Unconventional Flatband Line States in Photonic Lieb Lattices

Flatband systems typically host "compact localized states"(CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice(LL), we show that conventional localized flatband states are inherently incomplete, with the missing modes manifested as extended line states which form non-contractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially-tailored boundaries, thereby directly observe the unusually extended flatband line states.Such unconventional line states cannot be expressed as a linear combination of the previously observed CLS but rather arise from the nontrivial real-space topology.The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated

Photonic realization of a generic type of graphene edge states exhibiting topological flat band

Cutting a honeycomb lattice (HCL) can end up with three types of edges (zigzag, bearded and armchair), as is well known in the study of graphene edge states. Here we theoretically investigate and experimentally demonstrate a class of graphene edges, namely, the twig-shaped edges, using a photonic platform, thereby observing edge states distinctive from those observed before. Our main findings are: (i) the twig edge is a generic type of HCL edges complementary to the armchair edge, formed by choosing the right primitive cell rather than simple lattice cutting or Klein edge modification; (ii) the twig edge states form a complete flat band across the Brillouin zone with zero-energy degeneracy, characterized by nontrivial topological winding of the lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly localized along the boundary, manifesting both flat band and topological features. Such new edge states are realized in a laser-written photonic graphene and well corroborated by numerical simulations. Our results may broaden the understanding of graphene edge states, bringing about new possibilities for wave localization in artificial Dirac-like materials.Comment: 13 pages, 4 figure

Persistent homology analysis of a generalized Aubry-Andr\'{e}-Harper model

Observing critical phases in lattice models is challenging due to the need to analyze the finite time or size scaling of observables. We study how the computational topology technique of persistent homology can be used to characterize phases of a generalized Aubry-Andr\'{e}-Harper model. The persistent entropy and mean squared lifetime of features obtained using persistent homology behave similarly to conventional measures (Shannon entropy and inverse participation ratio) and can distinguish localized, extended, and crticial phases. However, we find that the persistent entropy also clearly distinguishes ordered from disordered regimes of the model. The persistent homology approach can be applied to both the energy eigenstates and the wavepacket propagation dynamics.Comment: Published version. 8 pages, 9 figure

Flatband Line States in Photonic Super-Honeycomb Lattices

We establish experimentally a photonic super-honeycomb lattice (sHCL) by use of a cw-laser writing technique, and thereby demonstrate two distinct flatband line states that manifest as noncontractible-loop-states in an infinite flatband lattice. These localized states (straight and zigzag lines) observed in the sHCL with tailored boundaries cannot be obtained by superposition of conventional compact localized states because they represent a new topological entity in flatband systems. In fact, the zigzag-line states, unique to the sHCL, are in contradistinction with those previously observed in the Kagome and Lieb lattices. Their momentum-space spectrum emerges in the high-order Brillouin zone where the flat band touches the dispersive bands, revealing the characteristic of topologically protected bandcrossing. Our experimental results are corroborated by numerical simulations based on the coupled mode theory. This work may provide insight to Dirac like 2D materials beyond graphene

Universal momentum-to-real-space mapping of topological singularities

Topological properties of materials, as manifested in the intriguing phenomena of quantum Hall effect and topological insulators, have attracted overwhelming transdisciplinary interest in recent years. Topological edge states, for instance, have been realized in versatile systems including electromagnetic-waves. Typically, topological properties are revealed in momentum space, using concepts such as Chern number and Berry phase. Here, we demonstrate a universal mapping of the topology of Dirac-like cones from momentum space to real space. We evince the mapping by exciting the cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned for a chosen pseudospin state s, leading to direct observation of topological charge conversion that follows the rule of l to l+2s. The mapping is theoretically accounted for all initial excitation conditions with the pseudospin-orbit interaction and nontrivial Berry phases. Surprisingly, such a mapping exists even in a deformed lattice where the total angular momentum is not conserved, unveiling its topological origin. The universality of the mapping extends beyond the photonic platform and 2D lattices: equivalent topological conversion occurs for 3D Dirac-Weyl synthetic magnetic monopoles, which could be realized in ultracold atomic gases and responsible for mechanism behind the vortex creation in electron beams traversing a magnetic monopole field

Realization of robust boundary modes and non-contractible loop states in photonic Kagome lattices

Corbino-geometry has well-known applications in physics, as in the design of graphene heterostructures for detecting fractional quantum Hall states or superconducting waveguides for illustrating circuit quantum electrodynamics. Here, we propose and demonstrate a photonic Kagome lattice in the Corbino-geometry that leads to direct observation of non-contractible loop states protected by real-space topology. Such states represent the "missing" flat-band eigenmodes, manifested as one-dimensional loops winding around a torus, or lines infinitely extending to the entire flat-band lattice. In finite (truncated) Kagome lattices, however, line states cannot preserve as they are no longer the eigenmodes, in sharp contrast to the case of Lieb lattices. Using a continuous-wave laser writing technique, we experimentally establish finite Kagome lattices with desired cutting edges, as well as in the Corbino-geometry to eliminate edge effects. We thereby observe, for the first time to our knowledge, the robust boundary modes exhibiting self-healing properties, and the localized modes along toroidal direction as a direct manifestation of the non-contractible loop states

Symmetry-protected higher-order exceptional points in staggered flatband rhombic lattices

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains as a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in PT -symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also nonHermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform towards the investigation of the higher-order EPs, and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.Comment: 10 pages, 10 figure

EEPD1 Rescues Stressed Replication Forks and Maintains Genome Stability by Promoting End Resection and Homologous Recombination Repair

Replication fork stalling and collapse is a major source of genome instability leading to neoplastic transformation or cell death. Such stressed replication forks can be conservatively repaired and restarted using homologous recombination (HR) or non-conservatively repaired using micro-homology mediated end joining (MMEJ). HR repair of stressed forks is initiated by 5' end resection near the fork junction, which permits 3' single strand invasion of a homologous template for fork restart. This 5' end resection also prevents classical non-homologous end-joining (cNHEJ), a competing pathway for DNA double-strand break (DSB) repair. Unopposed NHEJ can cause genome instability during replication stress by abnormally fusing free double strand ends that occur as unstable replication fork repair intermediates. We show here that the previously uncharacterized Exonuclease/Endonuclease/Phosphatase Domain-1 (EEPD1) protein is required for initiating repair and restart of stalled forks. EEPD1 is recruited to stalled forks, enhances 5' DNA end resection, and promotes restart of stalled forks. Interestingly, EEPD1 directs DSB repair away from cNHEJ, and also away from MMEJ, which requires limited end resection for initiation. EEPD1 is also required for proper ATR and CHK1 phosphorylation, and formation of gamma-H2AX, RAD51 and phospho-RPA32 foci. Consistent with a direct role in stalled replication fork cleavage, EEPD1 is a 5' overhang nuclease in an obligate complex with the end resection nuclease Exo1 and BLM. EEPD1 depletion causes nuclear and cytogenetic defects, which are made worse by replication stress. Depleting 53BP1, which slows cNHEJ, fully rescues the nuclear and cytogenetic abnormalities seen with EEPD1 depletion. These data demonstrate that genome stability during replication stress is maintained by EEPD1, which initiates HR and inhibits cNHEJ and MMEJ