Topological Phase Research Articles

An architecture for two-qubit encoding in neutral ytterbium-171 atoms

We present an architecture for encoding two qubits within the optical “clock” transition and nuclear spin-1/2 degree of freedom of neutral ytterbium-171 atoms. Inspired by recent high-fidelity control of all pairs of states within this four-dimensional quotes space, we present a toolbox for intra-ququart (single-atom) one- and two-qubit gates, inter-ququart (two-atom) Rydberg-based two- and four-qubit gates, and quantum nondemolition (QND) readout. We then use this toolbox to demonstrate the advantages of the ququart encoding for entanglement distillation and quantum error correction which exhibit superior hardware efficiency and better performance in some cases since fewer two-atom operations are required. Finally, leveraging single-state QND readout in our ququart encoding, we present a unique approach to studying interactive circuits and to realizing a symmetry protected topological phase of a spin-1 chain with a shallow, constant-depth circuit.

Tight-binding model of Pt-based jacutingaites as combination of the honeycomb and kagome lattices

We introduce a refined tight-binding (TB) model for Pt-based jacutingaite materialsPt2NX3, (N= Zn, Cd, Hg; X = S, Se, Te), offering a detailed representation of the low-energy physics of its monolayers. This model incorporates all elements with significant spin-orbit coupling contributions, which are essential for understanding the topological energy gaps in these materials. Through comparison with first-principles calculations, we meticulously fitted the TB parameters, ensuring an accurate depiction of the energy bands near the Fermi level. Our model reveals the intricate interplay between the Pt 3eandNmetal orbitals, forming distinct kagome and honeycomb lattice structures. Applying this model, we explore the edge states of Pt-based jacutingaite monolayer nanoribbons, highlighting the sensitivity of the topological edge states dispersion bands to the nanostructures geometric configurations. These insights not only deepen our understanding of jacutingaite materials but also assist in tailoring their electronic properties for future applications.

Bonding Interactions Can Drive Topological Phase Transitions in a Zintl Antiferromagnetic Insulator

AbstractWhile ∼30% of materials are reported to be topological, topological insulators are rare. Magnetic topological insulators (MTI) are even harder to find. Identifying crystallographic features that can host the coexistence of a topological insulating phase with magnetic order is vital for finding intrinsic MTI materials. Thus far, most materials that are investigated for the determination of an MTI are some combination of known topological insulators with a magnetic ion such as MnBi2Te4. Motivated by the recent success of EuIn2As2, the role of chemical pressure on topologically trivial insulator is investigated, Eu5In2Sb6 via Ga substitution. Eu5Ga2Sb6 is predicted to be topological but is synthetically difficult to stabilize. The intermediate compositions between Eu5In2Sb6 and Eu5Ga2Sb6 are observed through theoretical works to explore a topological phase transition and band inversion mechanism. The band inversion mechanism is attributed to changes in Eu–Sb hybridization as Ga is substituted for In due to chemical pressure. Eu5In4/3Ga2/3Sb6 is also synthesized, the highest Ga concentration in Eu5In2‐xGaxSb6, and report the thermodynamic, magnetic, transport, and Hall properties. Overall, the work paints a picture of a possible MTI via band engineering and explains why Eu‐based Zintl compounds are suitable for the co‐existence of magnetism and topology.

Hierarchical zero- and one-dimensional topological states in symmetry-controllable grain boundary

Structural imperfections can be a promising testbed to engineer the symmetries and topological states of solid-state platforms. Here, we present direct evidence of hierarchical transitions of zero- (0D) and one-dimensional (1D) topological states in symmetry-enforced grain boundaries (GB) in 1T′–MoTe2. Using a scanning tunneling microscope tip press-and-pulse procedure, we construct two distinct types of GBs, which are differentiated by the underlying symmorphic and nonsymmorphic symmetries. The GBs with the nonsymmorphic rotation symmetry harbor first-order topological edge states protected by a nonsymmorphic band degeneracy. On the other hand, the edge state of the symmorphic GBs attains a band gap. More interestingly, the gapped edge state realizes a hierarchical topological phase, evidenced by the additional 0D boundary states at the GB ends. We anticipate our experiments will pioneer the material platform for the hierarchical realization of first-order and higher-order topology.

Uniform Diffusion of Cooper Pairing Mediated by Hole Carriers in Topological Sb2Te3/Nb.

Spin-helical Dirac Fermions at a doped topological insulator's boundaries can support Majorana quasiparticles when coupled with s-wave superconductors, but in n-doped systems, the requisite induced Cooper pairing in topological states is often buried at heterointerfaces or complicated by degenerate coupling with bulk conduction carriers. Rarely probed are p-doped topological structures with nondegenerate Dirac and bulk valence bands at the Fermi level, which may foster long-range superconductivity without sacrificing Majorana physics. Using ultrahigh-resolution photoemission, we report proximity pairing with a large decay length in p-doped topological Sb2Te3 on superconducting Nb. Despite no momentum-space degeneracy, the topological and bulk states of Sb2Te3/Nb exhibit the same isotropic superconducting gaps at low temperatures. Our results unify principles for realizing accessible pairing in Dirac Fermions relevant to topological superconductivity.

Topological phase transitions via attosecond x-ray absorption spectroscopy

We present a numerical experiment that demonstrates the possibility to capture topological phase transitions via an x-ray absorption spectroscopy scheme. We consider a Chern insulator whose topological phase is tuned via a second-order hopping. We perform time-dynamics simulations of the out-of-equilibrium laser-driven electron motion that enables us to model a realistic attosecond spectroscopy scheme. In particular, we use an ultrafast scheme with a circularly polarized IR pump pulse and an attosecond x-ray probe pulse. A laser-induced dichroism-type spectrum shows a clear signature of the topological phase transition. We are able to connect these signatures with the Berry structure of the system. This work extend the applications of attosecond absorption spectroscopy to systems presenting a non-trivial topological phase.

Spectroscopic Evidence of Ultrafast Topological Phase Transition by Light-Driven Strain.

Enabling reversible control over the topological invariants, transitioning them from nontrivial to trivial states, has fundamental implications for quantum information processing and spintronics. It offers a promising avenue for establishing an efficient on/off switch mechanism for robust and dissipationless spin-currents. While mechanical strain has traditionally been advantageous for such manipulation of topological invariants, it often comes with the drawback of in-plane fractures, rendering it unsuitable for high-speed, time-dependent operations. This study employs ultrafast optical and THz spectroscopy to explore topological phase transitions induced by light-driven strain in Bi2Se3. Bi2Se3 requires substantial strain for Z2 switching. Our observations provide experimental evidence of ultrafast switching behavior, demonstrating a transition from a topological insulator with spin-momentum-locked surfaces to hybridized states and normal insulating phases under ambient conditions. Notably, applying light-induced strong out-of-plane strain effectively suppresses surface-bulk coupling, facilitating the differentiation of surface and bulk conductance even at room temperature─significantly surpassing the Debye temperature. We expect various time-dependent sequences of transient hybridization and manipulation of topological invariant through photoexcitation intensity adjustments. The sudden surface and bulk transport alterations near the transition point enable coherent conductance modulation at hypersound frequencies. Our findings on the potential of light-triggered ultrafast switching of topological invariants hold promise for high-speed topological switching and its related applications.

Visualization of spin-polarized surface resonances in Pb-based ternary topological insulators

The formation of the topological surface state originates from bulk band inversion at the top of the valence band and the bottom of the conduction band. The transition between normal and topological insulators is known as a topological phase transition. Here we show spin-polarized electronic states of Pb-based ternary topological insulators Pb(Bi1-xSbx)2Te4 (x = 0.55, 0.70, 0.79) investigated by spin- and angle-resolved photoemission spectroscopy and first-principles calculations. We visualize a pair of spin-polarized surface resonances dispersing along the upper edge of projected bulk bands in occupied states. Interestingly, a branch of the spin-polarized surface resonances continuously connects to the topological surface state. The coexistence of the topological surface state and the spin-polarized surface resonances can be explained by considering the topological phase transition.

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains.

Unlocking the potential of topological order in many-body spin systems has been a key goal in quantum materials research. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg chains by covalently linking Clar's goblets-nanographenes each hosting two antiferromagnetically coupled spins. Using scanning tunnelling microscopy, we exert atomic-scale control over chain lengths, parities and exchange-coupling terminations, and probe their magnetic response via inelastic tunnelling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons. Their dispersion relation is extracted from the spatial variation of tunnelling spectral amplitudes. Depending on the parity and termination of chains, we observe varying numbers of in-gap spin-1/2 edge excitations, reflecting the degeneracy of distinct topological ground states in the thermodynamic limit. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our findings present a phase-controlled many-body platform, opening avenues toward spin-based quantum devices.

Time-resolved counterpropagating edge transport in the topological insulating phase

We have investigated the time-resolved low-energy charge dynamics in counterpropagating edge channels formed in the quantum Hall regime of an electron-hole bilayer system in band-inverted InAs/InGaSb composite quantum wells. In the studied magnetic field range, the system remains in the topological phase where an equal number of counterpropagating electronlike and holelike edge channels exist in the bulk energy gap, analogous to the helical edge channels in a quantum spin Hall insulator. When the Fermi level was set in the conduction band, the injected charge pulses propagated unidirectionally as chiral edge magnetoplasmon (EMP) wave packets. In contrast, in the nonchiral regime with the Fermi level set in the band gap, the injected charge pulses propagated identically in both directions with significantly reduced velocity. In addition, as the channel length increased, we observed a sharp crossover from EMP transport to diffusive transport, manifested as pronounced waveform broadening and dissipation. Simulations using a distributed capacitance model including interchannel tunneling well reproduced the observed behavior in both chiral and nonchiral regimes, revealing that interchannel charge transfer between counterpropagating channels plays a crucial role. The slow EMP transport in the nonchiral regime and its crossover to diffusive transport are consequences of the strong interchannel interaction and interchannel tunneling, respectively. Our results will thus provide insights into charge dynamics and scattering mechanism in analogous one-dimensional systems, including a quantum spin Hall insulator with helical edge modes and its expected Tomonaga-Luttinger liquid behavior. Published by the American Physical Society 2024

Topological signatures of triply degenerate fermions in Heusler alloys: an ab initio study

Triply degenerate nodal point (TP) fermions, lacking elementary particle counterparts, have been theoretically anticipated as quasiparticle excitations near specific band crossing points constrained by distinct space-group symmetries instead of Lorentz invariance. Here, based onfirst-principlescalculations and symmetry analysis, we demonstrate the presence of TP fermions in Heusler alloys. Furthermore, we predict that these Heusler alloys are dynamically stable, exhibiting TP fermions along four distinctC3axes in the F-43m space group. We show thatα-LiCaPdSb harbours peculiar Fermi arcs and surface states on the (111) and (001) crystal facets, owing to the coexistence of threefold rotational and time reversal symmetry. More interestingly, a modest tensile strain can increase the distance of fermions along the Γ-Lhigh symmetric line by as much as 21.10%, which give rise to measurable Fermi arcs. Furthermore, we investigate non-trivial topological insulator phase inβ-LiCaPdSb, by changing the chemical environment through placing transition metal atoms at various Wyckoff positions. Theβ-LiCaPdSb harbour a semi-metallic nature, and by breaking cubic symmetry, it undergoes a transition from semi-metal to a non-trivial topological insulator. In addition, for the first time, rare-earth LaPtBi half-Heusler alloy is examined under strain to uncover multiple band inversions associated with the TP fermionic phase. The observed multiple band inversion is entirely unaffected by spin-orbit coupling. We show that the LaPtBi compound hosts TP fermions, which are linked to aZ2topological invariant. Remarkably, with clear band crossings and multiple band inversion, we point out the possibilities of the LaPtBi for displaying a rich topological phase diagram. Our work provides a prototype material platform for experimental detection through angle-resolved photoemission spectroscopy or scanning tunnelling spectroscopy and practical spintronic applications.

Topological traveling-wave radiation based on chiral edge states in photonic Chern insulators.

Topological chiral edge states in photonic Chern insulators, which exhibit the one-way propagation property with reflection-free behavior and excellent robustness against perturbations, have become an important frontier in topological photonics. Currently, there have been many studies on its robust propagation behavior, but few studies have focused on its radiation properties. In developing functional photonic devices (e.g., topological antennas) for real-world applications, studying traveling-wave radiation characteristics based on chiral edge states deserves more attention. In this Letter, we propose a topological traveling-wave radiation system based on chiral edge states in photonic Chern insulators that show a steerable beam and reflection-free property. By introducing the perturbation controlled by magnetic fields, we demonstrate that exploiting a certain strength of perturbation can flexibly manipulate the radiation beam. In particular, the proposed dual-channel topological traveling-wave radiation system can not only improve the gain but also overcome the issue of impedance matching. The proposed configurations provide a novel way to manipulate topological-wave radiation and have potential applications for designing topological traveling-wave antennas with a reflection-free property.

Quantized Integrated Shift Effect in Multigap Topological Phases

We show that certain three-dimensional multigap topological insulators can host quantized integrated shift photoconductivities due to bulk invariants that are defined under reality conditions imposed by additional symmetries. We recast the quantization in terms of the integrated torsion tensor and the non-Abelian Berry connection constituting Chern-Simons forms. Physically, we recognize that the topological quantization emerges purely from virtual transitions contributing to the optical response. Our findings provide another quantized electromagnetic dc response due to the nontrivial band topology, beyond the quantum anomalous Hall effect of Chern insulators and quantized circular photogalvanic effect found in Weyl semimetals. Published by the American Physical Society 2024

Magnetic Order in Nanogranular Iron Germanium (Fe0.53Ge0.47) Films.

We study the effect of strain on the magnetic properties and magnetization configurations in nanogranular FexGe1-x films (x = 0.53 ±0.05) with and without B20 FeGe nanocrystals surrounded by an amorphous structure. Relaxed films on amorphous silicon nitride membranes reveal a disordered skyrmion phase while films near and on top of a rigid substrate favor ferromagnetism and an anisotropic hybridization of Fe d levels and spin-polarized Ge sp band states. The weakly coupled topological states emerge at room temperature and become more abundant at cryogenic temperatures without showing indications of pinning at defects or confinement to individual grains. These results demonstrate the possibility to control magnetic exchange and topological magnetism by strain and inform magnetoelasticity-mediated voltage control of topological phases in amorphous quantum materials.

Unravelling topological states in quantum spin chains.

Unravelling topological states in quantum spin chains.

Double exchange interaction in Mn-based topological kagome ferrimagnet

Recently discovered Mn-based kagome materials, such as RMn6Sn6 (R = rare-earth element), exhibit the coexistence of topological electronic states and long-range magnetic order, offering a platform for studying quantum phenomena. However, understanding the electronic and magnetic properties of these materials remains incomplete. Here, we investigate the electronic structure and magnetic properties of GdMn6Sn6 using x-ray magnetic circular dichroism, photoemission spectroscopy, and theoretical calculations. We observe localized electronic states from spin frustration in the Mn-based kagome lattice and induced magnetic moments in the nonmagnetic element Sn experimentally, which originate from the Sn-p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document} and Mn-d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d$$\\end{document} orbital hybridization. Our calculations also reveal ferromagnetic coupling within the kagome Mn-Mn layer, driven by double exchange interaction. This work provides insights into the mechanisms of magnetic interaction and magnetic tuning in the exploration of topological quantum materials.

Robust Teleportation of a Surface Code and Cascade of Topological Quantum Phase Transitions

Teleportation is a facet where quantum measurements can act as a powerful resource in quantum physics, as local measurements allow us to steer quantum information in a nonlocal way. While this has long been established for a single Bell pair, the teleportation of a many-qubit entangled state using nonmaximally entangled resources presents a fundamentally different challenge. Here, we investigate a tangible protocol for teleporting a long-range entangled surface-code state using elementary Bell measurements and its stability in the presence of coherent errors that weaken the Bell entanglement. We relate the underlying threshold problem to the physics of anyon condensation under weak measurements and map it to a variant of the Ashkin-Teller model of statistical mechanics with Nishimori-type disorder, which gives rise to a cascade of phase transitions. Tuning the angle of the local Bell measurements, we find a continuously varying threshold. Notably, the threshold moves to infinity for the X+Z angle along the self-dual line—indicating that infinitesimally weak entanglement is sufficient in teleporting a self-dual topological surface code. Our teleportation protocol, which can be readily implemented in dynamically configurable Rydberg-atom arrays, thereby gives guidance for a practical demonstration of the power of quantum measurements. Published by the American Physical Society 2024

Topological Band Engineering of One-Dimensional π-d Conjugated Metal-Organic Frameworks.

One-dimensional (1D) π-d conjugated metal-organic frameworks (c-MOFs) have garnered widespread research interest in chemical energy storage and conversion. In this work, we introduce a universal principle to engineer the topological bands of 1D c-MOFs. Connected by d orbitals of transition metals, two equivalent hidden molecular π orbitals in 1D c-MOFs can generate a staggered hopping within and between the organic ligands, forming Su-Schrieffer-Heeger-shaped 1D topological bands. Guided by this discovery, we investigate the electronic structures of the typical 1D c-MOF assembled from Ni atoms and 2HQDI (QDI = 2,5-diamino-1,4-benzoquinonediimine) precursors (NiQDI) by first-principles calculations, revealing 1D topological bands around the Fermi level. Due to local bonding variations at the QDI terminations, these two hidden molecular π orbitals become atomically bonded but electronically separated at the edge QDI, creating spatially localized in-gap topological edge states at the end of the NiQDI chain. This definitive signature for 1D topological bands is identified through differential conductance spectra in scanning tunneling microscopy measurements. Our results provide conclusive experimental evidence for topological bands in 1D c-MOFs, paving the way for exploring the topological physics in organic materials through frontier molecular orbitals.

Intrinsic symmetry-protected topological mixed state from modulated symmetries and hierarchical structure of boundary anomaly

Intrinsic symmetry-protected topological mixed state from modulated symmetries and hierarchical structure of boundary anomaly

Multiple Broadband Infrared Topological Photonic Crystal Valley States Based on Liquid Crystals

Spectral tunable technology has to meet the requirements of strong robustness and wide spectral range. We propose a method for the transmission and manipulation of infrared topological photonic crystal valley states based on tunable refractive index method that exhibits broad-spectrum and multi-band characteristics, along with a tunable emission angle. With this structure, different rotational directions of vortex light sources can independently excite the K valley and K′ valley within the frequency band ranging from 75.64 THz to 99.61 THz. At frequencies from 142.60 THz to 171.12 THz, it is possible to simultaneously excite both the K valley and K′ valley. The dual refractive index tunable design allows for the adjustment of the emission angle at a fixed frequency, enabling control over the independent excitation of either a single K valley or K′ valley, as well as their simultaneous excitation. This capability has significant implications for photonic computation and tunable filtering, offering enhanced operational flexibility and expanded functionality for future optical communications and integrated optical circuits.