Topological Matter Research Articles

Topological phases for extended objects: Semiclassical phase-space approach with tensorial coordinates

It has long been established that certain higher-dimensional topological phases of matter support extended objects like quasistrings and quasimembranes in their bulk states. In this study, we investigate the physics of these topological systems using a phase-space approach in the semiclassical regime, incorporating tensorial coordinates related to the extended objects. Specifically, we explore the semiclassical currents associated to open quasistrings in topological phases in three spatial dimensions, considering the presence of both coordinate-space Kalb-Ramond fields and momentum-space tensor Berry connections. Our results show that the currents associated to the endpoints of open quasistrings on the system’s boundary exhibit a quantum Hall response. This formalism accurately reproduces the boundary response as predicted by an Abelian BF theory proving a novel way to study extended objects in topological matter. Published by the American Physical Society 2025

Observing non-Hermiticity induced chirality breaking in a synthetic Hall ladder

Non-Hermitian topological photonics plays a key role in bridging topological matter with gain and loss engineering in optics. Here we report the experimental observation of the break of chiral currents in a Hall ladder from the non-Hermiticity by constructing synthetic frequency dimension in two rings, where currents on both legs of the ladder co-propagate in the same direction. The origin of such phenomena is resulted from the interplay between the effective magnetic flux and the on-site gain and loss. Such non-Hermitian co-propagating currents exhibit characteristics of unidirectional frequency conversion in both rings, and moreover, different from the counterpart in Hermitian systems, can provide a method to probe the signatures of the non-Hermitian skin effect from steady-state bulk dynamics. Our model is further extended to models including next-nearest-neighbor couplings, pointing to a way for observing the non-Hermitian signature with higher winding number, and provides a new control knob for light manipulation with the topological dissipation engineering.

Quantum computing topological invariants of two-dimensional quantum matter

Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers. Published by the American Physical Society 2024

Topological Fermiology of gate-tunable Rashba electron gases.

By introducing first-order quantum phases as topological invariants, recent symmetry analysis-based theories have reinvigorated magnetic quantum oscillations as a versatile quantum probe for unfolding the Fermi surface topology along with the geometry information, i.e., topo-Fermiology. Here, we demonstrate the comprehensive topo-Fermiology of high-mobility Rashba two-dimensional electron gases with ultragate tunability of spin-orbit coupling parameter in few-layer black arsenic. The remarkable consistencies with the key theoretical predictions of period doubling in quantum oscillations, gate-tunable aperiodic beating patterns, and the symmetry-enforced Landau level crossing phenomena controlled by the competition between Rashba coupling and the Zeeman interaction, which ultimately manifests as all odd-filling factor integer quantum Hall effect with superb sensitivity to quantum phases, establish topo-Fermiology as an indispensable methodology for studying topological quantum matters.

Charge-neutral electronic excitations in quantum insulators.

Experiments on quantum materials have uncovered many interesting quantum phases ranging from superconductivity to a variety of topological quantum matter including the recently observed fractional quantum anomalous Hall insulators. The findings have come in parallel with the development of approaches to probe the rich excitations inherent in such systems. In contrast to observing electrically charged excitations, the detection of charge-neutral electronic excitations in condensed matter remains difficult, although they are essential to understanding a large class of strongly correlated phases. Low-energy neutral excitations are especially important in characterizing unconventional phases featuring electron fractionalization, such as quantum spin liquids, spin ices and insulators with neutral Fermi surfaces. In this Perspective, we discuss searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators, highlighting theoretical and experimental progress in probing excitonic insulators, new quantum spin liquid candidates and emergent correlated insulators based on two-dimensional layered crystals and moiré materials. We outline the promises and challenges in probing and using quantum insulators, and discuss exciting new opportunities for future advancements offered by ideas rooted in next-generation quantum materials, devices and experimental schemes.

Fractional Chern Insulators in Twisted Bilayer MoTe_{2}: A Composite Fermion Perspective.

The discovery of fractional Chern insulators (FCIs) in twisted bilayer MoTe_{2} has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This Letter examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe_{2}, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities σ_{xy}=[C/(2C+1)](e^{2}/h) linked to partial filling ν_{h} of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number C within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities σ_{xy}=(2/3)e^{2}/h and σ_{xy}=(3/5)e^{2}/h at fractional fillings ν_{h}=2/3 and ν_{h}=3/5 observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This Letter offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.

Topological and chiral matter—Physics and applications

Topological and chiral matter—Physics and applications

Microscopic probing of the superconducting and normal state properties of Ta2V3.1Si0.9 by muon spin rotation

The two-dimensional kagome lattice is an experimental playground for novel physical phenomena, from frustrated magnetism and topological matter to chiral charge order and unconventional superconductivity. A newly identified kagome superconductor, Ta2V3.1Si0.9 has recently gained attention for possessing a record high critical temperature, TC = 7.5 K for kagome metals at ambient pressure. In this study we conducted a series of muon spin rotation measurements to delve deeper into understanding the superconducting and normal state properties of Ta2V3.1Si0.9. We demonstrate that Ta2V3.1Si0.9 is a bulk superconductor with either a s+s-wave or anisotropic s-wave gap symmetry, and has an unusual paramagnetic shift in response to external magnetic fields in the superconducting state. Additionally, we observe an exceptionally low superfluid density − a distinctive characteristic of unconventional superconductivity − which remarkably is comparable to the superfluid density found in hole-doped cuprates. In its normal state, Ta2V3.1Si0.9 exhibits a significant increase in the zero-field muon spin depolarisation rate, starting at approximately 150 K, which has been observed in other kagome-lattice superconductors, and therefore hints at possible hidden magnetism. These findings characterise Ta2V3.1Si0.9 as an unconventional superconductor and a noteworthy new member of the vanadium-based kagome material family.

Searching for topological dark matter in LIGO data

Searching for topological dark matter in LIGO data

Anderson Localization of Walking Droplets

Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the random landscape. In stark contrast, wave-particle duality causes electrons in disordered media to come to rest even when the potential is weak—a remarkable phenomenon known as Anderson localization. Here, we present a hydrodynamic active system with wave-particle features, a millimetric droplet self-guided by its own wave field over a submerged random topography, whose dynamics exhibits localized statistics analogous to those of electronic systems. Consideration of an ensemble of particle trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography. We rationalize mechanistically the emergent statistics by virtue of the wave-mediated resonant coupling between the droplet and topography, which produces an attractive wave potential about the localization region. This hydrodynamic analog, which demonstrates how a classical particle may localize like a wave, suggests new directions for future research in various areas, including active matter, wave localization, many-body localization, and topological matter. Published by the American Physical Society 2024

Photonic defect modes in cholesteric liquid crystal resonators with embedded isotropic layers

Photonic defect modes are explored as a viable alternative to standard photonic band edge modes in photonic crystal applications, especially due to their typically high Q-factors and local density of states. For example, they can be used in nonlinearity enhancement, lasing, and cavity quantum electrodynamics. However, they are strongly dependent on any structural change and need to be well-controlled to ensure the desired resonance frequency. Here, we present a study of the photonic defect modes that appear in a structure where a layer of isotropic material is embedded between two layers of cholesteric liquid crystal (CLC), using full electrodynamics numerical simulations. We present typical transmission spectra and electric field profiles of selected defect modes and then analyze the influence of geometrical and material parameters on the eigenfrequencies and Q-factors of the modes within and around the photonic bandgap, including refractive indices and thicknesses of isotropic and liquid crystal layers, and different anchoring orientations at the boundaries of the isotropic defect layer. Additionally, a connection of such defect modes to previously extensively analyzed twist defect modes is given. Eigenmodes in asymmetric resonators are also presented, where CLC layers surrounding the intermediate isotropic layer are not equally thick, enabling biasing of specific directional light emission. More generally, this work aims to contribute to the understanding and design capability in topological soft matter photonics where defect mode lasing could be realized in CLC geometries with different singular and solitonic topological defect structures.

Construction of topological quantum magnets from atomic spins on surfaces.

Artificial quantum systems have emerged as platforms to realize topological matter in a well-controlled manner. So far, experiments have mostly explored non-interacting topological states, and the realization of many-body topological phases in solid-state platforms with atomic resolution has remained challenging. Here we construct topological quantum Heisenberg spin lattices by assembling spin chains and two-dimensional spin arrays from spin-1/2 Ti atoms on an insulating MgO film in a scanning tunnelling microscope. We engineer both topological and trivial phases of the quantum spin model and thereby realize first- and second-order topological quantum magnets. We probe the many-body excitations of the quantum magnets by single-atom electron spin resonance with an energy resolution better than 100 neV. Making use of the atomically localized magnetic field of the scanning tunnelling microscope tip, we visualize various many-body topological bound modes including topological edge states, topological defects and higher-order corner modes. Our results provide a bottom-up approach for the simulation of exotic quantum many-body phases of interacting spins.

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

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

Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter

Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter

Dynamics of symmetry-protected topological matter on a quantum computer

Dynamics of symmetry-protected topological matter on a quantum computer

Axion‐Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

AbstractFundamental aspects of chiral anomaly‐driven interactions in conformal field theory (CFT) in four spacetime dimensions are discussed. These interactions find application in very general contexts, from early universe plasma to topological condensed matter. The key shared characteristics of these interactions are outlined, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman–Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, it is demonstrated how conformal Ward identities (CWIs) in momentum space allow to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern–Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial‐vector channel satisfies mass‐independent sum rules related to the anomaly in any chiral interaction. The detection of an axion‐like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analog of a similar one in ordinary axion physics, in the presence of an axion‐like condensate, which is rederived using axion electrodynamics.

Realization of a two-dimensional Weyl semimetal and topological Fermi strings

A two-dimensional (2D) Weyl semimetal, akin to a spinful variant of graphene, represents a topological matter characterized by Weyl fermion-like quasiparticles in low dimensions. The spinful linear band structure in two dimensions gives rise to distinctive topological properties, accompanied by the emergence of Fermi string edge states. We report the experimental realization of a 2D Weyl semimetal, bismuthene monolayer grown on SnS(Se) substrates. Using spin and angle-resolved photoemission and scanning tunneling spectroscopies, we directly observe spin-polarized Weyl cones, Weyl nodes, and Fermi strings, providing consistent evidence of their inherent topological characteristics. Our work opens the door for the experimental study of Weyl fermions in low-dimensional materials.

Emergent chiral spin textures in centrosymmetric iron garnet with spin alignment constraints

Chiral spin textures have emerged as a captivating class of topological matter. These intriguing structures harbor localized and topologically protected magnetic textures, rendering them promising candidates for novel spintronic applications. Here, the emergent chiral spin textures in an iron garnet with nanodisk configuration have been micromagnatically simulated based on the Landau-Lifshitz-Gilbert equation (LLG) of COMSOL Multiphysics. The modification of magnetic spin texture in the considered iron garnet has been controlled by introducing the interfacial Dzyaloshinskii-Moriya interaction (I-DMI) and spin alignment constraints as locally pinned spins and curvilinear defects at edges. These boundary conditions induced interesting chiral textures not commonly observed in such iron garnet due to its centrosymmetric crystal structure. The simulation results showed the presence of two distinct regions of spin texture: inside and outside the pinning boundary. By systematically varying the DMI strength (D) with the size of the pinning boundary (Rpin) and the number of defects (Ndef), the emerging chiral spin textures have been explored and reported, including the existence of ramified helical stripes, skyrmions, and skyrmions-like textures such as elongated skyrmions, chiral horseshoe domains, biskyrmions and target skyrmions (TSk) (2π-TSk and 3π-TSk). Also, it has been reported that various collapses occur in the final spin texture states, leading to the transition from one state to another when varying the values of Rpin and Ndef with D.

Interactions Enable Thouless Pumping in a Nonsliding Lattice

A topological “Thouless” pump represents the quantized motion of particles in response to a slow, cyclic modulation of external control parameters. The Thouless pump, like the quantum Hall effect, is of fundamental interest in physics, because it links physically measurable quantities, such as particle currents, to geometric properties of the experimental system, which can be robust against perturbations and, thus, technologically useful. So far, experiments probing the interplay between topology and interparticle interactions have remained relatively scarce. Here, we observe a Thouless-type charge pump in which the particle current and its directionality inherently rely on the presence of strong interactions. Experimentally, we utilize a two-component Fermi gas in a dynamical superlattice which does not exhibit a sliding motion and remains trivial in the single-particle regime. However, when tuning interparticle interactions from zero to positive values, the system undergoes a transition from being stationary to drifting in one direction, consistent with quantized pumping in the first cycle. Remarkably, the topology of the interacting pump trajectory cannot be adiabatically connected to a noninteracting limit, highlighted by the fact that only one atom is transferred per cycle. Our experiments suggest that Thouless charge pumps are promising platforms to gain insights into interaction-driven topological transitions and topological quantum matter. Published by the American Physical Society 2024

Realization of fractional quantum Hall state with interacting photons.

Fractional quantum Hall (FQH) states are known for their robust topological order and possess properties that are appealing for applications in fault-tolerant quantum computing. An engineered quantum platform would provide opportunities to operate FQH states without an external magnetic field and enhance local and coherent manipulation of these exotic states. We demonstrate a lattice version of photon FQH states using a programmable on-chip platform based on photon blockade and engineering gauge fields on a two-dimensional circuit quantum electrodynamics system. We observe the effective photon Lorentz force and butterfly spectrum in the artificial gauge field, a prerequisite for FQH states. After adiabatic assembly of Laughlin FQH wave function of 1/2 filling factor from localized photons, we observe strong density correlation and chiral topological flow among the FQH photons. We then verify the unique features of FQH states in response to external fields, including the incompressibility of generating quasiparticles and the smoking-gun signature of fractional quantum Hall conductivity. Our work illustrates a route to the creation and manipulation of novel strongly correlated topological quantum matter composed of photons and opens up possibilities for fault-tolerant quantum information devices.