Evidence for Dirac flat band superconductivity enabled by quantum geometry.

In a flat band superconductor, the charge carriers' group velocity vF is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors1 and heavy-fermion systems2. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small vF in the conventional Bardeen-Cooper-Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene3-7, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system8-13. Using Schwinger-limited non-linear transport studies14,15, we demonstrate an extremely slow normal state drift velocity vn ≈ 1,000 m s-1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid16. Importantly, our measurement of superfluid stiffness, which controls the superconductor's electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution8-12. We find evidence for small Cooper pairs, characteristic of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover17-19, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.

Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures.

Spontaneously broken time-reversal symmetry in magnetic materials leads to a Hall response, with a nonzero voltage transverse to an applied current, even in the absence of external magnetic fields. It is common to analyze the Hall resistivity of chiral magnets as the sum of two terms: an anomalous Hall effect arising from spin-orbit coupling and a topological Hall signal coming from skyrmions, which are topologically nontrivial spin textures. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures, we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature. We also present numerically exact results from a Kubo formalism that complement the semiclassical approach.

Quantum oscillations in the magnetization and density of states of insulators.

The observation of [Formula: see text]-periodic behavior in Kondo insulators and semiconductor quantum wells challenges the conventional wisdom that quantum oscillations (QOs) necessarily arise from Fermi surfaces in metals. We revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast to metals where all observables exhibit oscillations at the same frequency. The magnetization oscillations arising from occupied Landau levels occur at the same frequency that would exist in the unhybridized case. The LE-DOS oscillations in a disorder-free system are dominated by gap-edge states and exhibit a beat pattern between two distinct frequencies at low temperature. Disorder-induced in-gap states lead to an additional contribution to the DOS at the unhybridized frequency. The temperature dependence of the amplitude and phase of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz-Kosevich form well known in metals. We also compute transport to ensure that we are probing a regime with insulating upturns in the direct current (DC) resistivity.

Enhancing Perpendicular Magnetic Anisotropy in Garnet Ferrimagnet by Interfacing with Few-Layer WTe2.

Engineering magnetic anisotropy in a ferro- or ferrimagnetic (FM) thin film is crucial in a spintronic device. One way to modify the magnetic anisotropy is through the surface of the FM thin film. Here, we report the emergence of a perpendicular magnetic anisotropy (PMA) induced by interfacial interactions in a heterostructure comprised of a garnet ferrimagnet, Y3Fe5O12 (YIG), and a low-symmetry, high spin-orbit coupling (SOC) transition metal dichalcogenide, WTe2. At the same time, we also observed an enhancement in Gilbert damping in the WTe2-covered YIG area. Both the magnitude of interface-induced PMA and the Gilbert damping enhancement have no observable WTe2 thickness dependence down to a single quadruple layer, indicating that the interfacial interaction plays a critical role. The ability of WTe2 to enhance the PMA in FM thin film, combined with its previously reported capability to generate out-of-plane damping like spin torque, makes it desirable for magnetic memory applications.

Atomic-scale visualization of topological spin textures in the chiral magnet MnGe.

Topological spin textures in chiral magnets such as manganese germanide (MnGe) are of fundamental interest and may enable magnetic storage and computing technologies. Our spin-polarized scanning tunneling microscopy images of MnGe thin films reveal a variety of textures that are correlated to the atomic-scale structure. Our images indicate helical stripe domains, in contrast to bulk, and associated helimagnetic domain walls. In combination with micromagnetic modeling, we can deduce the three-dimensional (3D) orientation of the helical wave vectors, and we find that three helical domains can meet in two distinct ways to produce either a "target-like" or a "π-like" topological spin texture. The target-like texture can be reversibly manipulated through either current/voltage pulsing or applied magnetic field, which represents a promising step toward future applications.

Stimulated Nucleation of Skyrmions in a Centrosymmetric Magnet.

Understanding the dynamics of skyrmion nucleation and manipulation is important for applications in spintronic devices. In this contribution, the spin textures at magnetic domain-boundaries stimulated by application of in-plane magnetic fields in a centrosymmetric kagome ferromagnet, Fe3Sn2, with thickness gradient are investigated using Lorentz transmission electron microscopy. Switching of the in-plane magnetic field is shown to induce a reversible transformation from magnetic stripes to skyrmions, or vice versa, at the interface between differently oriented domains. Micromagnetic simulations combined with experiments reveal that the rotatable anisotropy and thickness dependence of the response to the external in-plane field are the critical factors for the skyrmion formation. In addition, it is shown that the helicity of skyrmions can also be controlled using this dynamic process. The results suggest that magnetic materials with rotatable anisotropy are potential skyrmionic systems and provides a different approach for nucleation and manipulation of skyrmions in spintronic devices.

Optical spectral weight, phase stiffness, and T c bounds for trivial and topological flat band superconductors.

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) [Formula: see text] We focus on on-site attraction [Formula: see text] on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight [Formula: see text] with [Formula: see text] , where n is the flat-band density and Ω is the Marzari-Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for [Formula: see text] linear in [Formula: see text] We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

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.

Spin-Hall Topological Hall Effect in Highly Tunable Pt/Ferrimagnetic-Insulator Bilayers.

Electrical detection of topological magnetic textures such as skyrmions is currently limited to conducting materials. Although magnetic insulators offer key advantages for skyrmion technologies with high speed and low loss, they have not yet been explored electrically. Here, we report a prominent topological Hall effect in Pt/Tm3Fe5O12 bilayers, where the pristine Tm3Fe5O12 epitaxial films down to 1.25 unit cell thickness allow for tuning of topological Hall stability over a broad range from 200 to 465 K through atomic-scale thickness control. Although Tm3Fe5O12 is insulating, we demonstrate the detection of topological magnetic textures through a novel phenomenon: "spin-Hall topological Hall effect" (SH-THE), where the interfacial spin-orbit torques allow spin-Hall-effect generated spins in Pt to experience the unique topology of the underlying skyrmions in Tm3Fe5O12. This novel electrical detection phenomenon paves a new path for utilizing a large family of magnetic insulators in future skyrmion technologies.

Tuning across the BCS-BEC crossover in the multiband superconductor Fe1+y Se x Te1-x : An angle-resolved photoemission study.

The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal, Fe1+y Se x Te1-x , by tuning the Fermi energy εF via chemical doping, which permits us to systematically change Δ/εF from 0.16 to 0.50, where Δ is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap, and characteristic changes in the SC state electronic dispersion as the system evolves from a BCS to a BEC regime. Our results raise important questions about the crossover in multiband superconductors, which go beyond those addressed in the context of cold atoms.

Are the surface Fermi arcs in Dirac semimetals topologically protected?

Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at [Formula: see text] where gapless states on the side surfaces are protected only near [Formula: see text] We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na3Bi and Cd3As2 Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments.

Electronic Structure of Oxide Interfaces: A Comparative Analysis of GdTiO3/SrTiO3 and LaAlO3/SrTiO3 Interfaces.

Emergent phases in the two-dimensional electron gas (2DEG) formed at the interface between two insulating oxides have attracted great attention in the past decade. We present ab-initio electronic structure calculations for the interface between a Mott insulator GdTiO3 (GTO) and a band insulator SrTiO3 (STO) and compare our results with those for the widely studied LaAlO3/SrTiO3 (LAO/STO) interface between two band insulators. Our GTO/STO results are in excellent agreement with experiments, but qualitatively different from LAO/STO. We find an interface carrier density of 0.5 e(-)/Ti, independent of GTO thickness in both superlattice and thin film geometries, in contrast to LAO/STO. The superlattice geometry in LAO/STO offers qualitatively the same result as in GTO/STO. On the other hand, for a thin film geometry, the interface carrier density builds up only beyond a threshold thickness of LAO. The positive charge at the vacuum surface that compensates the 2DEG at the interface also exhibits distinct behaviors in the two systems. The compensating positive charge at the exposed surface of GTO charge disproportionates due to correlation effect making the surface insulating as opposed to that in LAO which remains metallic within band theory and presumably becomes insulating due to surface disorder or surface reconstruction.

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.

Doping a correlated band insulator: a new route to half-metallic behavior.

We demonstrate in a simple model the surprising result that turning on an on-site Coulomb interaction U in a doped band insulator leads to the formation of a half-metallic state. In the undoped system, we show that increasing U leads to a first order transition at a finite value UAF between a paramagnetic band insulator and an antiferomagnetic Mott insulator. Upon doping, the system exhibits half-metallic ferrimagnetism over a wide range of doping and interaction strengths on either side of UAF. Our results, based on dynamical mean field theory, suggest a new route to half metallicity, and will hopefully motivate searches for new materials for spintronics.

Universal features in the photoemission spectroscopy of high-temperature superconductors.

The energy gap for electronic excitations is one of the most important characteristics of the superconducting state, as it directly reflects the pairing of electrons. In the copper-oxide high-temperature superconductors (HTSCs), a strongly anisotropic energy gap, which vanishes along high-symmetry directions, is a clear manifestation of the d-wave symmetry of the pairing. There is, however, a dramatic change in the form of the gap anisotropy with reduced carrier concentration (underdoping). Although the vanishing of the gap along the diagonal to the square Cu-O bond directions is robust, the doping dependence of the large gap along the Cu-O directions suggests that its origin might be different from pairing. It is thus tempting to associate the large gap with a second-order parameter distinct from superconductivity. We use angle-resolved photoemission spectroscopy to show that the two-gap behavior and the destruction of well-defined electronic excitations are not universal features of HTSCs, and depend sensitively on how the underdoped materials are prepared. Depending on cation substitution, underdoped samples either show two-gap behavior or not. In contrast, many other characteristics of HTSCs, such as the dome-like dependence of on doping, long-lived excitations along the diagonals to the Cu-O bonds, and an energy gap at the Brillouin zone boundary that decreases monotonically with doping while persisting above (the pseudogap), are present in all samples, irrespective of whether they exhibit two-gap behavior or not. Our results imply that universal aspects of high- superconductivity are relatively insensitive to differences in the electronic states along the Cu-O bond directions.

Theory of quantum oscillations in the vortex-liquid state of high-Tc superconductors.

The observation of quantum oscillations in underdoped cuprates has generated intense debate about the nature of the field-induced resistive state and its implications for the 'normal state' of high-Tc superconductors. Quantum oscillations suggest an underlying Fermi liquid at high magnetic fields H and low temperatures, in contrast with the pseudogap seen in zero-field, high-temperature spectroscopic experiments. Recent specific heat measurements show quantum oscillations in addition to a large field-dependent suppression of the electronic density of states. Here we present a theoretical analysis that reconciles these seemingly contradictory observations. We model the resistive state as a vortex liquid with short-range d-wave pairing correlations. We show that this state exhibits quantum oscillations, with a period determined by a Fermi surface reconstructed by a competing order parameter, in addition to a large suppression of the density of states that goes like √H at low fields.

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.

Apparent low-energy scale invariance in two-dimensional Fermi gases.

Recent experiments on a 2D Fermi gas find an undamped breathing mode at twice the trap frequency over a wide range of parameters. To understand this seemingly scale-invariant behavior in a system with a scale, we derive two exact results valid across the entire Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover at all temperatures. First, we relate the shift of the mode frequency from its scale-invariant value to γ(d)≡(1+2/d)P-ρ(∂P/∂ρ)(s) in d dimensions. Next, we relate γ(d) to dissipation via a new low-energy bulk viscosity sum rule. We argue that 2D is special, with its logarithmic dependence of the interaction on density, and thus γ(2) is small in both the BCS-BEC regimes, even though P-2ε/d, sensitive to the dimer binding energy that breaks scale invariance, is not.