffness at low temperature and the normal state conductivity monotonically increase. In some devices, we find direct signatures in agreement with a Berezinskii-Kosterlitz-Thouless transition, whereas in others we find a broadened onset of the superfluid response. We show that the observed behavior is consistent with disorder playing an important role in determining the properties of superconducting MoS2. Our work demonstrates that magnetic property measurements are within reach for superconducting devices based on exfoliated sheets and reveals that the superfluid response significantly deviates from simple BCS-like behavior.

Thermal chiral anomaly in the magnetic-field-induced ideal Weyl phase of Bi1-xSbx.

The chiral anomaly is the predicted breakdown of chiral symmetry in a Weyl semimetal with monopoles of opposite chirality when an electric field is applied parallel to a magnetic field. It occurs because of charge pumping between monopoles of opposite chirality. Experimental observation of this fundamental effect is plagued by concerns about the current pathways. Here we demonstrate the thermal chiral anomaly, energy pumping between monopoles, in topological insulator bismuth-antimony alloys driven into an ideal Weyl semimetal state by a Zeeman field, with the chemical potential pinned at the Weyl points and in the absence of any trivial Fermi surface pockets. The experimental signature is a large enhancement of the thermal conductivity in an applied magnetic field parallel to the thermal gradient. This work demonstrates both pumping of energy and charge between the two Weyl points of opposite chirality and that they are related by the Wiedemann-Franz law.

Topological Magnons with Nodal-Line and Triple-Point Degeneracies: Implications for Thermal Hall Effect in Pyrochlore Iridates.

We analyze the magnon excitations in pyrochlore iridates with all-in-all-out (AIAO) antiferromagnetic order, focusing on their topological features. We identify the magnetic point group symmetries that protect the nodal-line band crossings and triple-point degeneracies that dominate the Berry curvature. We find three distinct regimes of magnon band topology, as a function of the ratio of Dzyaloshinskii-Moriya interaction to the antiferromagnetic exchange. We show how the thermal Hall response provides a unique probe of the topological magnon band structure in AIAO systems.

Distinct magneto-Raman signatures of spin-flip phase transitions in CrI3.

The discovery of 2-dimensional (2D) materials, such as CrI3, that retain magnetic ordering at monolayer thickness has resulted in a surge of both pure and applied research in 2D magnetism. Here, we report a magneto-Raman spectroscopy study on multilayered CrI3, focusing on two additional features in the spectra that appear below the magnetic ordering temperature and were previously assigned to high frequency magnons. Instead, we conclude these modes are actually zone-folded phonons. We observe a striking evolution of the Raman spectra with increasing magnetic field applied perpendicular to the atomic layers in which clear, sudden changes in intensities of the modes are attributed to the interlayer ordering changing from antiferromagnetic to ferromagnetic at a critical magnetic field. Our work highlights the sensitivity of the Raman modes to weak interlayer spin ordering in CrI3.

Local Spectroscopies Reveal Percolative Metal in Disordered Mott Insulators.

We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, we find a collapse of the Mott gap toward a V-shaped pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites but an increase of bond conductivity. These metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Bond conductivity measured via local microwave impedance combined with charge and spin local spectroscopies are ideal tools to corroborate our predictions.

Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI_{3}.

We lay the foundation for determining the microscopic spin interactions in two-dimensional (2D) ferromagnets by combining angle-dependent ferromagnetic resonance (FMR) experiments on high quality CrI_{3} single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with K∼-5.2 meV, 25 times larger than the Heisenberg exchange J∼-0.2 meV, and responsible for opening the ∼5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy Γ∼-67.5 µeV, though small, is crucial for opening a ∼0.3 meV gap in the magnon spectrum at the zone center and stabilizing ferromagnetism in the 2D limit. The high resolution of the FMR data further reveals a µeV-scale quadrupolar contribution to the S=3/2 magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher T_{C} as well as magnetically frustrated quantum spin liquids based on Kitaev physics.

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface.

The Kitaev model with an applied magnetic field in the [Formula: see text] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at [Formula: see text] and a second transition at a higher field [Formula: see text] to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function [Formula: see text] and the Fermi surface [Formula: see text] of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.

Overdamped Antiferromagnetic Strange Metal State in Sr_{3}IrRuO_{7}.

The unconventional electronic ground state of Sr_{3}IrRuO_{7} is explored via resonant x-ray scattering techniques and angle-resolved photoemission measurements. As the Ru content approaches x=0.5 in Sr_{3}(Ir_{1-x}Ru_{x})_{2}O_{7}, intermediate to the J_{eff}=1/2 Mott state in Sr_{3}Ir_{2}O_{7} and the quantum critical metal in Sr_{3}Ru_{2}O_{7}, a thermodynamically distinct metallic state emerges. The electronic structure of this intermediate phase lacks coherent quasiparticles, and charge transport exhibits a linear temperature dependence over a wide range of temperatures. Spin dynamics associated with the long-range antiferromagnetism of this phase show nearly local, overdamped magnetic excitations and an anomalously large energy scale of 200 meV-an energy far in excess of exchange energies present within either the Sr_{3}Ir_{2}O_{7} or Sr_{3}Ru_{2}O_{7} solid-solution end points. Overdamped quasiparticle dynamics driven by strong spin-charge coupling are proposed to explain the incoherent spectral features of the strange metal state in Sr_{3}IrRuO_{7}.

Disorder induced power-law gaps in an insulator-metal Mott transition.

A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and a variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems. Theory predicts that disorder might play a role in driving a Mott insulator across an IMT, with the emergent metallic state hosting a power-law suppression of the density of states (with exponent close to 1; V-shaped gap) centered at the Fermi energy. Such V-shaped gaps have been observed in Mott systems, but their origins are as-yet unknown. To investigate this, we use scanning tunneling microscopy and spectroscopy to study isovalent Ru substitutions in Sr3(Ir1-xRux)2O7 (0 ≤ x ≤ 0.5) which drive the system into an antiferromagnetic, metallic state. Our experiments reveal that many core features of the IMT, such as power-law density of states, pinning of the Fermi energy with increasing disorder, and persistence of antiferromagnetism, can be understood as universal features of a disordered Mott system near an IMT and suggest that V-shaped gaps may be an inevitable consequence of disorder in doped Mott insulators.

Spin-imbalance in a 2D Fermi-Hubbard system.

The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model-a paradigm for strongly correlated fermions on a lattice-in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.

Localized-itinerant dichotomy and unconventional magnetism in SrRu2O6.

Electron correlations tend to generate local magnetic moments that usually order if the lattices are not too frustrated. The hexagonal compound SrRu2O6 has a relatively high Neel temperature but small local moments, which seem to be at odds with the nominal valence of Ru5+ in the [Formula: see text] configuration. Here, we investigate the electronic property of SrRu2O6 using density functional theory (DFT) combined with dynamical-mean-field theory (DMFT). We find that the strong hybridization between Ru d and O p states results in a Ru valence that is closer to +4, leading to the small ordered moment ~1.2 µ B . While this is consistent with a DFT prediction, correlation effects are found to play a significant role. The local moment per Ru site remains finite ~2.3 µ B in the whole temperature range investigated. Due to the lower symmetry, the t 2g manifold is split and the quasiparticle weight is renormalized significantly in the a 1g state, while the renormalization in [Formula: see text] states is about a factor of 2-3 weaker. Our theoretical Neel temperature ~700 K is in reasonable agreement with experimental observations. SrRu2O6 is a unique system in which localized and itinerant electrons coexist with the proximity to an orbitally-selective Mott transition within the t 2g sector.

Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model.

Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling strong bunching of doublons and holes, in agreement with numerical calculations. The dynamics of the doublon-hole correlations should play an important role for transport in the Fermi-Hubbard model.

Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2.

In a type I Dirac or Weyl semimetal, the low-energy states are squeezed to a single point in momentum space when the chemical potential µ is tuned precisely to the Dirac/Weyl point. Recently, a type II Weyl semimetal was predicted to exist, where the Weyl states connect hole and electron bands, separated by an indirect gap. This leads to unusual energy states, where hole and electron pockets touch at the Weyl point. Here we present the discovery of a type II topological Weyl semimetal state in pure MoTe2, where two sets of Weyl points (, ) exist at the touching points of electron and hole pockets and are located at different binding energies above EF. Using angle-resolved photoemission spectroscopy, modelling, density functional theory and calculations of Berry curvature, we identify the Weyl points and demonstrate that they are connected by different sets of Fermi arcs for each of the two surface terminations. We also find new surface 'track states' that form closed loops and are unique to type II Weyl semimetals. This material provides an exciting, new platform to study the properties of Weyl fermions.

Temperature-Induced Lifshitz Transition in WTe2.

We use ultrahigh resolution, tunable, vacuum ultraviolet laser-based, angle-resolved photoemission spectroscopy (ARPES), temperature- and field-dependent resistivity, and thermoelectric power (TEP) measurements to study the electronic properties of WTe2, a compound that manifests exceptionally large, temperature-dependent magnetoresistance. The Fermi surface consists of two pairs of electron and two pairs of hole pockets along the X-Γ-X direction. Using detailed ARPES temperature scans, we find a rare example of a temperature-induced Lifshitz transition at T≃160 K, associated with the complete disappearance of the hole pockets. Our electronic structure calculations show a clear and substantial shift of the chemical potential µ(T) due to the semimetal nature of this material driven by modest changes in temperature. This change of Fermi surface topology is also corroborated by the temperature dependence of the TEP that shows a change of slope at T≈175 K and a breakdown of Kohler's rule in the 70-140 K range. Our results and the mechanisms driving the Lifshitz transition and transport anomalies are relevant to other systems, such as pnictides, 3D Dirac semimetals, and Weyl semimetals.

Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals.

We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαß(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.

Compressibility of a fermionic mott insulator of ultracold atoms.

We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in situ imaging to extract the central density of the gas and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature of the gas is of the order of, or below, the tunneling energy scale. Our results hold great promise for the exploration of many-body phenomena with ultracold atoms, where the local compressibility can be a useful tool to detect signatures of different phases or phase boundaries at specific values of the filling.

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms.

Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature superconductivity. The Hubbard model--a simplified representation of fermions moving on a periodic lattice--is thought to describe the essential details of copper oxide superconductivity. This model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realization of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realization of the three-dimensional Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques, particularly at metallic densities. We reach these low temperatures using a compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinant quantum Monte Carlo simulations and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for producing and characterizing other novel quantum states of matter, such as the pseudogap regime and correlated metallic states of the two-dimensional Hubbard model.

Theory of high Tc ferrimagnetism in a multiorbital Mott insulator.

We propose a model for the multiorbital material Sr(2)CrOsO(6), an insulator with remarkable magnetic properties and the highest T(c) ~/= 725 K among all perovskites with a net moment. We derive a new criterion for the Mott transition (U(1)U(2))(1/2)>2.5W by using slave-rotor mean field theory, where W is the bandwidth and U(1(2)) are the effective Coulomb interactions on Cr(Os) including Hund's coupling. We show that Sr(2)CrOsO(6) is a Mott insulator, where the large Cr U(1) compensates for the small Os U(2). The spin sector is described by a frustrated antiferromagnetic Heisenberg model that naturally explains the net moment arising from canting and also the observed nonmonotonic magnetization M(T). We predict characteristic magnetic structure factor peaks that can be probed by neutron experiments.

Theory of strain-controlled magnetotransport and stabilization of the ferromagnetic insulating phase in manganite thin films.

We show that applying strain on half-doped manganites makes it possible to tune the system to the proximity of a metal-insulator transition and thereby generate a colossal magnetoresistance (CMR) response. This phase competition not only allows control of CMR in ferromagnetic metallic manganites but can be used to generate CMR response in otherwise robust insulators at half-doping. Further, from our realistic microscopic model of strain and magnetotransport calculations within the Kubo formalism, we demonstrate a striking result of strain engineering that, under tensile strain, a ferromagnetic charge-ordered insulator, previously inaccessible to experiments, becomes stable.

Photon counting as a probe of superfluidity in a two-band Bose-Hubbard system coupled to a cavity field.

We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a robust correlation between the field's quench dynamics and the initial superfluid order parameter, thereby providing a novel and accurate method of determining the order parameter.