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The kagomé metals RbTi 3 Bi 5 and CsTi 3 Bi 5

Abstract The kagomé metals RbTi 3 Bi 5 and CsTi 3 Bi 5 were synthesized both as polycrystalline powders by heating the elements in an argon atmosphere and as single crystals grown using a self-flux method. The compounds crystallize in the hexagonal crystal system isotypically to KV 3 Sb 5 ( P 6/ mmm , Z = 1, CsTi 3 Bi 5 : a = 5.7873(1), c = 9.2062(1) Å; RbTi 3 Bi 5 : a = 5.773(1), c = 9.065(1) Å). The titanium atoms form a kagomé net with bismuth atoms in the hexagons as well as above and below the triangles. The alkali metal atoms are coordinated by 12 bismuth atoms and form AlB 2 -like slabs between the kagomé layers. Magnetic susceptibility measurements with CsTi 3 Bi 5 and RbTi 3 Bi 5 single crystals reveal Pauli-paramagnetism and traces of superconductivity caused by CsBi 2 /RbBi 2 impurities. Magnetotransport measurements reveal conventional Fermi liquid behavior and quantum oscillations indicative of a single dominant orbit at low temperature. DFT calculations show the characteristic metallic kagomé band structure similar to that of CsV 3 Sb 5 with reduced band filling. A symmetry analysis of the band structure does not reveal an obvious and unique signature of a nontrivial topology.

Chemistry↗

Topological insulator-based high efficiency switching of magnetic unit, method and applications

A magneto-electronic device may include: a spin-orbit torque (SOT) generator layer; a magnetic memory layer; and/or sensing electrodes configured to measure a Hall effect of the magnetic memory layer. The SOT generator layer may include topological insulator material, and the magnetic memory layer may include ferromagnetic material with perpendicular magnetic anisotropy. A magneto-electronic device may include: a spin-orbit torque (SOT) generator layer; a first magnetic memory layer on the SOT generator layer; an insulating layer on the first magnetic memory layer; and/or a second magnetic memory layer on the insulating layer. The SOT generator layer may include topological insulator material. The first magnetic memory layer and the second magnetic memory layer may include ferromagnetic material with either perpendicular magnetic anisotropy or in-plane magnetic anisotropy.

36 MATERIALS SCIENCE↗

Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials (CCDM) August 1, 2014 - July 31, 2018; Center for Complex Materials from First Principles (CCM) August 1, 2018 - July 31, 2021 (Final Report)

The mission of the DOE Energy Frontier Research Centers CCDM (2014-2018) and CCM (2018-2021) was to theoretically develop, computationally apply, and experimentally validate electronic structure methods for all materials, with a focus on the complex materials, especially layered and two-dimensional materials, strongly-correlated materials, and liquid water. This was achieved by over 200 published journal articles authored by about 17 senior investigators from physics and chemistry and from theory, computation, and experiment, plus their collaborators. In particular, the Centers confirmed the predictive power of the SCAN (strongly constrained and appropriately normed) density functional, which was constructed to satisfy 17 known exact constraints and several appropriate norms. Without being fitted to real bonded systems, and at a modest computational cost, SCAN correctly predicted covalent, ionic, metallic, hydrogen, and van der Waals bonds in many challenging materials. SCAN gave an improved description of defects in semiconductors, surface properties of metals, seven phases of ice, liquid water, liquid and supercooled silicon, subtle structural distortions in ferroelectrics, formation energies and structural predictions for solids, and critical pressures for structural phase transitions. Perhaps most remarkably, SCAN correctly described some strongly-correlated materials that were previously believed to be beyond the reach of density-functional approximations. SCAN is the only density functional that correctly predicts the band gap closing under chemical doping of the cuprate high-temperature superconducting materials. SCAN also predicts a landscape of competing stripe and magnetic phases in the cuprates. For some materials with some codes, SCAN has convergence problems that are greatly reduced by the CCM-developed r 2 SCAN, without loss of accuracy or rigor. SCAN and r 2 SCAN still make some self-interaction error, which is greatly reduced by the CCDM/ CCM-developed local orbital scaling correction (LOSC). These Centers further proved that the fundamental energy gaps of a solid from an orbital energy difference and from total energy differences are the same for a large class of generalized Kohn-Sham (GKS) functionals, including SCAN and standard hybrid functionals, and that symmetry breaking arises when a dynamic density fluctuation drops to zero frequency. The Centers identified new mechanisms for catalysis in layered materials with ions intercalated between the layers, investigated charge density waves both in model systems and in real layered materials, studied changes of band gap with the number of layers, and explored topological ultrathin films, bent nanoribbons, and defects.

08 HYDROGEN↗

Anomalous normal fluid response in a chiral superconductor UTe2

Abstract Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe 2 with surface normal fluid response. The microwave surface impedance of the UTe 2 crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe 2 can be a new platform to study exotic topological excitations in higher dimension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electric-field control of the nucleation and motion of isolated three-fold polar vertices

Recently various topological polar structures have been discovered in oxide thin films. Despite the increasing evidence of their switchability under electrical and/or mechanical fields, the dynamic property of isolated ones, which is usually required for applications such as data storage, is still absent. Here, we show the controlled nucleation and motion of isolated three-fold vertices under an applied electric field. At the PbTiO 3 /SrRuO 3 interface, a two-unit-cell thick SrTiO 3 layer provides electrical boundary conditions for the formation of three-fold vertices. Utilizing the SrTiO 3 layer and in situ electrical testing system, we find that isolated three-fold vertices can move in a controllable and reversible manner with a velocity up to ~629 nm s -1 . Microstructural evolution of the nucleation and propagation of isolated three-fold vertices is further revealed by phase-field simulations. This work demonstrates the ability to electrically manipulate isolated three-fold vertices, shedding light on the dynamic property of isolated topological polar structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Hidden non-collinear spin-order induced topological surface states

Abstract Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Néel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Enhanced Dirac node separation in the strained Cd 3 As 2 topological semimetal

In topological semimetals, nodes appear at symmetry points in the Brillouin zone as a result of band inversion, and yield quasirelativistic massless fermions at low energies. Cd 3 As 2 is a three-dimensional topological semimetal that hosts two Dirac cones responsible for a variety of quantum phenomena. In this work, we demonstrate the strain tuning of the Dirac nodes of Cd 3 As 2 through a combination of magneto-optical infrared spectroscopy and high-resolution x-ray-diffraction studies performed on epitaxial films. In these thin films, we observe a giant enhancement of the node separation in momentum space by close to a factor of 4. A combination of experimental measurements and theoretical modeling allows us to relate the origin of this enhancement to a strengthening of the topological band inversion driven by lattice strain. Finally, our results demonstrate how strain can be used as a knob to tune the topological properties of semimetals and to potentially enhance their performance and response for various applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Proximity Effects and Topological Spin Currents in van der Waals Heterostructures (Final Report)

The major goal of this grant has been to study spin-polarized topological edge states. The original proposal was focused specifically on those of the quantum anomalous Hall (QAH) effect, which was proposed to be realizable via a (simultaneous) magnetic and spin-orbit proximity effect in graphene. En route to realizing the QAH effect, the goal was also to study the newly-discovered 2D magnetic insulators, which have finally been isolated in the single-to-few atomic layers from compounds whose bulk properties have known since the 1970s, and the extent to which magnetic effects could be seen in graphene via proximity coupling. Since the original proposal, the scope of the work has expanded to include study of the topological edge states of the quantum spin Hall (QSH) effect and how they are modified by proximity effects and in twisted bilayers. The broader scientific context of the experiments in this proposal is to understand the physical mechanisms behind proximity effects in van der Waals heterostructures. Perhaps the ultimate scientific and technological goal of realizing topological states through proximity effects is the creation of Majorana zero modes in solid-state devices, which has been identified as a major priority in condensed-matter physics and quantum information because of the potential use of Majorana zero modes in topological quantum computing. Van der Waals materials offer advantages in this area because of the diversity of materials that can potentially be used and the unique device architectures that are possible using the van der Waals assembly techniques.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

CORC $^{\circledR}$ cable terminations with integrated Hall arrays for quench detection

ReBCO superconducting cables have the potential to enable compact thermonuclear fusion reactors that operate at magnetic fields exceeding 20 T and allow operation at temperatures far exceeding the boiling point of liquid helium, potentially allowing for demountable magnets. Normal zone detection remains a challenge, and while novel quench detection techniques are an active area of research, few are non-invasive, provide real-time quench detection, and have been demonstrated with current ramp rates relevant for fusion reactors. To address this problem, a CORC$^{\circledR}$ cable termination is developed with integrated Hall sensors to monitor current redistribution as a proxy for quench detection. The methodology exploits the current sharing and layered topology in CORC$^{\circledR}$ cables, and allows quench detection using a localized sensor instead of co-wound voltage wires or optical fibers. Furthermore, experiments are presented where current redistribution is measured from induced quenches, and in a 0.2 meter CORC$^{\circledR}$ sample it is found that the Hall sensors detect normal zone transitions with a similar magnitude and temporal resolution as voltage measurements. To emulate the conditions of dynamic poloidal and central solenoidal fields, experiments are repeated with ramp rates up to 10 kA s -1 that demonstrate the potential to detect normal zone development over a range of experimental parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Microscopic scattering approach to in-gap states: Cr adatoms on superconducting 𝛽−Bi 2 ⁢Pd

We develop a microscopic scattering formalism to describe Yu-Shiba-Rusinov (YSR) states due to a single Cr adatom on the Bi-terminated surface of 𝛽−Bi 2 ⁢Pd, by combining ab initio Wannier functions with a real-space Green's function approach in the Bogoliubov–de Gennes formalism. Our framework reproduces key scanning tunneling spectroscopy features, including a single particle-hole asymmetric YSR peak and isotropic 𝑑⁢𝐼/𝑑⁢𝑉 maps around the impurity. Decomposing the YSR states reveals contributions from four nearly degenerate 𝐶 4⁢𝑣 representations, with energy broadening masking their individual signatures. Spin-orbit coupling induces partial spin polarization, while the spatial asymmetry between particle and hole components arises from Cr 𝑑−Bi 𝑝 hybridization. These results highlight the importance of realistic band structures and microscopic modeling for interpreting STM data and provide a foundation for studying impurity chains hosting topological excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nanoscale studies of electric field effects on monolayer 1T′-WTe2

Abstract Monolayer 1 T′-WTe 2 is a quantum spin Hall insulator with a gapped 2D-bulk and gapless helical edge states persisting to temperatures ~100 K. Despite the far-ranging interest, the magnitude of the bulk gap, the effect of gating on the 2D-band structure, as well the role interactions are not established. In this work we use STM spectroscopy to measure the intrinsic bulk gap of monolayer 1 T′-WTe 2 and show that gate induced electric fields cause large changes of the gap magnitude. Our first-principles DFT-derived tight-binding model reveal that a combination of spatial localization of the conduction and valance bands and Rashba-like spin-orbit coupling leads to a gating induced spin-splitting of the 2D-bulk bands in the tens of meV, thereby reducing the band gap. Our work explains the large sensitivity of the band structure to electric fields and suggests a new avenue for realizing proximity induced non-trivial superconductivity in monolayer 1 T′-WTe 2 .

36 MATERIALS SCIENCE↗

Charge dynamics of a noncentrosymmetric magnetic Weyl semimetal

The interplay of topology with magnetism in Weyl semimetals recently arose to a vanguard topic, because of novel physical scenarios with anomalous transport properties. Here, we address the charge dynamics of the noncentrosymmetric and ferromagnetic (T C ~ 15 K) PrAlGe material and discover that it harbours electronic correlations, which are reflected in a sizeable reduction of the Fermi velocity with respect to the bare band value at low temperatures (T). At T < T C , the optical response registers a band reconstruction, which additionally causes a reshuffling of spectral weight, pertinent to the electronic environment of the type-I Weyl fermions and tracing the remarkable anomalous Hall conductivity (AHC). With the support of first-principles calculations, we provide evidence for the intimate relationship between a topological resonance of the absorption spectrum and the progressively enhanced occupation of non-trivial states with large Berry curvatures, a requirement for AHC.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robustness of topological insulating phase against vacancy, vacancy cluster, and grain boundary bulk defects

One distinguished property of the topological insulator (TI) is its robust quantized edge conductance against edge defect. However, this robustness, underlined by the topological principle of bulk-boundary correspondence, is conditioned by assuming a perfect bulk. Here, we investigate the robustness of the TI phase against bulk defects, including vacancy (VA), vacancy cluster (VC), and grain boundary (GB), instead of edge defect. In this work, based on a tight-binding model analysis, we show that a two-dimensional (2D) TI phase, as characterized by a nonzero spin Bott index, will vanish beyond a critical VA concentration ($n^\text{c}_\text{v}$). Generally, $n^\text{c}_\text{v}$ decreases monotonically with the decreasing topological gap induced by spin-orbit coupling. Interestingly, the $n^\text{c}_\text{v}$ to destroy the topological order, namely, the robustness of the TI phase, is shown to be increased by the presence of VCs but decreased by GBs. As a specific example of a large-gap 2D TI, we further show that the surface-supported monolayer Bi can sustain a nontrivial topology up to $n^\text{c}_\text{v}$ ~ 17%, based on a density-functional theory–Wannier-function calculation. Our findings should provide useful guidance for future experimental studies of effects of defects on TIs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Construction of a series of new $\textit{ν}$ = 2/5 fractional quantum Hall wave functions by conformal field theory

In this paper, a series of $\textit{ν}$ = 2/5 fractional quantum Hall wave functions are constructed from conformal field theory(CFT). They share the same topological properties with states constructed by Jain's composite fermion approach. Upon exact lowest Landau level (LLL) projection, some of Jain's composite fermion states would not survive if constraints on Landau level indices given in the appendices of this paper were not satisfied. By contrast, states constructed from CFT are always in LLL. These states are characterized by different topological shifts and multibody relative angular momenta. Further, as a by-product, in the appendices we prove the necessary conditions for general $\textit{ν = p}$/(2$\textit{p}$ + 1) composite fermion states to have nonvanishing LLL projection.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Increased localization of Majorana modes in antiferromagnetic chains on superconductors

Magnet-superconductor hybrid (MSH) systems are a key platform for custom-designed topological superconductors. Ideally, the ends of a one-dimensional MSH structure will host Majorana zero-modes (MZMs), the fundamental unit of topological quantum computing. However, some experiments with ferromagnetic (FM) chains show a more complicated picture. Due to tiny gap sizes and hence long coherence lengths, MZMs might hybridize and lose their topological protection. Recent experiments on a niobium surface have shown that both FM and antiferromagnetic (AFM) chains may be engineered, with the magnetic order depending on the crystallographic direction of the chain. While FM chains are well understood, AFM chains are less so. Here, we study two models inspired by the niobium surface: A minimal model to elucidate the general topological properties of AFM chains and an extended model to more closely simulate a real system by mimicking the proximity effect. Here, we find that, in general, for AFM chains, the topological gap is larger than for FM ones, and thus, coherence lengths are shorter for AFM chains, yielding more pronounced localization of MZMs in these chains. While for some parameters AFM chains may be topologically trivial, we find in these cases that adding an adjacent chain can result in a nontrivial system, with a single MZM at each chain end.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Probing the edge states of Chern insulators using microwave impedance microscopy

Microwave impedance microscopy (MIM) has been utilized to directly visualize topological edge states in many quantum materials. While the microwave response for conventional metals and insulators can be accurately quantified using simple lumped-element circuits, whose applicability to more exotic quantum systems remain limited. In this work, we present a general theoretical framework of the MIM response of arbitrary quantum materials. Applying it to topological edge states in a Chern insulator predicts an enhanced MIM response at the crystal boundaries due to collective edge magnetoplasmon (EMP) excitations. The unique resonance frequency of these plasmonic modes allows one to disentangle the signatures of topological versus trivial edge states. To benchmark our analytical predictions, we experimentally probe the MIM response of quantum anomalous Hall edge states in a Cr-doped (Bi,Sb) 2 Te 3 topological insulator and perform numerical simulations using a classical formulation of the EMP modes based on this realistic tip-sample geometry, both of which yield results consistent with our theoretical picture. Here we also show how the technique of MIM can be used to quantitatively extract the topological invariant of a Chern insulator and shed light on the microscopic nature of dissipation along the crystal boundaries.

36 MATERIALS SCIENCE↗

Effects of Anisotropic Strain on Spin–Orbit Torque Produced by the Dirac Nodal Line Semimetal IrO 2

We report spin-torque ferromagnetic resonance studies of the efficiency of the damping-like (ξ DL ) spin–orbit torque exerted on an adjacent ferromagnet film by current flowing in epitaxial (001) and (110) IrO 2 thin films. IrO 2 possesses Dirac nodal lines (DNLs) in the band structure that are gapped by spin–orbit coupling, which could enable a very high spin Hall conductivity, σ SH . We find that the (001) films do exhibit exceptionally high ξ DL ranging from 0.45 at 293 K to 0.65 at 30 K, which sets the lower bounds of σ SH to be 1.9 × 10 5 and 3.75 × 10 5 Ω –1 m –1 , respectively, 10 times higher and of opposite sign than the theoretical prediction. Furthermore, ξ DL and σ SH are substantially reduced in anisotropically strained (110) films. Here, we suggest that this high sensitivity to anisotropic strain is because of changes in contributions to σ SH near the DNLs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

1/4 is the new 1/2 when topology is intertwined with Mottness

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗