arXiv subjects

Zhengyou Liu

Publications and source records attributed to Zhengyou Liu.

At least 19 recordsLinked to original sources

arXiv2026

Implementing non-Abelian Hatano-Nelson model in electric circuits

Non-Hermitian systems generally host complex spectra that bring unique spectral topologies, leading to the spectral braiding and non-Hermitian skin effect. The experimental exploration of non-Hermitian physics is mainly concentrated in artificial systems due to the flexibility in the introduction of the non-Hermiticity, but to date has focused only on the systems without gauge fields or with Abelian gauge fields. Here, we propose a non-Abelian Hatano-Nelson model with a nonreciprocal U(2) gauge field. The gauge field induces two non-Hermitian phenomena: the first is the Hopf-link-shaped complex energy braiding, and the second is the bipolar skin effect arising under the non-Abelian condition. The non-Abelian Hatano-Nelson model is implemented in electric circuits, and the Hopf-link-shaped admittance spectra and bipolar skin admittance modes are observed. Our work enriches the experimental non-Hermitian physics, and provides an approach to designing multifunctional non-Hermitian devices.

quant-ph↗

arXiv2026

Observation of exceptional topology and nonlocal skin effect in Klein bottle electric circuits

Symmetry and its representation play a crucial role in topological phases, including both Hermitian and non-Hermitian paradigms. In the presence of synthetic gauge field, spatial symmetries should be projectively represented, which can modify the Brillouin manifold. However, this is often overlooked in non-Hermitian systems. Here, we present that momentum-space non-symmorphic reflection symmetry, a typical projective symmetry, induce exceptional topology and the nonlocal skin effect in a two-dimensional non-Hermitian electric circuit. We observe the total topological charges 2, rather than 0, for all exceptional points in a Brillouin Klein bottle manifold, and the phase transition when an exceptional point crosses the antiparallel boundary and flips its topological charge. We further observe a novel skin effect that the skin modes at one side are nonlocally connected to those on the opposite side separated by half of the reciprocal lattice. Our results unveil the unique non-Hermitian phenomena enabled by the projective symmetry, and open avenues for exploring the non-Hermitian topology beyond Brillouin torus manifold.

cond-mat.mes-hall↗

arXiv2025

Higher-order exceptional ring semimetal with real hinge states in phononic crystals

Non-Hermitian topological phase, with the novel concepts such as exceptional points and skin effect, has opened up a new paradigm beyond Hermitian topological physics. Exceptional ring semimetal, featured by a stable ring of exceptional points in three dimensions, exhibits first-order topological properties, including topological surface states and surface-dependent skin effect. Nevertheless, despite extensive research on Hermitian higher-order insulators and semimetals, higher-order exceptional ring semimetal is just emerging. Here, we report the first realization of a higher-order Weyl exceptional ring semimetal in a three-dimensional lossy phononic crystal. The non-Hermitian higher-order topology reflects in the topological hinge states and hinge-dependent skin effect. Counterintuitively, the topological hinge states maintain purely real energy even under a high loss level, ensuring robust hinge-state propagation. Our findings evidence the non-Hermitian higher-order bulk-boundary correspondence of exceptional ring semimetal, and may pave the way to non-Hermitian functional acoustic devices.

cond-mat.mes-hall↗

arXiv2025

Lossy phononic metamaterials for valley manipulation

Non-Hermitian physics characterized by complex band spectra has established a new paradigm in condensed matter systems and metamaterials. Recently, non-Hermitian gain and nonreciprocity are deliberately introduced to valley manipulation, leading to various phenomena beyond the Hermitian scenarios, such as the amplified topological whispering gallery modes as an acoustic laser. In contrast, pure loss is inevitable in practice and generally regarded as a detrimental factor. Here, we reveal that the coupling loss can manipulate valley degrees of freedom in a phononic metamaterial. Three distinct valley-related effects, including valley-resolved nonreciprocity that functions as a valley filter, valley-dependent skin effects where bulk states from different valleys localize at opposite boundaries, and valley-projected edge states with boundary-dependent lifetimes that leads to an anomalous beam splitting, are demonstrated through theoretical analysis and airborne sound experiments. Owing to the easy preparation of loss, our findings shed light on both non-Hermitian and valley physics and may facilitate innovative applications of valley-related devices.

cond-mat.mtrl-sci↗

arXiv2025

Dimensional hierarchy of topological bound states in the continuum

Bound states in the continuum (BICs), with the ability of trapping and manipulating waves within the radiation continuum, have gained significant attention for their potential applications in optics and acoustics. However, challenges arise in reducing wave leakage and noise from fabrication imperfections. The emergence of robust wave manipulations based on topological BICs (TBICs) offers promising solutions. Traditionally, TBICs of different dimensions are observed separately in distinct systems. Here, we report the experimental discovery of the coexistence of two-dimensional surface TBICs and one-dimensional hinge TBICs in a single three-dimensional phononic crystal system. Such an unprecedented dimensional hierarchy of TBICs is triggered by the mechanism of separability and protected by the valley Chern numbers. Notably, these TBICs inherit dispersive propagation characteristics from valley topology and can propagate robustly against defects without leakage. Our findings offer an efficient approach to multidimensional TBICs and can be applied in designing highly efficient acoustic devices for wave trapping and manipulation in multidimensional environments.

cond-mat.mtrl-sci↗

arXiv2025

Braiding rule of boundary Majorana-like zero mode

The study of topological states has become an important topic in both solid-state systems and artificial structures such as photonic crystals and phononic crystals. Among them, Majorana zero modes, which exhibit nontrivial braiding process, have attracted extensive research interest. The analog of Majorana zero modes in classical waves, or the Majorana-like zero modes (MLZMs), have also got a lot of attention recently. However, the vast majority of previous works concerned with MLZMs that were bounded to vortexes inside the bulk. Here in this work, we unveil the braiding rule of MLZMs that are tunable around the boundary of a vortex-texture Kekule modulated graphene. We show that the existence of these zero-dimensional boundary MLZMs is protected by the Zak phase of 1D boundary states. As such, we are able to construct multiple MLZMs and analyze the corresponding braiding process. In addition, we also provide an implementation scheme of the boundary MLZMs in acoustic crystals. The tunability of the boundary MLZMs proposed herein offer new freedom for topological states braiding in both solid-state systems and artificial structures.

cond-mat.mes-hall↗

arXiv2024

Observation of exceptional line semimetal in three-dimensional non-Hermitian phononic crystals

Non-Hermitian topological phases, which exhibit unique features such as skin effect and exceptional points originated from nontrivial band topologies in complex plane, have attracted enormous attention in condensed-matter physics and metamaterials. Here we report the realization of an exceptional line semimetal in a three-dimensional non-Hermitian phononic crystal. A pair of exceptional rings with opposite topologies are connected by the drumhead bulk states in the first Brillouin zone. The exceptional rings not only possess wave-function topology and thus result in the drumhead surface states, but also host spectral topology and thereby give rise to the hybrid-order geometry-dependent skin effect in three dimensions. Our experimental results evidence the complete non-Hermitian bulk-boundary correspondence of the three-dimensional exceptional line semimetal, and may pave the way for designing non-Hermitian acoustic devices.

cond-mat.mes-hall↗

arXiv2024

Observation of oriented Landau levels in Berry dipole semimetals

Band crossing points, such as Weyl and Dirac points, play a crucial role in the topological classification of materials and guide the exploration of exotic topological phases. The Berry dipole, a three-dimensional band crossing point beyond the Chern class, hosts a dipolar Berry curvature field and gives rise to numerous nontrivial quantum geometric effects. It has been proposed that the Berry dipole exhibits oriented Landau levels, whose spectrum critically relies on the orientation of the applied magnetic field. However, experimental demonstration of this phenomenon has remained elusive. Here we experimentally demonstrate oriented Landau levels by carefully engineering an inhomogeneous acoustic lattice. We observe distinct Landau level spectra and different propagation properties when the orientation of the pseudomagnetic field is reversed. Notably, we discover a new type of helical zero modes whose existence critically depends on the magnetic field's orientation. Our work paves the way for studying band crossings beyond Chern-class crossing points, including Berry multipoles and even-dimensional monopoles. Furthermore, it offers new insight for exploring topological devices.

cond-mat.mes-hall↗

arXiv2024

Valley edge states as bound states in the continuum

Bound states in the continuum (BICs) are spatially localized states with energy embedded in the continuum spectrum of extended states. The combination of BICs physics and nontrivial band topology theory giving rise to topological BICs, which are robust against disorders and meanwhile of the merit of conventional BICs, is attracting wide attention recently. Here, we report valley edge states as topological BICs, which appear at domain wall between two distinct valley topological phases. The robustness of such BICs is demonstrated. The simulations and experiments show great agreement. Our findings of valley related topological BICs shed light on both BICs and valley physics, and may foster innovative applications of topological acoustic devices.

cond-mat.mes-hall↗

arXiv2024

Observation of Higher Order Nodal Line Semimetal in Phononic Crystals

Higher-order topological insulators and semimetals, which generalize the conventional bulk-boundary correspondence, have attracted extensive research interest. Among them, higher-order Weyl semimetals feature two-fold linear crossing points in three-dimensional (3D) momentum space, 2D Fermi-arc surface states, and 1D hinge states. Higher-order nodal-point semimetals possessing Weyl points or Dirac points have been implemented. However, higher-order nodal-line or nodal-surface semimetals remain to be further explored in experiments in spite of many previous theoretical efforts. In this work, we realize a second-order nodal-line semimetal in 3D phononic crystals. The bulk nodal lines, 2D drumhead surface states guaranteed by Zak phases, and 1D flat hinge states attributed to kz-dependent quadrupole moments, are observed in simulations and experiments. Our findings of nondispersive surface and hinge states may promote applications in acoustic sensing and energy harvesting.

cond-mat.mes-hall↗

arXiv2023

Spin-dependent localization of helical edge states in a non-Hermitian phononic crystal

As a distinctive feature unique to non-Hermitian systems, non-Hermitian skin effect displays fruitful exotic phenomena in one or higher dimensions, especially when conventional topological phases are involved. Among them, hybrid skin-topological effect is theoretically proposed recently, which exhibits anomalous localization of topological boundary states at lower-dimensional boundaries accompanied by extended bulk states. Here we experimentally realize the hybrid skin-topological effect in a non-Hermitian phononic crystal. The phononic crystal, before tuning to be non-Hermitian, is an ideal acoustic realization of the Kane-Mele model, which hosts gapless helical edge states at the boundaries. By introducing a staggered distribution of loss, the spin-dependent edge modes pile up to opposite corners, leading to a direct observation of the spin-dependent hybrid skin-topological effect. Our work highlights the interplay between topology and non-Hermiticity and opens new routes to non-Hermitian wave manipulations.

cond-mat.mes-hall↗

arXiv2023

Real-projective-plane hybrid-order topological insulator realized in phononic crystals

The manifold of the fundamental domain of the Brillouin zone is always considered to be a torus. However, under the synthetic gauge field, the Brillouin manifold can be modified by the projective symmetries, resulting in unprecedented topological properties. Here, we realize a real-projective-plane hybrid-order topological insulator in a phononic crystal by introducing the Z_2 gauge field. Such insulator hosts two momentum-space non-symmorphic reflection symmetries, which change the Brillouin manifold from a torus to a real projective plane. These symmetries can simultaneously lead to Klein-bottle and quadrupole topologies in different bulk gaps. The non-symmorphic reflection symmetries on Brillouin real projective plane, edge states of Klein-bottle insulator, and corner states of quadrupole insulator are observed. These results evidence the hybrid-order topology on Brillouin manifold beyond the torus, and enrich the topological physics.

cond-mat.mes-hall↗

arXiv2023

Brillouin Klein space and half-turn space in three-dimensional acoustic crystals

The Bloch band theory and Brillouin zone (BZ) that characterize wave behaviors in periodic mediums are two cornerstones of contemporary physics ranging from condensed matter to topological physics. Recent theoretical breakthrough revealed that, under the projective symmetry algebra enforced by artificial gauge fields, the usual two-dimensional (2D) BZ (orientable Brillouin two-torus) can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct topology and novel topological phases. However, the physical consequence of artificial gauge fields on the more general three-dimensional (3D) BZ (orientable Brillouin three-torus) was so far missing. Here, we report the first theoretical discovery and experimental observation of non-orientable Brillouin Klein space and orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields. We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures. Moreover, we demonstrate a novel 3D Klein bottle insulator featuring a nonzero Z_2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist, radically distinct from all previous topological insulators. Our discovery not only fundamentally modifies the 3D Bloch band theory and 3D BZ, but also opens the door towards a wealth of previously overlooked momentum-space topologies and unexplored topological physics with gauge symmetry beyond the existing paradigms.

physics.class-ph↗

arXiv2023

Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum

Higher-order topological phases have raised widespread interest in recent years with the occurrence of the topological boundary states of dimension two or more less than that of the system bulk. The higher-order topological states have been verified in gapped phases, in a wide variety of systems, such as photonic and acoustic systems, and recently also observed in gapless semimetal phase, such as Weyl and Dirac phases, in systems alike. The higher-order topology is signaled by the hinge states emerging in the common bandgaps of the bulk states and the surface states. In this Letter, we report our first prediction and observation of a new type of hinge states, the bound hinge states in the continuum (BHICs) bulk band, in a higher-order Weyl semimetal implemented in phononic crystal. In contrast to the hinge state in gap, which is characterized by the bulk polarization, the BHIC is identified by the nontrivial surface polarization. The finding of the topological BHICs broadens our insight to the topological states, and may stimulate similar researches in other systems such as electronic, photonic, and cold atoms systems. Our work may pave the way toward high-Q acoustic devices in application.

cond-mat.mes-hall↗

arXiv2023

Topological phononic metamaterials

The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limited to, topological negative refraction, topological 'sasers' (i.e., the phonon analog of lasers), higher-order topological insulating states, non-Abelian topological phases, higher-order Weyl semimetal phases, Majorana-like modes in Dirac vortex structures and fragile topological phases with spectral flows. Here we review the developments in the field of topological phononic metamaterials from both theoretical and experimental perspectives with emphasis on the underlying physics principles. To give a broad view of topological phononics, we also discuss the synergy with non-Hermitian effects and cover topics including synthetic dimensions, artificial gauge fields, Floquet topological acoustics, bulk topological transport, topological pumping, and topological active matters as well as potential applications, materials fabrications and measurements of topological phononic metamaterials. Finally, we discuss the challenges, opportunities and future developments in this intriguing field and its potential impact on physics and materials science.

cond-mat.mes-hall↗

arXiv2023

Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals

Exceptional points and skin effect, as the two distinct hallmark features unique to the non-Hermitian physics, have each attracted enormous interests. Recent theoretical works reveal that the topologically nontrivial exceptional points can give rise to the non-Hermitian skin effect, which is geometry-dependent. However, this kind of novel correspondence between the exceptional points and skin effect remains to be confirmed by experiments. Here, we corroborate the correspondence in a non-Hermitian phononic crystal. The exceptional points connected by the bulk Fermi arcs, and the skin effects with the geometry dependence, are evidenced in simulations and experiments. Our work, building an experimental bridge between the exceptional points and skin effect and uncovering the unconventional geometry-dependent skin effect, expands a horizon in non-Hermitian physics.

cond-mat.mes-hall↗

arXiv2022

Observation of quadruple Weyl point in hybrid-Weyl phononic crystals

The discovery of Weyl semimetals opens the door for searching topological semimetals in physical science. The Weyl points are generally recognized as conventional, quadratic, spin-1, and those of high topological charges. Here we report the observation of the quadruple Weyl point of charge 4, the highest topological charge a twofold degenerate node can carry. Besides the quadruple Weyl point, the phononic semimetal also hosts conventional, quadratic, and spin-1 Weyl points, which stands as a system with yet the richest types of Weyl points. The quadruple-helicoid surface states, specific to the quadruple Weyl point, are demonstrated. The finding of the high-charge Weyl point enriches the knowledge of Weyl semimetals and may stimulate related researches in other systems, such as photonic, mechanical and cold atom systems.

cond-mat.mes-hall↗

arXiv2022

Observation of boundary induced chiral anomaly bulk states and their transport properties

The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined by the bulk topological invariants. To obtain robust transport on the edge, we need to make volumetric changes to many bulk atoms to control the properties of a few edge atoms in a lower dimension. We suggest here that we can do the reverse in some cases: the properties of the edge can guarantee chiral transport phenomena in some bulk modes, achieving phenomena that are essentially the same as those observed in topological valley-Hall systems. Specifically, we show that a topologically trivial 2D hexagonal phononic crystal slab (waveguide) bounded by hardwall boundaries guarantees the existence of bulk modes with chiral anomaly inside a pseudogap. We experimentally observed robust valley-selected transport, complete valley state conversion, and valley focusing of the chiral anomaly bulk states (CABSs) in such phononic crystal waveguides.

cond-mat.mes-hall↗