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Spin-resolved topology and partial axion angles in three-dimensional insulators
Abstract Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ( $${{{{{{{\mathcal{T}}}}}}}}$$ T -) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and $${{{{{{{\mathcal{T}}}}}}}}$$ T -doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β -MoTe 2 realizes a spin-Weyl state and that α -BiBr hosts both 3D QSHI and T-DAXI regimes.
Electronic Structure Theory and Novel Materials
This grant supported research on electronic structure and materials theory, with focus on three main issues: (i) novel techniques to deal with correlation in the electronic ground-state, (ii) topological materials, (iii) the phase diagram of lattice spin models. Regarding (i), we applied to the homogeneous electron liquid an approach that we previously developed in the context of molecular systems. In this scheme the electronic occupation probabilities and the natural spin orbitals are used to construct an approximate two-body density matrix for the electronic ground-state. Regarding (ii) we used standard electronic structure methods based on density functional theory to model topological materials and interpret experimental observations. Finally, regarding (iii) we further developed a numerical approach to compute the renormalized couplings within real space renormalization group theory in the context of lattice spin models. The main findings were the following. (i) We found that with our approximate two-body density matrix, which works well for small molecules, is not sufficiently accurate for condensed phase systems. Missing a systematic way of improving on the adopted approximations, we decided not to pursue this approach. (ii) We performed two studies. In one, we investigated the influence of Te defects on the topological properties of a WTe2 monolayer, finding that while Te vacancies, even in modest concentration, destroy the topological character, Te adatoms do not, consistent with a recent experiment. In another study, we predicted Weyl semimetal character and strong anomalous Hall effect in the Heusler compensated ferrimagnet Ti2MnAl. (iii) We developed a new Monte Carlo method to do real space renormalization group calculations for lattice spin models. We subsequently extended the scheme to deal with lattice spin models in presence of quenched disorder, finding that the approach can distinguish systems with finite and strong disorder. In the finite disorder case, the method allows one to find with good approximation the critical coupling distribution and the critical exponents.
Transition-metal phthalocyanine monolayers as new Chern insulators
To explore new materials for the realization of the quantum anomalous Hall effect (QAHE), we studied the electronic, magnetic and topological properties of transition-metal phthalocyanine (TMPc) monolayers in a square lattice. Many of them have large topologically nontrivial band gaps and integer Chern numbers. In particular, the Fermi level of MoPc lies right in the band gap (E g = 8.1 meV) and has large magnetic anisotropy energy (MAE = 2.0 meV per Mo atom) and a Curie temperature of 16 K, showing its usefulness for applications. The presence of the topologically protected edge state in a MoPc nanoribbon further confirms it as a new two-dimensional topological insulator. This much widens the search for QAHE materials for the design of quantum devices.
Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry
A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal (C 4 in-plane) symmetry is not a necessary condition for the creation of zero-energy metallic surface states on TCI slabs of finite-thicknesses, because zero-energy states persist even as all the in-plane rotational symmetries—furnishing topological protection—are completely removed. In other words, zero-energy levels on the model are not due to (nor are they protected by) topology. Furthermore, effective two-fold energy degeneracies taking place at few discrete k-points away from zero energy in the bulk Hamiltonian—that are topologically protected—persist at the u.c. thickness limit. Here, the chiral nature of the bulk TCI Hamiltonian permits creating a $2\times 2$ square Hamiltonian, whose topological properties remarkably hold invariant at both the bulk and at the single u.c. thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians. This way, a two-atom-thick TCI is deployed hereby, in a demonstration of a topological phase that holds both in the bulk, and in two dimensions.
All topological bands of all nonmagnetic stoichiometric materials
Topological quantum chemistry and symmetry-based indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy ( E F ). We report the implementation of a publicly accessible catalog of stable and fragile topology in all of the bands both at and away from E F in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations, which represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, have enabled the discovery of repeat-topological and supertopological materials, including rhombohedral bismuth and Bi 2 Mg 3 . We find that 52.65% of all materials are topological at E F , roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topology, and 87.99% of all materials contain at least one stable or fragile topological band.
Ultrahigh supercurrent density in a two-dimensional topological material
Ongoing advances in superconductors continue to revolutionize technology thanks to the increasingly versatile and robust availability of lossless supercurrents. In particular, high supercurrent density can lead to more efficient and compact power transmission lines, high-field magnets, as well as high-performance nanoscale radiation detectors and superconducting spintronics. In this work, we report the discovery of an unprecedentedly high superconducting critical current density (17 MA / cm 2 at 0 T and 7 MA / cm 2 at 8 T) in 1T'–WS 2 , exceeding those of all reported two-dimensional superconductors to date. 1T'–WS 2 features a strongly anisotropic (both in- and out-of-plane) superconducting state that violates the Pauli paramagnetic limit signaling the presence of unconventional superconductivity. Spectroscopic imaging of the vortices further substantiates the anisotropic nature of the superconducting state. More intriguingly, the normal state of 1T'–WS 2 carries topological properties. The band structure obtained via angle-resolved photoemission spectroscopy and first-principles calculations points to a Z 2 topological invariant. The concomitance of topology and superconductivity in 1T'–WS 2 establishes it as a topological superconductor candidate, which is promising for the development of quantum computing technology.
Epitaxial Multifunctional Oxide Heterostructures (DOE Final Technical Report)
The conducting interface that forms between the two band insulators LaAlO 3 (LAO) and SrTiO 3 (STO) continues to attract tremendous attention nearly 15 years after its discovery. Until recently, most of the work on this system has been done in samples grown in the (001) crystal orientation. More recently, interest has focused on samples grown in the (110) and (111) crystal orientations. While the underlying cubic crystal structure is the same, the lattice symmetry at the interface in each case is different, raising the possibility of different properties. In particular, the symmetry of the Ti atoms at the (111) interface is hexagonal, similar to graphene, leading to predictions of topological properties of the band structure. The major part of this proposal is devoted to exploring the properties of (111) LAO/STO interfaces and (111) (La 0.3 Sr 0.7 )(Al 0.65 Ta 0.35 )/STO (LSAT/STO) interfaces, where we have recently discovered interesting new effects.
Berry Curvature and Spin-One Color Superconductivity
Here, we explore the interplay between Berry curvature and topological properties in single-flavor color superconductors, where quarks form spin-one Cooper pairs. By deriving a new relation, we connect the topological nodal structure of the gap function in momentum space to the (non-Abelian) Berry flux associated with paired quarks. This generalizes the early work by Li and Haldane [Phys. Rev. Lett. 120, 067003 (2018)] to systems with additional internal quantum numbers, such as color. In the ultrarelativistic limit, we uncover rich topological structures driven by the interplay of spin, chirality, and color. Specifically, we identify chirality-induced topological nodes in the transverse (opposite chirality pairing) polar and 𝐴 phases. In contrast, the color-spin-locking phase lacks these nodes due to a nontrivial color Berry flux, which in turn induces gapless excitations with total Berry monopole charges of ±3/2—differing from conventional Weyl fermions. Our findings can be potentially extended to other fermionic systems carrying additional internal degrees of freedom.
Gaps in topological magnon spectra: Intrinsic versus extrinsic effects
Determining and explaining the presence of a gap at a magnon crossing point is a critical step to characterize the topological properties of a material. An inelastic neutron scattering study of a single crystal is a powerful experimental technique to probe the magnetic excitation spectra of topological materials. Here, we show that when the scattering intensity rapidly disperses in the vicinity of a crossing point, such as a Dirac point, the apparent topological gap size is extremely sensitive to experimental conditions including sample mosaic, resolution, and momentum integration range. In this work, we demonstrate these effects using comprehensive neutron scattering measurements of CrCl 3 . Our measurements confirm the gapless nature of the Dirac magnon in CrCl 3 , but also reveal an artificial, i.e., extrinsic, magnon gap unless the momentum integration range is carefully controlled. Our study provides an explanation of the discrepancies between spectroscopic and first-principles estimates of Dirac magnon gap sizes and provides guidelines for accurate measurement of topological magnon gaps.
Observation of Weyl fermions in a magnetic non-centrosymmetric crystal
The absence of inversion symmetry in non-centrosymmetric materials has a fundamental role in the emergence of a vast number of fascinating phenomena, like ferroelectricity, second harmonic generation, and Weyl fermions. The removal of time-reversal symmetry in such systems further extends the variety of observable magneto-electric and topological effects. Here we report the striking topological properties in the non-centrosymmetric spin-orbit magnet PrAlGe by combining spectroscopy and transport measurements. By photoemission spectroscopy below the Curie temperature, we observe topological Fermi arcs that correspond to projected topological charges of ±1 in the surface Brillouin zone. In the bulk, we observe the linear energy-dispersion of the Weyl fermions. We further observe a large anomalous Hall response in our magneto-transport measurements, which is understood to arise from diverging bulk Berry curvature fields associated with the Weyl band structure. These results establish a novel Weyl semimetal phase in magnetic non-centrosymmetric PrAlGe.
Prediction of topological phases in metastable ferromagnetic $MPX_3$ monolayers
Density functional theory calculations are carried out to study the electronic and topological properties of MPX 3 (M = Mn, Fe, Co,Ni; X = S, Se) monolayers in the ferromagnetic (FM) metastable magnetic state. Here we find that FM MnPSe 3 monolayers host topological semimetal signatures that are gapped out when spin-orbit coupling is included. These findings are supported by explicit calculations of the Berry curvature and the Chern number. The choice of the Hubbard-U parameter to describe the d-electrons is thoroughly discussed, as well as the influence of using a hybrid-functional approach. The presence of band inversions and the associated topological features are found to be formalism-dependent. Nevertheless, routes to achieve the topological phase via the application of external biaxial strain are demonstrated. Within the hybrid-functional picture, topological band structures are recovered under a pressure of 15% (17 GPa). The present work provides a potential avenue for uncovering new topological phases in metastable ferromagnetic phases.
Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor
Abstract Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials—the Janus transition metal dichalcogenides in the 1 T’ phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1 T’ MoSSe (e.g., > 50 times higher than 2 H MoS 2 for 18 th order harmonic generation; > 20 times higher than 2 H MoS 2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit.
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.
Engineering a non-Hermitian second-order topological insulator state in quasicrystals
Non-Hermitian topological phases have gained immense attention due to their potential to unlock novel features beyond Hermitian bounds. PT -symmetric (parity time-reversal symmetric) non-Hermitian models have been studied extensively over the past decade. In recent years, the topological properties of general non-Hermitian models, regardless of the balance between gains and losses, have also attracted vast attention. Here, we propose a non-Hermitian second-order topological (SOT) insulator that hosts gapless corner states on a two-dimensional quasicrystalline lattice (QL). We first construct a non-Hermitian extension of the Bernevig-Hughes-Zhang model on a QL generated by the Amman-Beenker tiling. This model has real spectra and supports helical edge states. Corner states emerge by adding a proper Wilson-mass term that gaps out the edge states. We propose two variations of the mass term that result in fascinating characteristics. In the first variation, we obtain a purely real spectra for the second-order topological phase. In the latter, we get a complex spectra with corner states localized at only two corners due to the higher-order non-Hermitian skin effect of the edge modes. Furthermore, our findings pave a path to engineering exotic SOT phases where corner states can be localized at designated corners.
Topological Hall Effect Anisotropy in Kagome Bilayer Metal Fe 3 Sn 2
Kagome lattice materials attract growing interest for their topological properties and flat-bands in electronic structure. We present comprehensive study on the anisotropy and out-of-plane electric transport in Fe 3 Sn 2 , a metal with bilayer of Fe kagome planes and with massive Dirac fermions that features high-temperature non-collinear magnetic structure and magnetic skyrmions. For the electrical current path along the c-axis, in micron-size crystals, we found a large topological Hall effect (THE) over a wide temperature range down to spin-glass state. Twofold and fourfold angular magnetoresistance are observed for different magnetic phases, reflecting the competition of magnetic interactions and magnetic anisotropy in kagome lattice that preserve robust topological Hall effect for inter kagomebilayer currents. This information provides new insight into the anisotropy in Fe 3 Sn 2 , of interest in skyrmionicbubble application-related micron-size devices.
Simulating Dynamical Phases of Chiral p + i p Superconductors with a Trapped ion Magnet
Two-dimensional p + ip superconductors and superfluids are systems that feature chiral behavior emerging from the Cooper pairing of electrons or neutral fermionic atoms with nonzero angular momentum. Their realization has been a longstanding goal because they offer great potential utility for quantum computation and memory. However, they have so far eluded experimental observation both in solid-state systems as well as in ultracold quantum gases. Here, we propose to leverage the tremendous control offered by rotating two-dimensional trapped-ion crystals in a Penning trap to simulate the dynamical phases of two-dimensional p + ip superfluids. This is accomplished by mapping the presence or absence of a Cooper pair into an effective spin-1/2 system encoded in the ions’ electronic levels. We show how to infer the topological properties of the dynamical phases, and discuss the role of beyond mean-field corrections. More broadly, our work opens the door to use trapped-ion systems to explore exotic models of topological superconductivity and also paves the way to generate and manipulate skyrmionic spin textures in these platforms.
Manipulating magnetism in the topological semimetal EuCd[subscript 2]As[subscript 2]
Abstract not provided