arXiv subjects

Zhichan Hu

Publications and source records attributed to Zhichan Hu.

10 recordsLinked to original sources

arXiv2026

Fractal hierarchy enables exponential scaling of topological boundary states

Exponential growth describes an extremely rapid process ubiquitous across mathematics and diverse physical, biological, and technological systems. Here, we introduce a class of fractal-inspired lattices that combine long-range periodic order with self-similar hierarchy, establishing a structural motif that enables exponential scaling of topological boundary states. We demonstrate this phenomenon in (i) a quasi-one-dimensional lattice chain constructed from Koch-curve unit cells and (ii) a two-dimensional periodic tiling lattice composed of Sierpinski-gasket unit cells. We show that, for suitable coupling parameters, both the number of topological boundary states $N_{\ell}$ and the number of topological minigaps $M_{\ell}$ grow exponentially with the fractal generation index $\ell$. We find that $N_{\ell}$ is an integer multiple of $M_{\ell}$, with the integer determined by the underlying symmetry. This hierarchical scaling law is captured by multi-topological-phase theory and confirmed experimentally in laser-written photonic lattices. Our results identify fractal hierarchy as a materials architecture principle for controlling boundary-state multiplicity, revealing an interplay between topology, self-similar geometry, and periodic order. More broadly, this work suggests a route to synthetic materials and integrated photonic platforms in which large numbers of robust boundary modes can be engineered within compact architectures.

physics.optics↗

arXiv2026

Subsymmetry-protected compact edge states

Sub-symmetry (SubSy) protected topological states represent a concept that goes beyond the conventional framework of symmetry-protected topological (SPT) phases, demonstrating that topological boundary states can remain robust even when the pertinent symmetry holds only in a subset of Hilbert space. Typical SPT and SubSy boundary states decay exponentially into the bulk, which means they are not confined in just few lattice sites close to the boundary. Here, we introduce topologically compact edge states protected by SubSy, featuring extreme two-site localization at boundaries of a lattice, without any decay into the bulk. The compactness arises from local destructive interference at the boundary, while topological protection is ensured by SubSy, characterized by quantized winding numbers. Experimentally, we observe compact edge states in laser-written photonic lattices with engineered rhombic-like unit cells, confirming their robustness against perturbations under both chiral symmetry and SubSy conditions. Our results highlight the potential of SubSy protection for achieving topological confinement of light, paving the way for applications in compact waveguides, lasers, and high-sensitivity photonic sensors.

physics.optics↗

arXiv2025

Quadratic Band Touching and Nontrivial Winding Reveal Generalized Angular Momentum Conservation

Angular momentum conservation stands as one of the most fundamental and robust laws of physics. In discrete lattices, however, its realization can deviate markedly from the continuous case, especially in the presence of nontrivial momentum-space band touchings. Here, we investigate angular momentum conservation associated with quadratic band-touching points (QBTPs) in two-dimensional lattices. We show that, unlike in graphene lattices hosting linear band-touching points (LBTPs), the conventional angular momentum is no longer conserved near QBTPs. Instead, we identify a generalized total angular momentum (GTAM) that remains conserved for both LBTPs and QBTPs, inherently determined by the topological winding number at the band-touching point (BTP). Using a photonic Kagome lattice, we experimentally demonstrate GTAM conservation through pseudospin-orbital angular momentum conversion. Furthermore, we show that this conservation principle extends to a broad class of discrete lattices with arbitrary pseudospin textures and higher-order winding numbers. These results reveal a fundamental link between pseudospin, angular momentum, and topology, establishing a unified framework for angular-momentum dynamics in discrete systems.

physics.optics↗

arXiv2024

Multi-topological phases of matter

The discovery of topological phases of matter and topological boundary states had tremendous impact on condensed matter physics and photonics, where topological phases are defined via energy bands, giving rise to topological band theory. However, topological systems that cannot be described by band topology but still support non-trivial boundary states are little-known and largely unexplored. Here, we uncover a new kind of topological phase of matter named "multi-topological phase" (MTP) that features multiple sets of boundary states, where each set is associated with one distinct topological invariant. Unlike conventional topological phase transitions, the MTP transitions can occur without band-gap closing. We present typical examples of MTPs in a one-dimensional topological insulator and a two-dimensional higher-order topological insulator, where the systems are otherwise trivial according to band topology. Furthermore, MTPs can exist also in indirectly gapped Chern insulators, beyond the regime where the conventional bulk-boundary correspondence predicts the existence of boundary states. Experimentally, we demonstrate the first two examples of MTPs in laser-written photonic lattices. Our findings constitute a fundamental advance in topological physics and provide a route for designing novel topological materials.

physics.optics↗

arXiv2023

Observation of topologically distinct corner states in "bearded" photonic Kagome lattices

Kagome lattices represent an archetype of intriguing physics, attracting a great deal of interest in different branches of natural sciences, recently in the context of topological crystalline insulators. Here, we demonstrate two distinct classes of corner states in breathing Kagome lattices (BKLs) with "bearded" edge truncation, unveiling their topological origin. The in-phase corner states are found to exist only in the topologically nontrivial regime, characterized by a nonzero bulk polarization. In contrast, the out-of-phase corner states appear in both topologically trivial and nontrivial regimes, either as bound states in the continuum or as in-gap states depending on the lattice dimerization conditions. Furthermore, the out-of-phase corner states are highly localized, akin to flat-band compact localized states, and they manifest both real- and momentum-space topology. Experimentally, we observe both types of corner states in laser-written photonic bearded-edge BKLs, corroborated by numerical simulations. Our results not only deepen the current understanding of topological corner modes in BKLs, but also provide new insight into their physical origins, which may be applied to other topological BKL platforms beyond optics.

physics.optics↗

arXiv2023

Topologically protected vortex transport via chiral-symmetric disclination

Vortex phenomena are ubiquitous in nature, from vortices of quantum particles and living cells [1-7], to whirlpools, tornados, and spiral galaxies. Yet, effective control of vortex transport from one place to another at any scale has thus far remained a challenging goal. Here, by use of topological disclination [8,9], we demonstrate a scheme to confine and guide vortices of arbitrary high-order charges10,11. Such guidance demands a double topological protection: a nontrivial winding in momentum space due to chiral symmetry [12,13] and a nontrivial winding in real space arising from collective complex coupling between vortex modes. We unveil a vorticity-coordinated rotational symmetry, which sets up a universal relation between the topological charge of a guided vortex and the order of rotational symmetry of the disclination structure. As an example, we construct a C3-symmetry photonic lattice with a single-core disclination, thereby achieving robust transport of an optical vortex with preserved orbital angular momentum (OAM) that corresponds solely to one excited vortex mode pinned at zero energy. Our work reveals a fundamental interplay of vorticity, disclination and higher-order topological phases14-16, applicable broadly to different fields, promising in particular for OAM-based photonic applications that require vortex guides, fibers [17,18] and lasers [19].

physics.optics↗

arXiv2022

Photonic p-orbital higher-order topological insulators

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous efforts in engineering synthetic cold-atom, electronic and photonic lattices to explore orbital physics, thus far high orbitals in an important class of materials, namely, the higher-order topological insulators (HOTIs), have not been realized. Here, we demonstrate p-orbital corner states in a photonic HOTI, unveiling their underlying topological invariant, symmetry protection, and nonlinearity-induced dynamical rotation. In a Kagome-type HOTI, we find that topological protection of the p-orbital corner states demands an orbital-hopping symmetry, in addition to the generalized chiral symmetry. Due to orbital hybridization, the nontrivial topology of the p-orbital HOTI is hidden if bulk polarization is used as the topological invariant, but well manifested by the generalized winding number. Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher band topology applicable to a broad spectrum of systems.

physics.optics↗

arXiv2022

Sub-symmetry protected topological states

A hallmark of symmetry-protected topological phases (SPTs) are topologically protected boundary states, which are immune to perturbations that respect the protecting symmetry. It is commonly believed that any perturbation that destroys an SPT phase simultaneously destroys the boundary states. However, by introducing and exploring a weaker sub-symmetry (SubSy) requirement on perturbations, we find that the nature of boundary state protection is in fact more complex. We demonstrate that the boundary states are protected by only the SubSy using prototypical Su-Schrieffer-Heeger (SSH) and breathing Kagome lattice (BKL) models, even though the overall topological invariant and the SPT phase are destroyed by SubSy preserving perturbations. By employing judiciously controlled symmetry breaking in photonic lattices, we experimentally demonstrate such SubSy protection of topological states. Furthermore, we introduce a long-range hopping symmetry in BKLs, which resolves a debate on the topological nature of their corner states. Our results apply to other systems beyond photonics, heralding the possibility of exploring the intriguing properties of SPT phases in the absence of full symmetry in different physical contexts.

physics.optics↗

arXiv2021

Nonlinear control of photonic higher-order topological bound states in the continuum

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we demonstrate the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which, serendipitously, are also BICs in a laser-written second-order topological lattice. We further demonstrate nonlinear coupling with edge states at a low nonlinearity, transitioning to solitons at a high nonlinearity. Theoretically, we calculate the analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by both focusing and defocusing nonlinearities. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

physics.optics↗

arXiv2021

Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices

We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger (SSH) lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify emergent nonlinear topological phenomena. The phase transitions occur from topologically trivial-to-nontrivial phase in periodic succession with crossovers from topologically nontrivial-to-trivial regime. The signature of phase transition is gap-closing and re-opening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.

nlin.PS↗