Spectroscopic Evidence of Edge‐Localized States in an Antiferromagnet Topological Insulator NdBi
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Almoalem, Avior [Department of Physics and Materia↗
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Direct Measurement of Helicoid Surface States in RhSi Using Nonlinear Optics
Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction G. Chang et al., Phys. Rev. Lett. 124, 166404 (2020), we have measured the linear and circular photogalvanic effect currents deriving from the Fermi arcs of the nonsymmorphic, chiral Weyl semimetal RhSi over the 0.45-1.1 eV incident photon energy range. Our data are in good agreement with the predicted spectral shape of the circular photogalvanic effect as a function of photon energy, although the direction of the surface photocurrent departed from the theoretical expectation over the energy range studied. In conclusion, surface currents arising from the linear photogalvanic effect were observed as well, with the unexpected result that only two of the six allowed tensor element were required to describe the measurements, suggesting an approximate emergent mirror symmetry inconsistent with the space group of the crystal.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Magnetic multilayer edges in Bernal-stacked hexagonal boron nitride
Single-layer h-BN is known to have edges with unique magnetism; however, in the commonly fabricated multilayer AA'-h-BN, edge relaxations occur that create interlayer bonds and eliminate the unpaired electrons at the edge. Recently, a robust method of growing the unconventional Bernal-stacked h-BN (AB-h-BN) has been reported. Here, we use theoretical approaches to investigate the nitrogen-terminated zigzag edges in AB-h-BN that can be formed in a controlled fashion using a high-energy electron beam. We find that these "open"edges remain intact in bilayer and multilayer AB-h-BN, enabling researchers potentially to investigate these edge states experimentally. We also investigate the thermodynamics of the spin configurations at the edge by constructing a lattice model that is based on parameters extracted from a set of first-principles calculations. We find that the edge spins in neighboring layers interact very weakly, resulting in a sequence of independent spin chains in multilayer samples. By solving this model using Monte Carlo simulations, we can determine nm-scale correlation lengths at liquid-N 2 temperatures and lower. At low temperatures, these edges may be utilized in magnetoresistance and spintronics applications.
1-dimensional spin chains↗
Transition to the Haldane phase driven by electron-electron correlations
One of the most famous quantum systems with topological properties, the spin S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic S = 1/2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two orbital Hubbard model—with increasing repulsion strength U and Hund interaction J H . We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Squeezing quantum states in three-dimensional twisted crystals
Bloch's theorem provides a conventional starting point for describing wave propagation in periodic media, but in ordered materials where competing spatial periods coexist it is rendered ineffective, often with dramatic consequences. Here we develop an alternate approach that uses coherent free-particle vortex states to study quantum states in supertwisted crystals: three-dimensional stacks of atomically thin two-dimensional layers. Here, this formalism leads naturally to the representation of the spectrum using squeezed coherent states, and it reveals the crucial role of a Coriolis coupling in the equations of motion. This identifies an underlying noncommutative geometry and novel edge state structure in a family of complex ordered structures.
36 MATERIALS SCIENCE↗
Half-Integer Conductance Plateau at the ν = 2 / 3 Fractional Quantum Hall State in a Quantum Point Contact
The v = 2/3 fractional quantum Hall state is the hole-conjugate state to the primary Laughlin v = 1/3 state. Here, we investigate transmission of edge states through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure designed to have a sharp confining potential. When a small but finite bias is applied, we observe an intermediate conductance plateau with G = 0.5(e 2 /ℎ). This plateau is observed in multiple QPCs, and persists over a significant range of magnetic field, gate voltage, and source-drain bias, making it a robust feature. Using a simple model that considers scattering and equilibration between counterflowing charged edge modes, we find this half-integer quantized plateau to be consistent with full reflection of an inner counterpropagating -1/3 edge mode while the outer integer mode is fully transmitted. In a QPC fabricated on a different heterostructure which has a softer confining potential, we instead observe an intermediate conductance plateau at G = (1/3)(e 2 /ℎ). These results provide support for a model at v = 2/3 in which the edge transitions from a structure having an inner upstream -1/3 charge mode and outer downstream integer mode to a structure with two downstream 1/3 charge modes when the confining potential is tuned from sharp to soft and disorder prevails.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Edge magnetoplasmon dispersion and time-resolved plasmon transport in a quantum anomalous Hall insulator
A quantum anomalous Hall (QAH) insulator breaks reciprocity by combining magnetic polarization and spin-orbit coupling to generate a unidirectional transmission of signals in the absence of an external magnetic field. Such behavior makes QAH materials a good platform for the innovation of circulator technologies. However, it remains elusive as to how the wavelength of the chiral edge plasmon relates to its frequency and how the plasmon wave packet is excited in the time domain in a QAH insulator. Here, we investigate the edge magnetoplasmon (EMP) resonances in Cr-(Bi,Sb) 2 Te 3 by frequency and time domain measurements. From disk shaped samples with various dimensions, we obtain the dispersion relation of EMPs and extract the drift velocity of the chiral edge state. From the time-resolved transport measurements, we identify the velocity of the plasmon wave packet and observe a transition from the edge to bulk transport at an elevated temperature. We show that the frequency and time domain measurements are well modeled by loss from the microwave induced dissipative channels in the bulk area. Our results demonstrate that the EMP decay rate can be significantly reduced by applying a low microwave power and fabricating devices of larger diameter ≥ 100 µ m . In a R = 125 µ m sample, a nonreciprocity of 20 dB has been realized at 1.3 GHz, shining light on using QAH insulators to develop on-chip nonreciprocal devices. Published by the American Physical Society 2024
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
Here, we study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of U c ≈5t these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Bloch and Bethe Ansätze for the Harper model: A butterfly with a boundary
Based on a recent generalization of Bloch's theorem, herein we present a Bloch Ansatz for the Harper model with an arbitrary rational magnetic flux in various geometries, and solve the associated Ansatz equations analytically. In the case of a cylinder and a particular boundary condition, the energy spectrum of edge states has no dependence on the length of the cylinder, which allows us to construct a quasi-one-dimensional edge theory that is exact and describes two edges simultaneously. We prove that energies of bulk states, generating the so-called Hofstadter's butterfly, depend on a single geometry-dependent spectral parameter and have exactly the same functional form for the cylinder and the torus with general twisted boundary conditions, and argue that the (edge) bulk spectrum of a semi-infinite cylinder in an irrational magnetic field is (the complement of) a Cantor set. Finally, realizing that the bulk projection of the Harper Hamiltonian is a linear form over a deformed Weyl algebra, we introduce a Bethe Ansatz valid for both cylinder and torus geometries.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Demonstration of a third-order hierarchy of topological states in a three-dimensional acoustic metamaterial
Classical wave systems have constituted an excellent platform for emulating complex quantum phenomena, such as demonstrating topological phenomena in photonics and acoustics. Recently, a new class of topological states localized in more than one dimension of a D -dimensional system, referred to as higher-order topological (HOT) states, has been reported, offering an even more versatile platform to confine and control classical radiation and mechanical motion. Here, we design and experimentally study a 3D topological acoustic metamaterial supporting third-order (0D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of nontrivial bulk polarization–induced states in three dimensions. The assembled 3D topological metamaterial represents the acoustic analog of a pyrochlore lattice made of interconnected molecules, and is shown to exhibit topological bulk polarization, leading to the emergence of boundary states.
Science & Technology - Other Topics↗
Reversible and Irreversible Layer Edge Relaxation in Laser–Radiation–Hardened 2D Organic–Inorganic Perovskite Crystals
The layer edge states or low energy state (LES) in 2D hybrid organic–inorganic perovskites demonstrate a prolonged carrier lifetime for better performance of optoelectronic devices. However, the fundamental understanding of LES in 2D perovskites is still inconclusive. Herein, a photoluminescence (PL) study of LES in 2D Ruddlesden–Popper perovskites is presented with n = 2 and n = 3 from their cleaved cross sections that are more stable than the natural edge. The PL measurements clearly observe reversible, and irreversible surface relaxations (case I and case II) in three laser intensity ranges, further supported by a PL excitation cycle from low to high laser intensity, and vice versa. The PL wavelength of LES is tunable with laser intensity and blueshifts with increasing laser intensity during irreversible surface relaxation process (case I). Fluorescence lifetime imaging (FLIM) shows that the LES has a longer lifetime than the band-edge emission in the sample without a photodegradation, while the BE lifetime becomes relatively longer in the area with a photodegradation. Furthermore, the presented laser tunable LES and the related irreversible relaxation process provide a new insight that can help improve the photostability in 2D perovskites and understand roles of LESs in optoelectronic device performance.
2D organic-inorganic perovskite↗
Symmetry-breaking polymorphous descriptions for correlated materials without interelectronic U
Correlated materials with open-shell d- and f-ions having degenerate band edge states show a rich variety of interesting properties ranging from metal-insulator transition to unconventional superconductivity. The textbook view for the electronic structure of these materials is that mean-field approaches are inappropriate, as the interelectronic interaction U is required to open a band gap between the occupied and unoccupied degenerate states while retaining symmetry. We show that the latter scenario often defining what Mott insulators are, is in fact not needed for the 3d binary oxides MnO, FeO, CoO, and NiO. The mean-field-like band theory can indeed lift such degeneracies in the binaries when nontrivial unit cell representations (polymorphous networks) are allowed to break symmetries, in conjunction with a recently developed non-empirical exchange and correlation density-functional without an on-site interelectronic interaction U. We explain how density-functional theory (DFT) in the polymorphous representation achieves band gap opening in correlated materials through a separate mechanism to the Mott-Hubbard approach. Here, we show the method predicts magnetic moments and gaps for the four binary monoxides in both the antiferromagnetic and paramagnetic phases, offering an effective alternative to symmetry-conserving approaches for studying a range of functionalities in open d- and f-shell complex materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Rotational symmetry protected edge and corner states in Abelian topological phases
Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Finally, our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Low-energy edge signatures of the Kitaev spin liquid
Recent experimental work indicates that the Kitaev spin liquid may be realizable close to zero magnetic field in exfoliated 𝛼−RuCl 3 flakes, thus providing a more versatile setting for studying non-Abelian anyons. Here, we propose a robust nanoscale signature of the Kitaev spin liquid that results from its edge states and manifests in the low-energy spin dynamics. In particular, we highlight a singular peak in the dynamical spin structure factor of a zigzag edge whose energy scales linearly with only one component of the magnetic field. This sharp feature in the local spin dynamics directly reflects the bond-directional Kitaev spin interactions and, more generally, the projective symmetries of the Kitaev spin liquid. In conclusion, we demonstrate that our proposed signature survives in the presence of edge disorder as well as non-Kitaev interactions, and provide detailed guidelines for experimentally observing it using inelastic electron tunneling spectroscopy and color-center relaxometry.
Color centers↗
Defect-induced states, defect-induced phase transition, and excitonic states in bent tungsten disulfide (WS 2 ) nanoribbons: Density functional vs. many body theory
Two-dimensional (2D) transition metal dichalcogenide (TMD) materials have versatile electronic and optical properties. TMD nanoribbons exhibit interesting properties due to reduced dimensionality, quantum confinement, and edge states, which make them suitable for various electronic and optoelectronic applications. In a previous work conducted by our group, we demonstrated that the edge bands evolved with bending can tune the optical properties for various widths of TMD nanoribbons. Defects are commonly present in 2D TMD materials, and can dramatically change the material properties. Here, in this following work, we investigate the interaction between the edge and the defect states in tungsten disulfide (WS 2 ) nanoribbons with lines of W- or S-atom vacancies defects under different bending conditions, using density functional theory (DFT). To gain understanding about the limits of density functional approximations, we compare results on band gaps and energies of defect states with quasiparticle GW. We reveal interesting semiconductor-metal phase transitions, suggesting potential applications in nanoelectronics or molecular electronics. We also calculate the optical absorption of the bent and defective nanoribbons with the many-body GW-BSE (Bethe-Salpeter equation) approach, revealing a tunable optical spectrum and diverse exciton states in the defective WS 2 nanoribbons.
36 MATERIALS SCIENCE↗
Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice
Studies of two-dimensional electron systems in a strong magnetic field revealed the quantum Hall effect, a topological state of matter featuring a finite Chern number C and chiral edge states. Haldane later theorized that Chern insulators with integer quantum Hall effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (ABC-TLG/hBN) moiré superlattice provides an attractive platform with which to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent, electrically tunable Chern number. In this work, we report the experimental observation of a correlated Chern insulator in an ABC-TLG/hBN moiré superlattice. We show that reversing the direction of the applied vertical electric field switches the moiré minibands of ABC-TLG/hBN between zero and finite Chern numbers, as revealed by large changes in magneto-transport behaviour. For topological hole minibands tuned to have a finite Chern number, we focus on quarter filling, corresponding to one hole per moiré unit cell. The Hall resistance is well quantized at h/2e 2 (where h is Planck’s constant and e is the charge on the electron), which implies C = 2, for a magnetic field exceeding 0.4 tesla. The correlated Chern insulator is ferromagnetic, exhibiting substantial magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Finally, our discovery of a C = 2 Chern insulator at zero magnetic field should open up opportunities for discovering correlated topological states, possibly with topological excitations, in nearly flat and topologically nontrivial moiré minibands.
36 MATERIALS SCIENCE↗
Magnetic proximity and nonreciprocal current switching in a monolayer WTe2 helical edge
The integration of diverse electronic phenomena, such as magnetism and nontrivial topology, into a single system is normally studied either by seeking materials that contain both ingredients, or by layered growth of contrasting materials. The ability to simply stack very different two-dimensional van der Waals materials in intimate contact permits a different approach. Here we use this approach to couple the helical edges states in a two-dimensional topological insulator, monolayer WTe 2 , to a two-dimensional layered antiferromagnet, CrI 3 . We find that the edge conductance is sensitive to the magnetization state of the CrI 3 , and the coupling can be understood in terms of an exchange field from the nearest and next-nearest CrI 3 layers that produces a gap in the helical edge. We also find that the nonlinear edge conductance depends on the magnetization of the nearest CrI 3 layer relative to the current direction. At low temperatures this produces an extraordinarily large nonreciprocal current that is switched by changing the antiferromagnetic state of the CrI 3 .
36 MATERIALS SCIENCE↗
Evidence for valence-bond pairing in a one-dimensional two-orbital system
Valence bond (VB) states as the formation mechanism of Cooper pairs, eventually leading to high-temperature superconductivity, remain a controversial topic. Although various VB-like states find variational relevance in the description of specific spin models and quantum spin liquids, in the realm of many-body fermionic Hamiltonians, the evidence for such states as ground-state wave functions remains elusive, challenging the valence-bond pairing mechanism. Here, we present evidence of a VB ground state with pairing tendencies, particularly at finite doping. Here, we achieved this for the generic two-orbital Hubbard model in low dimension, where the VB states can be associated with the presence of the topological order manifested by edge states.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗