The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial ...dimensions. We use electric circuits to experimentally implement a four-dimensional (4D) topological lattice. The lattice dimensionality is established by circuit connections, and not by mapping to a lower-dimensional system. On the lattice's three-dimensional surface, we observe topological surface states that are associated with a nonzero second Chern number but vanishing first Chern numbers. The 4D lattice belongs to symmetry class AI, which refers to time-reversal-invariant and spinless systems with no special spatial symmetry. Class AI is topologically trivial in one to three spatial dimensions, so 4D is the lowest possible dimension for achieving a topological insulator in this class. This work paves the way to the use of electric circuits for exploring high-dimensional topological models.
Higher-order topological insulators
are a family of recently predicted topological phases of matter that obey an extended topological bulk-boundary correspondence principle. For example, a ...two-dimensional (2D) second-order topological insulator does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D topological insulator, but instead has topologically protected zero-dimensional (0D) corner states. The first prediction of a second-order topological insulator
, based on quantized quadrupole polarization, was demonstrated in classical mechanical
and electromagnetic
metamaterials. Here we experimentally realize a second-order topological insulator in an acoustic metamaterial, based on a 'breathing' kagome lattice
that has zero quadrupole polarization but a non-trivial bulk topology characterized by quantized Wannier centres
. Unlike previous higher-order topological insulator realizations, the corner states depend not only on the bulk topology but also on the corner shape; we show experimentally that they exist at acute-angled corners of the kagome lattice, but not at obtuse-angled corners. This shape dependence allows corner states to act as topologically protected but reconfigurable local resonances.
Artificial magnetic fields have been constructed in 2D and 3D acoustic structures to manipulate sound, in much the same way as Dirac and Weyl fermions respond to magnetic fields in their quantum ...levels.
The realization of integrated, low-cost and efficient solutions for high-speed, on-chip communication requires terahertz-frequency waveguides and has great potential for information and communication ...technologies, including sixth-generation (6G) wireless communication, terahertz integrated circuits, and interconnects for intrachip and interchip communication. However, conventional approaches to terahertz waveguiding suffer from sensitivity to defects and sharp bends. Here, building on the topological phase of light, we experimentally demonstrate robust terahertz topological valley transport through several sharp bends on the all-silicon chip. The valley kink states are excellent information carriers owing to their robustness, single-mode propagation and linear dispersion. By leveraging such states, we demonstrate error-free communication through a highly twisted domain wall at an unprecedented data transfer rate (exceeding ten gigabits per second) that enables real-time transmission of uncompressed 4K high-definition video (that is, with a horizontal display resolution of approximately 4,000 pixels). Terahertz communication with topological devices opens a route towards terabit-per-second datalinks that could enable artificial intelligence and cloud-based technologies, including autonomous driving, healthcare, precision manufacturing and holographic communication.Robust terahertz wave transport is demonstrated on a silicon chip using the valley Hall topological phase. Error-free communication is achieved at a data rate of 11 Gbit s−1, enabling real-time transmission of uncompressed 4K high-definition video.
Topological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently ...discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.
The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to ...include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.
Nonlinear transmission lines (NLTLs) are nonlinear electronic circuits used for parametric amplification and pulse generation, and it is known that left-handed NLTLs support enhanced harmonic ...generation while suppressing shock wave formation. We show experimentally that in a left-handed NLTL analogue of the Su-Schrieffer-Heeger (SSH) lattice, harmonic generation is greatly increased by the presence of a topological edge state. Previous studies of nonlinear SSH circuits focused on solitonic behaviours at the fundamental harmonic. Here, we show that a topological edge mode at the first harmonic can produce strong propagating higher-harmonic signals, acting as a nonlocal cross-phase nonlinearity. We find maximum third-harmonic signal intensities five times that of a comparable conventional left-handed NLTL, and a 250-fold intensity contrast between topologically nontrivial and trivial configurations. This work advances the fundamental understanding of nonlinear topological states, and may have applications for compact electronic frequency generators.
Abstract
The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the ...introduction of non-Hermitian band topology. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop. As recently characterized along a synthetic dimension on a photonic platform, non-Hermitian band topology can exhibit almost arbitrary windings in momentum space, but their actual phenomena in real physical systems remain unclear. Here, we report the experimental realization of NHSE in a one-dimensional (1D) non-reciprocal acoustic crystal. With direct acoustic measurement, we demonstrate that a twisted winding, whose topology consists of two oppositely oriented loops in contact rather than a single loop, will dramatically change the NHSE, following previous predictions of unique features such as the bipolar localization and the Bloch point for a Bloch-wave-like extended state. This work reveals previously unnoticed features of NHSE, and provides the observation of physical phenomena originating from complex non-Hermitian winding topology.
Optical logic operations lie at the heart of optical computing, and they enable many applications such as ultrahigh-speed information processing. However, the reported optical logic gates rely ...heavily on the precise control of input light signals, including their phase difference, polarization, and intensity and the size of the incident beams. Due to the complexity and difficulty in these precise controls, the two output optical logic states may suffer from an inherent instability and a low contrast ratio of intensity. Moreover, the miniaturization of optical logic gates becomes difficult if the extra bulky apparatus for these controls is considered. As such, it is desirable to get rid of these complicated controls and to achieve full logic functionality in a compact photonic system. Such a goal remains challenging. Here, we introduce a simple yet universal design strategy, capable of using plane waves as the incident signal, to perform optical logic operations via a diffractive neural network. Physically, the incident plane wave is first spatially encoded by a specific logic operation at the input layer and further decoded through the hidden layers, namely, a compound Huygens' metasurface. That is, the judiciously designed metasurface scatters the encoded light into one of two small designated areas at the output layer, which provides the information of output logic states. Importantly, after training of the diffractive neural network,
basic types of optical logic operations can be realized by the same metasurface. As a conceptual illustration, three logic operations (NOT, OR, and AND) are experimentally demonstrated at microwave frequencies.
Confining photons in a finite volume is highly desirable in modern photonic devices, such as waveguides, lasers and cavities. Decades ago, this motivated the study and application of photonic ...crystals, which have a photonic bandgap that forbids light propagation in all directions
. Recently, inspired by the discoveries of topological insulators
, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators
, with promising applications in topological lasers
and robust optical delay lines
. However, a fully three-dimensional (3D) topological photonic bandgap has not been achieved. Here we experimentally demonstrate a 3D photonic topological insulator with an extremely wide (more than 25 per cent bandwidth) 3D topological bandgap. The composite material (metallic patterns on printed circuit boards) consists of split-ring resonators (classical electromagnetic artificial atoms) with strong magneto-electric coupling and behaves like a 'weak' topological insulator (that is, with an even number of surface Dirac cones), or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk band structure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D topological insulators from fermions to bosons and paves the way for applications in topological photonic cavities, circuits and lasers in 3D geometries.
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