Chern Insulator Research Articles

Plasmonic detection of the parity anomaly in a two-dimensional Chern insulator

In this paper, we present an analytic study on the surface plasmon polaritons in a two-dimensional parity anomaly Chern insulator. The two-dimensional conductivities derived from the BHZ model are antisymmetric, based on which two surface plasmon modes each contains two branches of dispersions have been found. In the absence of parity anomaly, the half-integer-valued Hall conductivities with positive and negative Dirac mass terms differ by a sign; two branches of each surface plasmon mode are exactly degenerate. However, the parity anomaly can lift such degeneracy and lead to significant modifications of these dispersion curves or even the occurrence of an extra branch of surface plasmons under particular condition. Our investigations have revealed the effects of the interplay of parity anomaly and topology on the dispersion relations of the surface plasmon polaritons, which may pave a possible way for the detection of the parity anomaly in a two-dimensional Chern insulator via plasmonic responses.

Real higher-order Weyl photonic crystal

Higher-order Weyl semimetals are a family of recently predicted topological phases simultaneously showcasing unconventional properties derived from Weyl points, such as chiral anomaly, and multidimensional topological phenomena originating from higher-order topology. The higher-order Weyl semimetal phases, with their higher-order topology arising from quantized dipole or quadrupole bulk polarizations, have been demonstrated in phononics and circuits. Here, we experimentally discover a class of higher-order Weyl semimetal phase in a three-dimensional photonic crystal (PhC), exhibiting the concurrence of the surface and hinge Fermi arcs from the nonzero Chern number and the nontrivial generalized real Chern number, respectively, coined a real higher-order Weyl PhC. Notably, the projected two-dimensional subsystem with kz = 0 is a real Chern insulator, belonging to the Stiefel-Whitney class with real Bloch wavefunctions, which is distinguished fundamentally from the Chern class with complex Bloch wavefunctions. Our work offers an ideal photonic platform for exploring potential applications and material properties associated with the higher-order Weyl points and the Stiefel-Whitney class of topological phases.

Topological phase transitions and flat bands on an islamic lattice

We construct an islamic lattice by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-NN hoppings. This model supports abundant quantum phases for various values of filling fractions. At filling, Chern insulator (CI) phases with Chern numbers and a zero-Chern-number topological insulator (ZCNTI) phase exist. At filling, several CI phases with Chern numbers and the ZCNTI phase are obtained. For the filling fraction 3/4, CI phases with Chern numbers and two ZCNTI phase areas appear. Interestingly, these ZCNTI phases host both robust corner states and gapless edge states which can be characterized by the quantized polarization and quadrupole moment. We further find that staggered magnetic fluxes can give rise to the ZCNTI state at and fillings. Phase diagrams for filling fractions , , and are presented as well. In addition, flat bands are obtained for various filling fractions by tuning the hopping parameters. At 1/8 filling, a best topological flat band (TFB) with flatness ratio about 12 appears. Several trivial flat bands but with total Chern number emerge in this model and exactly flat band is found at 3/8 filling. We further investigate fractional Chern insulate state when hard-core bosons fill into this TFB model.

Floquet fractional Chern insulators and competing phases in twisted bilayer graphene

We study the many-body physics in twisted bilayer graphene coupled to periodic driving of a circularly polarized light when electron-electron interactions are taken into account. In the limit of high driving frequency \OmegaΩ, we use Floquet theory to formulate the system by an effective static Hamiltonian truncated to the order of \Omega^{-2}Ω−2, which consists of a single-electron part and the screened Coulomb interaction. We numerically simulate this effective Hamiltonian by extensive exact diagonalization in the parameter space spanned by the twist angle and the driving strength. Remarkably, in a wide region of the parameter space, we identify Floquet fractional Chern insulator states in the partially filled Floquet valence bands. We characterize these topologically ordered states by ground-state degeneracy, spectral flow, and entanglement spectrum. In regions of the parameter space where fractional Chern insulator states are absent, we find topologically trivial charge density waves and band-dispersion-induced Fermi liquids which strongly compete with fractional Chern insulator states.

Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene.

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n = 0 and displacement field D = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a magnetic field of around 1 T. At high D and n, we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering.

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}.

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.

Acoustic realization of projective mirror Chern insulators

Symmetry plays a key role in classifying topological phases. Recent theory shows that in the presence of gauge fields, the algebraic structure of crystalline symmetries needs to be projectively represented, which brings extra chance for topological physics. Here, we report a concrete acoustic realization of mirror Chern insulators by exploiting the concept of projective symmetry. Specifically, we introduce a simple but universal recipe for constructing projective mirror symmetry, and conceive a minimal model for achieving the projective symmetry-enriched mirror Chern insulators. Based on our selective-excitation measurements, we demonstrate unambiguously the projective mirror eigenvalue-locked topological nature of the bulk states and associated chiral edge states. We extract the non-abelian Berry curvature and identify the mirror Chern number directly, providing experimental evidence for this exotic topological phase. All experimental results agree well with the theoretical predictions. Our findings give insights into topological systems equipped with gauge fields.

Zero-Frequency Chiral Magnonic Edge States Protected by Nonequilibrium Topology.

Topological bosonic excitations must, in contrast to their fermionic counterparts, appear at finite energies. This is a key challenge for magnons, as it prevents straightforward excitation and detection of topologically protected magnonic edge states and their use in magnonic devices. In this Letter, we show that in a nonequilibrium state, in which the magnetization is pointing against the external magnetic field, the topologically protected chiral edge states in a magnon Chern insulator can be lowered to zero frequency, making them directly accessible by existing experimental techniques. We discuss the spin-orbit torque required to stabilize this nonequilibrium state, and show explicitly using numerical Landau-Lifshitz-Gilbert simulations that the edge states can be excited with a microwave field. Finally, we consider a propagating spin wave spectroscopy experiment, and demonstrate that the edge states can be directly detected.

Chern-Insulator Phase in Antiferromagnets.

The long-sought Chern insulators that manifest a quantum anomalous Hall effect are typically considered to occur in ferromagnets. Here, we theoretically predict the realizabilities of Chern insulators in antiferromagnets, in which the magnetic sublattices are connected by symmetry operators enforcing zero net magnetic moment. Our symmetry analysis provides comprehensive magnetic layer point groups that allow antiferromagnetic (AFM) Chern insulators, revealing that an in-plane magnetic configuration is required. Followed by first-principles calculations, such design principles naturally lead to two categories of material candidates, exemplified by monolayer RbCr4S8 and bilayer Mn3Sn with collinear and noncollinear AFM orders, respectively. We further show that the Chern number could be tuned by slight ferromagnetic canting as an effective pivot. Our work elucidates the nature of the Chern-insulator phase in AFM systems, paving a new avenue for designing quantum anomalous Hall insulators with the integration of nondissipative transport and the promising advantages of the AFM order.

Bi2Te3-intercalated MnBi2Te4: ideal candidate to explore intrinsic Chern insulator and high-temperature quantum anomalous Hall effect

The recently discovered magnetic topological insulator of MnBi2Te4 (MBT), has been demonstrated to realize the quantum anomalous Hall (QAH) effect, while the naturally antiferromagnetic (AFM) interlayer coupling in MBT results in that the QAH effect can only be realized in odd-layered systems and at low temperature. Using first-principles calculations, we find that intercalating Bi2Te3 (BT) layers into MBT by forming MBT/(BT) n /MBT (n = 1–6) heterostructures can induce magnetic phase transition from AFM to ferromagnetic (FM) interlayer coupling when n⩾ 3. Specifically, MBT/(BT)3/MBT and MBT/(BT)4/MBT respectively host Curie temperatures T c of 14 K and 11 K, which fits well the experimentally measured T c of 12 K. Detailed band structure calculations and topological identification show that the QAH phases are well preserved for all FM heterostructures. And the topological mechanism of MBT/(BT) n /MBT as a function of n is revealed by employing continuum model analysis. Most importantly, the FM MBT/(BT)4/MBT has already been experimentally fabricated. Thus, our work provides a practical guideline to explore high-temperature QAH effect in MBT family of materials.

High-order harmonics from elliptically polarized laser for classification of topological states in 2D Chern insulators and 2D topological insulators

High-order harmonics (HH) have drawn attention in the field of condensed matter physics mainly because of the capability of light to encode structural, dynamical, and topological information. In this paper, we address the fundamental question whether HH can map topological information in two-dimensional (2D) quantum materials by studying the interaction between topological materials and an elliptically polarized laser. We use the Haldane model for topological Chern insulators (CIs) and the Kane–Mele model for topological insulators (TIs). In the case of a circularly polarized or nearly circularly polarized driving field in CIs and TIs, the harmonic intensity of the co-rotating orders is increased. This increase in topologically non-trivial materials implies that HH can be used to detect topological transitions in 2D CIs and TIs. Moreover, interference between two spin bands in TIs does not affect the elliptical dependence of co-rotating harmonic orders in the plateau region.

Simulating Chern insulators on a superconducting quantum processor

The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions on a programable 30-qubit-ladder superconducting processor. We directly measure the band structures of the 2D Chern insulator along synthetic dimensions with various configurations of Aubry-André-Harper chains and observe dynamical localisation of edge excitations. With these two signatures of topology, our experiments implement the bulk-edge correspondence in the synthetic 2D Chern insulator. Moreover, we simulate two different bilayer Chern insulators on the ladder-type superconducting processor. With the same and opposite periodically modulated on-site potentials for two coupled chains, we simulate topologically nontrivial edge states with zero Hall conductivity and a Chern insulator with higher Chern numbers, respectively. Our work shows the potential of using superconducting qubits for investigating different intriguing topological phases of quantum matter.

Phononic Weyl pair, phononic Weyl complex, phononic real Chern insulator state, and phononic corner modes in 2D Kekulé-order graphene

The conceptual framework of topological states has recently been extended to bosonic systems, particularly phononic systems. In this work, we chose the recently experimentally prepared two-dimensional (2D) Kekulé-order graphene as a target to propose the coexistence of gapless and gapped topological phonon states in its phonon curves. This is the first work to investigate rich gapped and gapless topological phonon states in experimentally feasible 2D materials. For the gapped topological phonons, 2D Kekulé-order graphene hosts phononic real Chern insulator states, i.e., second-order topological states, and corner vibrational modes inside frequency gaps at 27.96 and 37.065 THz. For the gapless topological phonons, 2D Kekulé-order graphene hosts a phononic Weyl pair [comprising two linear Weyl points (LWPs)] and a phononic Weyl complex [comprising one quadratic nodal point (QNP) and two LWPs] around 7.54 and 47.3 THz (39.2 THz), respectively. Moreover, the difference between the phononic Weyl pair and the phononic Weyl complex was investigated in detail. Our study not only promotes 2D Kekulé-order graphene as a concrete material platform for exploring the intriguing physics of phononic second-order topology but also proposes the coexistence of different categories of Weyl phonons, i.e., a Weyl complex that comprises two LWPs and one QNP, in two dimensions. Our work paves the way for new advancements in topological phononics comprising gapless and gapped topological phonons.

Bloch band structures and linear response theory of nonlinear systems

In this paper, we investigate the Bloch bands and develop a linear response theory for nonlinear systems, where the interplay between topological parameters and nonlinearity leads to new band structures. The nonlinear system under consideration is described by the Qi–Wu–Zhang model with Kerr-type nonlinearity, which can be treated as a nonlinear version of Chern insulator. We explore the eigenenergies of the Hamiltonian and discuss its Bloch band structures as well as the condition of gap closing. A cone structure in the ground Bloch band and tubed structure in the excited Bloch band is found. We also numerically calculate the linear response of the nonlinear Chern insulator to external fields, finding that these new band structures break the condition of adiabatic evolution and make the linear response not quantized. This feature of response can be understood by examining the dynamics of the nonlinear system.

Untwisting Moiré Physics: Almost Ideal Bands and Fractional Chern Insulators in Periodically Strained Monolayer Graphene.

Moiré systems have emerged in recent years as a rich platform to study strong correlations. Here, we will propose a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moiré heterostructures-but without introducing a twist. We consider a monolayer graphene sheet subject to a C_{2}-breaking periodic strain-induced pseudomagnetic field with period L_{M}≫a, along with a scalar potential of the same period. This system has almost ideal flat bands with valley-resolved Chern number ±1, where the deviation from ideal band geometry is analytically controlled and exponentially small in the dimensionless ratio (L_{M}/l_{B})^{2}, where l_{B} is the magnetic length corresponding to the maximum value of the pseudomagnetic field. Moreover, the scalar potential can tune the bandwidth far below the Coulomb scale, making this a very promising platform for strongly interacting topological phases. Using a combination of strong-coupling theory and self-consistent Hartree-Fock, we find quantum anomalous Hall states at integer fillings. At fractional filling, exact diagonaliztion reveals a fractional Chern insulator at parameters in the experimentally feasible range. Overall, we find that this system has larger interaction-induced gaps, smaller quasiparticle dispersion, and enhanced tunability compared to twisted graphene systems, even in their ideal limit.

Chiral-Flux-Phase-Based Topological Superconductivity in Kagome Systems with Mixed Edge Chiralities.

Recent studies have attracted intense attention on the quasi-2D kagome superconductors AV_{3}Sb_{5} (A=K, Rb, and Cs) where the unexpected chiral flux phase (CFP) associates with the spontaneous time-reversal symmetry breaking in charge density wave states. Here, commencing from the 2-by-2 charge density wave phases, we bridge the gap between topological superconductivity and time-reversal asymmetric CFP in kagome systems. Several chiral topological superconductor (TSC) states featuring distinct Chern numbers emerge for an s-wave or a d-wave superconducting pairing symmetry. Importantly, these CFP-based TSC phases possess unique gapless edge modes with mixed chiralities (i.e., both positive and negative chiralities), but with the net chiralities consistent with the Bogoliubov-de Gennes Chern numbers. We further study the transport properties of a two-terminal junction, using Chern insulator or normal metal leads via atomic Green's function method with Landauer-Büttiker formalism. In both cases, the normal electron tunneling and the crossed Andreev reflection oscillate as the chemical potential changes, but together contribute to plateau transmissions (1 and 3/2, respectively) that exhibit robustness against disorder. These behaviors can be regarded as the signature of a TSC hosting edge states with mixed chiralities.

Pressure-enhanced fractional Chern insulators along a magic line in moiré transition metal dichalcogenides

Pressure-enhanced fractional Chern insulators along a magic line in moiré transition metal dichalcogenides

Topological Phases in Magnonics

AbstractMagnonics or magnon spintronics is an emerging field focusing on generating, detecting, and manipulating magnons. As charge‐neutral quasi‐particles, magnons are promising information carriers because of their low energy dissipation and long coherence length. In the past decade, topological phases in magnonics have attracted intensive attention due to their fundamental importance in condensed‐matter physics and potential applications of spintronic devices. In this review, we mainly focus on recent progress in topological magnonics, such as the Hall effect of magnons, magnon Chern insulators, topological magnon semimetals, etc. In addition, the evidence supporting topological phases in magnonics and candidate materials are also discussed and summarized. The aim of this review is to provide readers with a comprehensive and systematic understanding of the recent developments in topological magnonics.

Polariton vortex Chern insulator [Invited

We propose a vortex Chern insulator, motivated by recent experimental demonstrations on programmable arrangements of cavity polariton vortices by [S. Alyatkin et al., arXiv, ArXiv:2207.01850 (2022)10.48550/arXiv.2207.01850 ] and [J. Wang et al, Natl. Sci. Rev. 10, Nwac096 (2022)10.1093/nsr/nwac096]. In the absence of any external fields, time-reversal symmetry is spontaneously broken through polariton condensation into structured arrangements of localized co-rotating vortices. We characterize the response of the rotating condensate lattice by calculating the spectrum of Bogoliubov elementary excitations and observe the crossing of edge-states, of opposite vorticity, connecting bands with opposite Chern numbers. The emergent topologically nontrivial energy gap stems from inherent vortex anisotropic polariton-polariton interactions and does not require any spin-orbit coupling, external magnetic fields, or elliptically polarized pump fields.

Interaction-driven Chern insulating phases in the [formula omitted] lattice with Rashba spin-orbit coupling

The magnetic interaction is a necessary ingredient to break the time-reversal symmetry in realizing quantum anomalous Hall, or Chern insulating phases. Here, we study topological phases in the model, a minimal theoretical model supporting the flat band, taking account of Rashba spin-orbit coupling and flat-band-induced spontaneous ferromagnetism. By analyzing the interaction-driven phase diagrams, band structures, topological edge states, and topological invariants, we demonstrate that this system offers a platform for realizing a wide range of phases, including normal insulators, semimetals, and Chern insulators. Uniquely, there exist both high-Chern-number insulators and valley-polarized Chern insulators. In the latter phase, edge channels exist in the single valley, leading to nearly valley polarization. These findings demonstrate the potential of interaction-driven systems in realizing exotic phases and their promising role in future applications in topology electronics and valleytronics.