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A central goal of topological photonics has been to develop compact isolators using protected, non-reciprocal edge states. Furthermore, a recent demonstration of a ferrite-based microwave isolator leverages the magnon-induced topological photonic bandgap to achieve over 100 dB of isolation in a device smaller than a single free-space wavelength.
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.
Abstract In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.
To explore new materials for the realization of the quantum anomalous Hall effect (QAHE), we studied the electronic, magnetic and topological properties of transition-metal phthalocyanine (TMPc) monolayers in a square lattice. Many of them have large topologically nontrivial band gaps and integer Chern numbers. In particular, the Fermi level of MoPc lies right in the band gap (E g = 8.1 meV) and has large magnetic anisotropy energy (MAE = 2.0 meV per Mo atom) and a Curie temperature of 16 K, showing its usefulness for applications. The presence of the topologically protected edge state in a MoPc nanoribbon further confirms it as a new two-dimensional topological insulator. This much widens the search for QAHE materials for the design of quantum devices.
Using synchrotron radiation in the tender X-ray regime, a photoelectron spectrum showing the formation of single site double-core-hole pre-edge states, involving the K shell of the O atom in CO, has been recorded by means of high-resolution electron spectroscopy. The experimentally observed structures have been simulated, interpreted and assigned, employing state-of-the-art ab initio quantum chemical calculations, on the basis of a theoretical model, accounting for their so-called direct or conjugate character. Features appearing above the double ionization threshold have been reproduced by taking into account the strong mixing between multi-excited and continuum states. The shift of the σ* resonance below the double ionization threshold, in combination with the non-negligible contributions of multi-excited configurations in the final states reached, gives rise to a series of avoided crossings between the different potential energy curves.
Single-component halide perovskites (HPs) rarely satisfy all the necessary criteria for optoelectronic applications, such as achieving an optimal band gap while maintaining high chemical and structural stability. Alloying halide perovskites has emerged as a promising strategy, not only to enhance stability but also to fine-tune their electronic and optical properties. In this work, we explore multiple degrees of freedom in alloy design, considering different substitution sublattices sites (A, B, or X in ABX3 perovskites), various chemical species (isovalent and hetero-valent elements), and multi-component compositions on a given sublattice. Using first-principles calculations based on density functional theory (DFT), we investigate how compositional variations influence the electronic (band gap) and structural properties (mixing enthalpy) of HP alloys. Our approach employs the polymorphous cell model, allowing full local relaxation which breaks local symmetry while preserving global cubic symmetry—an essential framework for accurately modeling HPs. Our results reveal that X-site mixing (halogen substitution) primarily affects the valence band maximum, allowing target band gap engineering. Additionally, variations in halogen radii introduce internal strain through octahedral distortions, influencing the mixing enthalpy. A-site substitution, while not directly contributing to the band edge states, modifies structural stability via volume effects, indirectly impacting the band gap. B-site alloying plays a dominant role in band gap modulation, leading to either positive or negative band gap bowing. Specifically, isovalent B-site mixing (Sn–Pb) induces strong positive bowing, where the alloy band gap is smaller than the average gap of parent compounds, whereas hetero-valent mixing (Cd–Pb) results in pronounced negative bowing. As an aside, we investigate the competition between the excess energy of disordered alloys vs. that of long-range ordered double perovskites of the same compositions, seeking examples of ordered phases emerging from disordered alloys. Furthermore, our findings provide fundamental insights into the electronic and structural behavior of HP alloys, offering valuable design principles for the development of stable and efficient materials for next-generation photovoltaic and optoelectronic devices.
The vacuum pocket retaining molecular beam epitaxial regrowth of the nano-patterned GaSb surface was demonstrated. The high contrast 2D photonic crystal layer was incorporated into the test 2 μm emitting laser heterostructure. The photonic dispersion determined from angle-resolved electroluminescence experiment showed four well-resolved bands corresponding to the model predictions for the square lattice. The single-mode lasing near 2 μm has been observed at the temperature corresponding to the alignment of the photonic crystal band-edge states and the quantum well gain peak. The reference devices without the photonic crystal layer emitted trivial spectra and did not lase at any temperature.
We propose a quantum gate architecture that allows for the systematic control of the effective exchange interactions between magnetic impurities embedded in nanoscale graphene flakes connected by a gated bridge. The entanglement between the magnetic moment and the edge states of the fragments is used to electrostatically tune the exchange interaction from ferro to antiferromagnetic by merely changing the bridge's carrier density. By characterizing the effects of size and coupling parameters, we explore different operation regimes of this device by means of exact calculations with the density matrix renormalization group. We analyze the results utilizing a simplified model that accounts for the main many-body mechanisms. Finally, we discuss how to use arrays of these devices to build quantum simulators for quantum many-body Hamiltonians.
Graphene has afforded an ideal 2D platform for investigating a rich and fascinating behavior of Dirac fermions. Here, we develop a theoretical mechanism for manipulating the Dirac fermions in graphene, such as from type-I to type-II and type-III, by a top-down nanopatterning approach. We demonstrate that by selective chemical adsorption to pattern the 2D graphene into coupled 1D armchair chains (ACs), the intrinsic isotropic upright Dirac cone becomes anisotropic and strongly tilted. Based on model analyses and first-principles calculations, we show that both the shape and tilt of Dirac cone can be tuned by the species of chemisorption, e.g., halogen vs hydrogen, which modifies the strength of inter-AC coupling. Furthermore, the topological edge states and transport properties of the engineered Dirac fermions are investigated. Our work sheds lights on understanding the Dirac fermions in a nanopatterned graphene platform, and provides guidance for designing nanostructures with novel functionality.
A predicted type-II staggered band alignment with an approximately 1.4 eV valence band offset at the ZnGeN 2 /GaN heterointerface has inspired novel band-engineered III-N/ZnGeN 2 heterostructure-based device designs for applications in high performance optoelectronics. We report on the determination of the valence band offset between metalorganic chemical vapor deposition grown (ZnGe) 1- x Ga 2 x N 2 , for x = 0 and 0.06, and GaN using x-ray photoemission spectroscopy. The valence band of ZnGeN 2 was found to lie 1.45–1.65 eV above that of GaN. This result agrees well with the value predicted by first-principles density functional theory calculations using the local density approximation for the potential profile and quasiparticle self-consistent GW calculations of the band edge states relative to the potential. For (ZnGe) 0.94 Ga 0.12 N 2 the value was determined to be 1.29 eV, ~10%–20% lower than that of ZnGeN 2 . The experimental determination of the large band offset between ZnGeN 2 and GaN provides promising alternative solutions to address challenges faced with pure III-nitride-based structures and devices.
Abstract 2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.
Employing temperature (T)-dependent angle-resolved photoemission spectroscopy (ARPES) near the Ce 4d absorption edge, we have investigated the electronic structures of the strongly correlated Kondo insulators (KIs) and/or Kondo semimetals of CeNiSn and CeRhX (X=As, Sb), which also belong to potential topological KIs (TKIs). Good agreement is found between the Fermi surfaces (FSs) measured at the Ce 4d→4f on resonance and those calculated and unfolded into the Ce-only Brillouin zone, supporting the crucial Ce 4f contribution to the Fermi-edge states in them. While the FSs of CeRhSb and CeNiSn are similar to each other, they are quite different from those of CeRhAs, which is understood to originate from the semimetallic Kondo ground states of CeNiSn and CeRhSb in contrast to the insulating Kondo ground state of CeRhAs. T-dependent ARPES demonstrates the existence of the Kondo resonance above the Fermi level (EF) and its T-driven decoherence in CeNiSn and CeRhSb, and the existence of the Ce 4f Kondo-like peak well below EF with a pseudogap in CeRhAs. With increasing T, the tail of the Kondo resonance in CeNiSn and CeRhSb loses its coherence, whereas the Ce 4f Kondo-like peak in CeRhAs persists up to T≥200 K. The Kondo temperatures (TKs) are estimated via the analysis of T-dependent ARPES, yielding TK≈80 K (CeNiSn), TK≈180 K (CeRhSb), and TK≫200 K (CeRhAs). High-resolution, low-T ARPES confirms the Kondo resonance just above EF in CeNiSn and CeRhSb Kondo semimetals and the KI ground state of CeRhAs with a pseudogap of Δ≈30 meV, demonstrating the importance of the coherent Kondo states in determining their potential topological properties. The differences in the T-dependent ARPES of CeNiSn and CeRhSb suggest the weaker f-c hybridization in CeNiSn than in CeRhSb (c: conduction electron), which is likely due to the more localized Ni 3d orbitals than the delocalized Rh 4d orbitals. The differences between the T-dependent ARPES of CeNiSn/CeRhSb Kondo semimetals and those of CeRhAs Kondo insulator are likely due to the smaller volume of CeRhAs than those of CeNiSn/CeRhSb.
Motivated by the experimental identification of magnetic compounds consisting of zigzag chains, we analyze the band structure topology of magnons in ferromagnets on a zigzag lattice. We account for the general lattice geometry by including spatially anisotropic Heisenberg exchange interactions and by Dzyaloshinskii-Moriya interaction on inversion asymmetric bonds. Within the linear spin-wave theory, we find two magnon branches, whose band structure topology (i.e., Chern numbers) we map out in a comprehensive phase diagram. Notably, besides topologically trivial and gapless phases, we identify topologically nontrivial phases that support chiral edge magnons. We show that these edge states are robust against elastic defect scattering.
Here, we consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong the coherence time of a fiducial qubit. The qubit is part of a network of other qubits and dissipative cavities whose coupling parameters are tunable, such that topological edge states can be stabilized. The evolution of the fiducial qubit is entirely determined by a non-Hermitian Hamiltonian which thus emerges from a bona fide physical process. Even in the presence of disorder, a winding number W can be defined and evaluated in real space, as long as certain symmetries are preserved. Hence we can construct the topological phase diagrams of noisy open quantum models, such as the non-Hermitian disordered Su-Schrieffer-Heeger dimer model and a trimer model that includes longer-range couplings. For finite-size systems we find that there are precisely W modes localized at one end of the chain. In such topological phases the qubit's coherence lifetime is exponentially large in the system size. In the presence of competing disorder parameters, interesting reentrance phenomena of topologically nontrivial sectors are observed. This means that in certain parameter regions, increasing disorder drastically increases the coherence time of the fiducial qubit.
The electronic band topology of monolayer β-Sb (antimonene) is studied from the flat honeycomb to the equilibrium buckled structure using first-principles calculations and analyzed using a tight-binding model and low-energy Hamiltonians. In flat monolayer Sb, the Fermi level occurs near the intersection of two warped Dirac cones, one associated with the pz orbitals, and one with the {p x , p y } orbitals. The differently oriented threefold warping of these two cones leads to an unusually shaped nodal line, which leads to anisotropic in-plane transport properties and goniopolarity. A slight buckling opens a gap along the nodal line except at six remaining Dirac points, protected by symmetry. Under increasing buckling, pairs of Dirac points of opposite winding number annihilate at a critical buckling angle. At a second critical angle, the remaining Dirac points disappear when the band structure opens a gap. Spin-orbit coupling and edge states are discussed.
Based on the nontrivial topology of buckled antimonene, we propose two conceptual device designs based on breaking the inversion symmetry which can be achieved by gating. The first one is a quantized topological switch obtained by breaking the degeneracy of the fractionalized charge conducting edge states, inducing a metal-insulator transition. In the second one, using local gating with different polarity in different areas, a domain wall is created at their interface, which hosts a soliton type electronic gap state in which transport could be accessed by doping and shown to be robust over a wide range of disorder.
UTe 2 is a likely spin-triplet superconductor that also exhibits evidence for chiral Majorana edge states. A characteristic structural feature of UTe 2 is inversion-symmetry related pairs of U atoms, forming rungs of ladders. Here we show how each rung's two sublattice degrees of freedom play a key role in understanding the electronic structure and the origin of superconductivity. In particular, DFT + U calculations generically reveal a topological band near the chemical potential originating from a band inversion associated with 5f electrons residing on these rungs, necessitating a microscopic description that includes these rung degrees of freedom. Furthermore, we show that a previously identified strong ferromagnetic interaction within a U-U rung leads to a pseudospin-triplet superconducting state that accounts for a nonzero polar Kerr angle, the observed magnetic field-temperature phase diagrams, and nodal Weyl fermions. Finally, our analysis may also be relevant for other U-based superconductors.
Here we develop a generic k ∙ p open momentum space method for calculating the Hofstadter butterfly of both continuum (moiré) models and tight-binding models, where the quasimomentum is directly substituted by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. For continuum models such as the moiré model for twisted bilayer graphene, our method gives a sparse Hamiltonian, making it much more efficient than existing methods. The spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers (t ν , s ν ) of a gap ν satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. While t ν is known as the Chern number, our theory identifies s ν as a dual Chern number for the momentum space, which corresponds to a quantized Lorentz susceptibility γ xy = eBs ν .