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Plasmons in Z 2 topological insulators

Here, we study plasmonic excitations in the Kane-Mele model, a two-dimensional Z 2 topological insulator on the honeycomb lattice, using the random phase approximation (RPA). In the topologically nontrivial phase, the model has conducting edge states that traverse the bulk energy gap and display spin-momentum locking. Such a state of matter is called the quantum spin hall (QSH) phase, which is robust against time-reversal (TR) invariant perturbations. We find that in the QSH phase, gapless spin-polarized plasmons can be excited on the edges of the system. The propagation of these plasmons is chiral for each individual spin component and shows spin-momentum locking for both spin components on the same edge. Moreover, we study the effect of external magnetic fields on the gapless edge plasmons. Specifically, out-of-plane magnetic fields delocalize edge plasmons propagating in one direction without affecting the other one, while an in-plane magnetic field can be applied to selectively excite a specific spin-plasmon branch with proper doping or gating to the system. Our findings may have potential applications in novel plasmonic and spintronic devices. We also investigate plasmons in the Kane-Mele model on a finite-sized diamond-shaped nanoflake and observe low-energy plasmons circulating the boundary of the material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Unusual Quasiparticles and Tunneling Conductance in Quantum Point Contacts in 𝜈 = 2/3 Fractional Quantum Hall Systems

Understanding topological matter in the fractional quantum Hall (FQH) effect requires identifying the nature of edge state quasiparticles. FQH edge state at the filling factor 𝜈 = 2/3 in the spin-polarized and unpolarized phases is represented by the two modes of composite fermions (CF) with the parallel or opposite spins described by the chiral Luttinger liquids. Tunneling through a quantum point contact (QPC) between different or similar spin phases is solved exactly. With the increase of the applied voltage, the QPC conductance grows from zero and saturates at 𝑒 2 /2⁢ℎ while a weak electron tunneling between the edge modes with the same spin transforms into a backscattering carried by the charge 𝑞 = 𝑒/2 quasiparticles. These unusual quasiparticles and conductance plateau emerge when one or two CF spin-polarized modes in the QPC tunnel into a single mode. Here, we propose experiments on the applied voltage and temperature dependence of the QPC conductance and noise that can shed light on the nature of edge states and FQH transport.

Anyons↗

Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators

Gapless helical edge modes are a hallmark of the quantum spin Hall effect. Protected by time-reversal symmetry, each edge contributes a quantized zero-temperature conductance quantum G 0 ≡ e 2 /h. However, the experimentally observed conductance in WT e2 decreases below G 0 per edge already at edge lengths around 100 nm, even in the absence of explicit time-reversal breaking due to an external field or magnetic impurities. Here we show how a time-reversal breaking excitonic condensate with a spin-spiral order that can form in WT e2 leads to the breakdown of conductance quantization. We perform Hartree-Fock calculations to compare time-reversal breaking and preserving excitonic insulators. Using these mean-field models we demonstrate via quantum transport simulations that weak nonmagnetic disorder reproduces the edge length scaling of resistance observed in the experiments. We complement this by analysis in the Luttinger liquid picture, shedding additional light on the mechanism behind the quantization breakdown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bismuthene Under Cover: Graphene Intercalation of a Large Gap Quantum Spin Hall Insulator

Abstract The quantum spin Hall insulator bismuthene, a two‐third monolayer of bismuth on SiC(0001), is distinguished by helical metallic edge states that are protected by a groundbreaking 800 meV topological gap, making it ideal for room temperature applications. This massive gap inversion arises from a unique synergy between flat honeycomb structure, strong spin orbit coupling, and an orbital filtering effect that is mediated by the substrate. However, the rapid oxidation of bismuthene in air has severely hindered the development of applications, so far confining experiments to ultra‐high vacuum conditions. Intercalating bismuthene between SiC and a protective sheet of graphene, this barrier is successfully overcome. As demonstrated by scanning tunneling microscopy and photoemission spectroscopy, graphene intercalation preserves the structural and topological integrity of bismuthene, while effectively shielding it from oxidation in air. Hereby, hydrogen is identified as the critical process gas that was missing in previous bismuth intercalation attempts. These findings facilitate ex‐situ experiments and pave the way for the development of bismuthene based devices, signaling a significant step forward in the development of next‐generation technologies.

Chemistry↗

Helical Edge States and Quantum Phase Transitions in Tetralayer Graphene

Helical conductors with spin-momentum locking are promising platforms for Majorana fermions. Here we report observation of two topologically distinct phases supporting helical edge states in charge neutral Bernal-stacked tetralayer graphene in Hall bar and Corbino geometries. As the magnetic field B ⊥ and out-of-plane displacement field D are varied, we observe a phase diagram consisting of an insulating phase and two metallic phases, with 0, 1, and 2 helical edge states, respectively. These phases are accounted for by a theoretical model that relates their conductance to spin-polarization plateaus. Transitions between them arise from a competition among interlayer hopping, electrostatic and exchange interaction energies. Finally, our work highlights the complex competing symmetries and the rich quantum phases in few-layer graphene.

36 MATERIALS SCIENCE↗

Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids

Topological quantum liquids contain internal degrees of freedom that are coupled to geometric response. Yet, an explicit and microscopic identification of the geometric response remains difficult. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol—the Dehn-twist deformation on the torus geometry—to probe the geometric response of correlated topological states and establish the relation between such response and universal properties of pertinent states. Based on analytical derivations and numerical simulations, we find that the geometry-induced Berry phase encodes features for a broad class of FQH states at the Laughlin, hierarchy, Halperin and non-Abelian Moore-Read fillings. Our findings conclusively demonstrate that the adiabatic Dehn-twist deformation can faithfully capture rich geometric and topological information, including the Hall viscosity and topological spin of the pertinent FQH state and the chiral central charge of the underlying edge conformal field theory. Our approach provides a powerful way to reveal topological orders of generic FQH states and address previously open questions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Edge majorana quasiparticles and qubits

Various embodiments described herein provide for a topological quantum computer that uses edge Majorana quasi-particles to form qubits. An inverted Indium Arsenide (InAs) and Gallium Antimonide (GaSb) heterostructure is disclosed that is a quantum spin Hall insulator. A layer of aluminum can be deposited over a nanotube that is placed across the layers of the heterostructure. Once the nanotube is removed, and a gate is formed on the heterostructure and the heterostructure is cooled so that the aluminum becomes superconducting, helical edge states are formed at the junction of the super conducting aluminum, the InAs, and the GaSb which creates a Majorana zero modes (MZMs) at zero magnetic field. The MZMs can be used to construct a topological qubit for fault-resistant topological quantum computation.

Pan, Wei↗

Magnetic brightening and nanoscale imaging of spin-polarized helical edge modes in ZrTe 5

Efficient charge transport remains a fundamental challenge for nanoelectronic devices, as their performance is constrained by high dissipation and the impedance mismatch between high-frequency signal sources and nanoscale circuit interfaces. Although topologically protected helical edge modes offer a dissipationless and backscattering-resilient alternative, achieving nanoscale control over these modes requires direct visualization of their spatial electrodynamics, especially under high-frequency operation. Here, by utilizing cryogenic magneto-infrared scattering-type scanning near-field optical microscopy (cm-IR-sSNOM), we image spin-polarized helical edge channels in ZrTe 5 at the nanoscale, revealing magnetic-field-induced brightening as a high-frequency electrodynamic signature of robust topological edge modes. Operating at 1.8 K and under a magnetic field of up to 5 T, we observe the emergence of edge-state polarizability at infrared frequencies that is notably resilient to the magnetic gaps that typically quench d.c. and microwave edge transport. Our results reveal a topological ‘two-lane’ spatial reorganization in which an external magnetic field induces a spin-population imbalance between counterpropagating edge modes. Favoured helical branches are confined against physical boundaries to activate a net infrared near-field contrast. This electrodynamic response scales linearly with the number of atomic layers, which confirms that individual layers in ZrTe 5 preserve their discrete quantum spin Hall identities. These findings may be useful for developing topological spintronic devices, as the magnetic infrared tunability of helical edge channels provides a pathway for low-loss nanoscale interconnects and high-speed information processing.

36 MATERIALS SCIENCE↗

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe 4

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order, not possible in quantum Hall and Chern insulator systems. Here, in this study, we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe 4 , arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe 4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe 4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe 4 . This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism.

electronic devices↗

The role of temperature on defect diffusion and nanoscale patterning in graphene

Graphene is of great scientific interest due to a variety of unique properties such as ballistic transport, spin selectivity, the quantum hall effect, and other quantum properties. Nanopatterning and atomic scale modifications of graphene are expected to enable further control over its intrinsic properties, providing ways to tune the electronic properties through geometric and strain effects, introduce edge states and other local or extended topological defects, and sculpt circuit paths. The focused beam of a scanning transmission electron microscope (STEM) can be used to remove atoms, enabling milling, doping, and deposition. Utilization of a STEM as an atomic scale fabrication platform is increasing; however, a detailed understanding of beam-induced processes and the subsequent cascade of aftereffects is lacking. Here, we examine the electron beam effects on atomically clean graphene at a variety of temperatures ranging from 400 to 1000 °C. We find that temperature plays a significant role in the milling rate and moderates competing processes of carbon adatom coalescence, graphene healing, and the diffusion (and recombination) of defects. The results of this work can be applied to a wider range of 2D materials and introduce better understanding of defect evolution in graphite and other bulk layered materials.

36 MATERIALS SCIENCE↗

Partial equilibration of anti-Pfaffian edge modes at ν = 5 / 2

The thermal Hall conductance K of the fractional quantum Hall state at filling fraction ν = 5/2 has recently been measured to be K = 2.5π 2 $k$$^{2}_{B}$T/3h [M. Banerjee et al. Nature (London) 559, 205 (2018)]. Here, the half-integer value of this result (in units of π 2 $k$$^{2}_{B}$T/3h) provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian or the anti-Pfaffian state has been the subject of debate. Here we consider the implications of this measurement for anti-Pfaffian edge-state transport. We show that in the limit of strong Coulomb interaction and an approximate spin degeneracy in the lowest Landau level, the anti-Pfaffian state admits low-temperature edge phases that are consistent with the Hall conductance measurements. Furthermore, these edge phases can exhibit fully equilibrated electrical transport coexisting with partially equilibrated heat transport over a range of temperatures. Through a study of the kinetic equations describing low-temperature electrical and heat transport of these edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes that agree with experiment.

36 MATERIALS SCIENCE↗

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. Yet, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Herein, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii–Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dis- sipationless spin-textured spintronic applications.

36 MATERIALS SCIENCE↗

Quantum Size Effects, Multiple Dirac Cones, and Edge States in Ultrathin Bi(110) Films

The presence of inherently strong spin–orbit coupling in bismuth, its unique layer-dependent band topology and high carrier mobility make it an interesting system for both fundamental studies and applications. Theoretically, it has been suggested that strong quantum size effects should be present in the Bi(110) films, with the possibility of Dirac Fermion states in the odd-bilayer (BL) films, originating from dangling p z orbitals and quantum-spin hall (QSH) states in the even-bilayer films. However, the experimental verification of these claims has been lacking. Here, we study the electronic structure of Bi(110) films grown on a high-T c superconductor, Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES). We observe an oscillatory behavior of electronic structure with the film thickness and identify the Dirac-states in the odd-bilayer films, consistent with the theoretical predictions. In the even-bilayer films, we find another Dirac state that was predicted to play a crucial role in the QSH effect. In the low thickness limit, we observe several extremely one-dimensional states, probably originating from the edge-states of Bi(110) islands. Our results provide a much needed experimental insight into the electronic and structural properties of Bi(110) films.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov–de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Edge Reconstruction in a Quantum Spin Hall Insulator

We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the Bernevig-Hughes-Zhang model with Kanamori-Hubbard interactions using the real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with a smooth edge, we identify discrete particle-number transitions that lead to a spin-polarized edge state stabilized by an emergent ferromagnetic exchange interaction. The reconstruction is orbital-selective, occurring predominantly in the 𝑠-orbital channel. Our results reveal a microscopic mechanism for emergent fluctuating moments at the edge that could compromise the topological protection of helical edge states by time-reversal symmetry.

Soni, Rahul [ORNL] (ORCID:0000000317714299)↗

Biasing topological charge injection in topological matter

Here we explore the interplay between topologies in the momentum and real spaces to formulate a thermodynamic description of nonequilibrium injection of topological charges under external bias. We show that the edge modes engendered by the momentum-space topology can play a functional role of connecting the external reservoirs to the bulk transport of topological charges in the real space. We illustrate our general results with two examples: the spin-torque injection of skyrmions in an electrically biased integer quantum Hall system, and the vortex injection in a topological $p + ip$ superconductor coupled to heat reservoirs. Based on the universal fractional entropy of the Majorana zero modes bound to the vortices, their controllable injection proposed in this work could provide a route for creating and manipulating Majorana fermions.

36 MATERIALS SCIENCE↗

Imaging orbital ferromagnetism in a moiré Chern insulator

Capturing exotic magnetism Ferromagnetism is associated with the breaking of time-reversal symmetry, most frequently by the spin degree of freedom. Although the orbital motion of electrons can also contribute to ferromagnetism, in most materials, it is small relative to the spin contribution. Tschirhart et al. showed that the reverse is true in an unusual magnetic state hosted by twisted bilayer graphene. Their scanning magnetometry measurements were consistent with ferromagnetism of predominantly orbital origin. Science , abd3190, this issue p. 1323

Science & Technology - Other Topics↗

Symmetry-driven persistent spin texture for the two-dimensional nonsymmorphic CdTe and ZnTe crystal structures

In this paper, two nonsymmorphic two-dimensional structures of CdTe and ZnTe are modeled, and using state-of-the-art density functional theory with the group theory of solids, their symmetry-enforced electronic properties are studied. The in-plane ferroelectricity coupled with strong spin-orbit coupling induces a unidirectional out-of-plane Rashba spin-orbit field that can host a momentum-independent uniform spin configuration known as persistent spin texture (PST) at the Brillouin zone center. PST in these structures is found to be robust against external perturbations such as strain, structural distortion, and independent of layer thickness. These unprecedented intrinsic spin transport properties hold utmost importance in spintronics, as the experimental stringent condition of equal Rashba and Dresselhaus constants [Phys. Rev. Lett. 90, 146801 (2003)] is eliminated. The calculated persistent spin helix wavelength of <~5 nm paves the way for developing next-generation nanosized nonballistic spin field-effect transistors compared with micrometer-sized GaAs/AlGaAs quantum wells. Further, these materials exhibit finite spin Hall conductivity at the band edges and hence can be used in ferromagnet-free spin Hall transistors. Although CdTe and ZnTe systems have been widely studied for photocatalysis and solar cell applications over the past few decades, their potential application in spintronic devices has not been explored. Mono/few layers of CdTe and ZnTe synthesized from (110) facets of bulk zinc-blende crystals [Nat. Commun. 3, 1057 (2012)] satisfy all symmetry operations of the nonsymmorphic space group and hence can be considered ideal materials to verify our theoretical results experimentally.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗