Observation of Topological Edge States in Thermal Diffusion

Hierarchical bound states in heat transport

Higher-order topological phases in non-Hermitian photonics revolutionize the understanding of wave propagation and modulation, which lead to hierarchical states in open systems. However, intrinsic insulating properties endorsed by the lattice symmetry of photonic crystals fundamentally confine the robust transport only at explicit system boundaries, letting alone the flexible reconfiguration in hierarchical states at arbitrary positions. Here, we report a dynamic topological platform for creating the reconfigurable hierarchical bound states in heat transport systems and observe the robust and nonlocalized higher-order states in both the real- and imaginary-valued bands. Our experiments showcase that the hierarchical features of zero-dimension corner and nontrivial edge modes occur at tailored positions within the system bulk states instead of the explicit system boundaries. Our findings uncover the mechanism of non-localized hierarchical non-trivial topological states and offer distinct paradigms for diffusive transport field management.

Topological phases of tight-binding trimer lattice in the BDI symmetry class

In this work, we theoretically study a modified Su-Schrieffer-Heeger (SSH) model in which each unit cell consists of three sites. Unlike existing extensions of the SSH model which are made by enlarging the periodicity of the (nearest-neighbor) hopping amplitudes, our modification is obtained by replacing the Pauli matrices in the system's Hamiltonian by their higher dimensional counterparts. This, in turn, leads to the presence of next-nearest neighbor hopping terms and the emergence of different symmetries than those of other extended SSH models. Moreover, the system supports a number of edge states that are protected by a combination of particle-hole, time-reversal, and chiral symmetry. Finally, our system could be potentially realized in various experimental platforms including superconducting circuits as well as acoustic/optical waveguide arrays.

Chiral edge waves in a dance-based human topological insulator

Topological insulators are insulators in the bulk but feature chiral energy propagation along the boundary. This property is topological in nature and therefore robust to disorder. Originally discovered in electronic materials, topologically protected boundary transport has since been observed in many other physical systems. Thus, it is natural to ask whether this phenomenon finds relevance in a broader context. We choreograph a dance in which a group of humans, arranged on a square grid, behave as a topological insulator. The dance features unidirectional flow of movement through dancers on the lattice edge. This effect persists when people are removed from the dance floor. Our work extends the applicability of wave physics to dance.

Localized and delocalized topological modes of heat

The topological physics has sparked intensive investigations into topological lattices in photonic, acoustic, and mechanical systems, powering counterintuitive effects otherwise inaccessible with usual settings. Following the success of these endeavors in classical wave dynamics, there has been a growing interest in establishing their topological counterparts in diffusion. Here, we propose an additional real-space dimension in diffusion, and the system eigenvalues are transformed from "imaginary" to "real." By judiciously tailoring the effective Hamiltonian with coupling networks, localized and delocalized topological modes are realized in heat transfer. Simulations and experiments in active thermal lattices validate the effectiveness of the proposed theoretical strategy. This approach can be applied to establish various topological lattices in diffusion systems, offering insights into engineering topologically protected edge states in dynamic diffusive scenarios.

A New Solution to the Grain Boundary Grooving Problem in Polycrystalline Thin Films When Evaporation and Diffusion Meet in Power Electronic Devices

This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thin films in the cases of evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation-condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation ∂y∂x2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that changes in the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.

Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement

Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX-YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan-Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin-spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.

Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle

We consider a nonequilibrium transition that leads to the formation of nonlinear steady-state structures due to the gas flow scattering on a partially penetrable obstacle. The resulting nonequilibrium steady state (NESS) corresponds to a two-domain gas structure attained at certain critical parameters. We use a simple mean-field model of the driven lattice gas with ring topology to demonstrate that this transition is accompanied by the emergence of local invariants related to a complex composed of the obstacle and its nearest gas surrounding, which we refer to as obstacle edges. These invariants are independent of the main system parameters and behave as local first integrals, at least qualitatively. As a result, the complex becomes insensitive to the noise of external driving field within the overcritical domain. The emerged invariants describe the conservation of the number of particles inside the obstacle and strong temporal synchronization or correlation of gas states at obstacle edges. Such synchronization guarantees the equality to zero of the total edge current at any time. The robustness against external drive fluctuations is shown to be accompanied by strong spatial localization of induced gas fluctuations near the domain wall separating the depleted and dense gas phases. Such a behavior can be associated with nonequilibrium protection effect and synchronization of edges. The transition rates between different NESSs are shown to be different. The relaxation rates from one NESS to another take complex and real values in the sub- and overcritical regimes, respectively. The mechanism of these transitions is governed by the generation of shock waves at the back side of the obstacle. In the subcritical regime, these solitary waves are generated sequentially many times, while only a single excitation is sufficient to rearrange the system state in the overcritical regime.

Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems

Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form similarity between Schrödinger equation and diffusion equation, research on higher-order topological insulators has been extended from condensed matter physics to thermal diffusion. Unfortunately, all the corner states of thermal higher-order topological insulator reside within the band gap. Another kind of corner state, which is embedded in the bulk states, has not been realized in pure diffusion systems so far. Here, we construct higher-dimensional Su-Schrieffer-Heeger models based on sphere-rod structure to elucidate these corner states, which we term "in-bulk corner states." Because of the anti-Hermitian properties of diffusive Hamiltonian, we investigate the thermal behavior of these corner states through theoretical calculation, simulation, and experiment. Furthermore, we study the different thermal behaviors of in-bulk corner state and in-gap corner state. Our results would open a different gate for diffusive topological states and provide a distinct application for efficient heat dissipation.

Bulk-Edge Correspondence for Nonlinear Eigenvalue Problems

Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.

Higher-order topological heat conduction on a lattice for detection of corner states

A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing kagome lattice. We show that the temperature measurement at a corner node can detect the corner state which causes rapid heat conduction toward the heat bath, and that several-nodes measurement can determine the precise energy of the corner states.

Edge states in coupled non-Hermitian resonators

Small perturbations may dramatically influence the physical properties of a single non-Hermitian cavity. However, how these small perturbations interplay with bulk-edge properties is still to be demonstrated by experimentation. Here, we experimentally demonstrate edge states in coupled non-Hermitian resonators, based on a chain of all-dielectric coupled resonators where each resonator consists of two target particles. The evanescent coupling between the cavity and the target particles leads to tunable asymmetric backscattering, which plays a key role in the appearance of edge states in the bulk bandgap. We also demonstrate that these observed edge states are robust against weak disorders introduced to the system. Our study may inspire further explorations of the non-Hermitian bulk-edge properties.

Convective Thermal Metamaterials: Exploring High-Efficiency, Directional, and Wave-Like Heat Transfer

Convective thermal metamaterials are artificial structures where convection dominates in the thermal process. Due to the field coupling between velocity and temperature, convection provides a new knob for controlling heat transfer beyond pure conduction, thus allowing active and robust thermal modulations. With the introduced convective effects, the original parabolic Fourier heat equation for pure conduction can be transformed to hyperbolic. Therefore, the hybrid diffusive system can be interpreted in a wave-like fashion, reviving many wave phenomena in dissipative diffusion. Here, recent advancements in convective thermal metamaterials are reviewed and the state-of-the-art discoveries are classified into the following four aspects, enhancing heat transfer, porous-media-based thermal effects, nonreciprocal heat transfer, and non-Hermitian phenomena. Finally, a prospect is cast on convective thermal metamaterials from two aspects. One is to utilize the convective parameter space to explore topological thermal effects. The other is to further broaden the convective parameter space with spatiotemporal modulation and multi-physical effects.

Higher-Order Topological States in Thermal Diffusion

Unlike conventional topological materials that carry topological states at their boundaries, higher-order topological materials are able to support topological states at boundaries of boundaries, such as corners and hinges. While band topology has been recently extended into thermal diffusion for thermal metamaterials, its realization is limited to a 1D thermal lattice, lacking access to the higher-order topology. In this work, the experimental realization is reported of a higher-order thermal topological insulator in a generalized 2D diffusion lattice. The topological corner states for thermal diffusion are observed in the bandgap of diffusion rate of the bulk, as a consequence of the anti-Hermitian nature of the diffusion Hamiltonian. The topological protection of these thermal corner states is demonstrated with the stability of their diffusion profile in the presence of amorphous deformation. This work constitutes the first realization of higher-order topology in purely diffusive systems and opens the door for future thermal management with topological protection beyond 1D geometries.