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Probing topological quantum matter with scanning tunnelling microscopy

The search for topological phases of matter is evolving towards strongly interacting systems, including magnets and superconductors, where exotic effects emerge from the quantum-level interplay between geometry, correlation and topology. Over the past decade or so, scanning tunnelling microscopy has become a powerful tool to probe and discover emergent topological matter, because of its unprecedented spatial resolution, high-precision electronic detection and magnetic tunability. Scanning tunnelling microscopy can be used to probe various topological phenomena, as well as complement results from other techniques. We discuss some of these proof-of-principle methodologies applied to probe topology, with particular attention to studies performed under a tunable vector magnetic field, which is a relatively new direction of recent focus. Finally, we then project the future possibilities for atomic-resolution tunnelling methods in providing new insights into topological matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observation of backscattering induced by magnetism in a topological edge state

Significance One of the predicted characteristics of helical topological boundary modes is the absence of backscattering when time-reversal symmetry (TRS) is preserved. While previous experiments have provided evidence for this topological protection, inducing backscattering by breaking TRS has yet to be demonstrated. We test this fundamental property by investigating quasiparticle scattering in the one-dimensional topological edge state of bismuth bilayers, coupled to ferromagnetic iron clusters, using a scanning tunneling microscope. Our experimental observations demonstrate that backscattering is induced by magnetism of iron clusters in these topological edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Clean 2D superconductivity in a bulk van der Waals superlattice

Alternative route to a 2D superconductor Single layers of transition metal dichalcogenides exhibit exotic properties, including superconductivity. The usual route to obtaining such samples is to exfoliate a three-dimensional (3D) crystal. Devarakonda et al. instead grew a superlattice comprising alternating layers of the transition metal dichalcogenide hexagonal NbS 2 and the material Ba 3 NbS 5 (see the Perspective by Schoop). The inert Ba 3 NbS 5 layers serve to dissociate the superconducting NbS 2 layers from one another, resulting in 2D superconductivity with high carrier mobility. The combination of high mobility and reduced dimensionality may give rise to exotic quantum phases. Science , this issue p. 231 see also p. 170

Science & Technology - Other Topics↗

Constructing non-Abelian quantum spin liquids using combinatorial gauge symmetry

We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic ZZ Z Z interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hopfions emerge in ferroelectrics

Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, attract an intense attention in the diverse areas of physics ranging from high-energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while being of broad interest, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions are of fundamental importance for the electromagnetic behavior of the nanocomposits and can result in advanced functionalities of these materials.

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Digital quantum simulation of Floquet symmetry-protected topological phases

Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions, solid-state spin systems, ultracold atoms and superconducting qubits. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamical topological phase realized in a trapped-ion quantum simulator

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase, in a quasiperiodically driven array of ten 171 Yb + hyperfine qubits in Quantinuum’s System Model H1 trapped-ion quantum processor. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. Here, this property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient manipulation of quantum information.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonlinear photoconductivities and quantum geometry of chiral multifold fermions

Here, chiral multifold fermions are quasiparticles that appear only in chiral crystals such as transition metal silicides in the cubic B20 structure (i.e., the CoSi family), and they may show exotic physical properties. Here we study the injection and shift photoconductivities and also the related geometrical quantities for several types of chiral multifold fermions, including spin-1/2 as well as pseudospin-1 and -3/2 fermions, dubbed as Kramers Weyl, triple-point, and Rarita-Schwinger-Weyl (RSW) fermions, respectively. We utilize the minimal symmorphic model to describe the triple-point fermions (TPF). We also consider the more realistic model Hamiltonian for the CoSi family including both linear and quadratic terms. We find that injection currents due to circularly polarized light are quantized as a result of the Chern numbers carried by the multifold fermions within the linear models. Surprisingly, we discover that in the TPF model, the linear shift conductivities, responsible for the shift current generation by linearly polarized light, are proportional to the pseudo spin-orbit coupling and independent of photon frequency. In contrast, for the RSW and Kramer Weyl fermions, the linear shift conductivity is linearly proportional to photon frequency. The numerical results agree with the power-counting analysis for quadratic Hamiltonians. The frequency independence of the linear shift conductivity could be attributed to the strong resonant symplectic Christoffel symbols of the flat bands. Moreover, the calculated symplectic Christoffel symbols show significant peaks at the nodes, suggesting that the shift currents are due to the strong geometrical response near the topological nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Large negative magnetoresistance in the off-stoichiometric topological semimetal PrSb x Te 2- x

Magnetic topological materials LnSbTe (Ln = lanthanide) have attracted intensive attention because of the presence of interplay between magnetism, topological, and electron correlations depending on the choices of magnetic Ln elements. Varying Sb and Te composition is an efficient approach to control structural, magnetic, and electronic properties. Here we report the composition-dependent properties in PrSb x Te 2-x . We identified the tetragonal-to-orthorhombic structure transitions in this material system, and very large negative magnetoresistance in the x = 0.3 composition, which might be ascribed to the coupling between magnetism and transport. Such unusual magnetotransport enables PrSb x Te 2-x topological materials as a promising platform for device applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quasi-two-dimensional ferromagnetism and anisotropic interlayer couplings in the magnetic topological insulator MnBi 2 Te 4

MnBi 2 Te 4 (MBT) is a promising van der Waals layered antiferromagnetic (AFM) topological insulator that combines a topologically nontrivial inverted Bi-Te band gap with ferromagnetic (FM) layers of Mn ions. Here, the inelastic neutron scattering on single crystals reported here describes rather complex magnetism in MBT. The magnetic anisotropy that controls the bulk and surface magnetic field response of MBT is found to have contributions from both single-ion and interlayer two-ion terms. A description of the quasi-two-dimensional intralayer FM spin waves requires long-range, competing FM and AFM interactions and anomalous damping. While this might suggest carrier-mediated magnetic coupling, abinitio calculations in insulating MBT also find long-range interactions, and classical spin dynamics simulations suggest that magnetic vacancies are at least partially responsible for observations of anomalous damping near the zone boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Intrinsic axion insulating behavior in antiferromagnetic MnBi 6 Te 10

A striking feature of time-reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when the surface states are gapped by time-reversal breaking perturbations. While TRS-protected TIs have become increasingly under control, magnetic analogs are still a largely unexplored territory with novel rich structures. In particular, magnetic topological insulators can also host a quantized axion term in the presence of lattice symmetries. Since these symmetries are naturally broken on the boundary, the surface states can develop a gap without external manipulation. In this work, we combine theoretical analysis, density-functional calculations and experimental evidence to reveal intrinsic axion insulating behavior in MnBi 6 Te 10 . Additionally, the quantized axion term arises from the simplest possible mechanism in the antiferromagnetic regime where it is protected by inversion symmetry and the product of a fractional translation and TRS. The anticipated gapping of the Dirac surface state at the edge is subsequently experimentally established using angle resolved photoemission spectroscopy (ARPES). As a result, this system provides the magnetic analog of the simplest TRS-protected TI with a single, gapped Dirac cone at the surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Gapless Dirac surface states in the antiferromagnetic topological insulator MnBi 2 Te 4

We used angle-resolved photoemission spectroscopy (ARPES) and density functional theory calculations to study the electronic properties of MnBi 2 Te 4 , a material that was predicted to be an intrinsic antiferromagnetic (AFM) topological insulator. In striking contrast to earlier literature showing a full gap opening between two surface band manifolds on the (0001) surface, we observed a gapless Dirac surface state with a Dirac point sitting at E B = -280 meV . Furthermore, our ARPES data revealed the existence of a second Dirac cone sitting closer to the Fermi level. Surprisingly, these surface states remain intact across the AFM transition. The presence of gapless Dirac states in this material may be caused by different ordering at the surface from the bulk or weaker magnetic coupling between the bulk and surface. Whereas the surface Dirac cones seem to be remarkably insensitive to the AFM ordering most likely due to weak coupling to magnetism, we did observe a splitting of the bulk band accompanying the AFM transition. Finally, with a moderately high ordering temperature and interesting gapless Dirac surface states, MnBi 2 Te 4 provides a unique platform for studying the interplay between magnetic ordering and topology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. Here, we report a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2–3 K and an AHE at T = 80–300 K. Over T = 3–80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii–Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effects of the Order Parameter Anisotropy on the Vortex Lattice in UPt3

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt 3 for the applied magnetic field along the crystalline c -axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal plane that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt ±15° vortex lattice rotation was previously reported by Huxley et al. , Nature 406 , 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al. , Nature Physics 16 , 531-535 (2020), can be attributed directly to the symmetry breaking field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effects of chemical disorder and spin-orbit coupling on the electronic-structure and Fermi-surface topology of YbSb-based monopnictides

Here, in this work, we study the influence of disorder on the electronic structure of YbSb—a rare-earth monopnictide featuring a simple rocksalt (B1) crystal structure and a well-defined Fermi-surface topology—by employing first-principles density-functional theory. We focus on chemical disorder introduced through Te and Al doping, selected based on their thermodynamic stability in alloyed configurations, to understand how such perturbations modify the electronic states of YbSb. Our results indicate that Te doping predominantly introduces electronlike states at the 𝑋 and 𝐿 points, while Al doping leads to a suppression of holelike states at Γ, effectively driving the system from a semimetallic state to one characterized by very narrow-gap behavior at Γ. This modulation of the Fermi surface, particularly the reduction of central hole pockets at Γ, plays a central role in altering interpocket scattering—a mechanism critical for tuning quantum transport properties, including superconductivity. This disorder-driven modulation of the Fermi surface, particularly the suppression of central hole pockets at Γ, controls interpocket scattering, which is essential for optimizing quantum transport properties, including superconductivity. Our results show that disorder can be effectively used for engineering band topology, thereby tuning quantum related response through a tailored electronic structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterization and classification of interacting ( 2 + 1 )-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this work, we develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions with charge conservation, discrete magnetic translation and M-fold point group rotation symmetries, which form the group G f = U(1) f × Φ [Z 2 $\rtimes$Z M ] for M = 1,2,3,4, and 6. Φ is the magnetic flux per unit cell. We derive a topological response theory in terms of background crystalline gauge fields, which gives a complete classification of different phases and a physical characterization in terms of quantized response to symmetry defects. We then derive the same classification in terms of a set of real space invariants {$Θ^±_o$} that can be obtained from ground state expectation values of suitable partial rotation operators. We explicitly relate these real space invariants to the quantized coefficients in the topological response theory, and find the dependence of the invariants on the chiral central charge c – of the invertible phase. Finally, when Φ = 0 we derive an explicit map between the free and interacting classifications.

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