arXiv subjects

Y. X. Zhao

Publications and source records attributed to Y. X. Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Complete Topological Classification with P and T Symmetries: Revealing a Topological Invariant Invisible to K-Theory

The K-theoretic framework provides a complete topological classification of the tenfold symmetry classes and has been generalized to incorporate crystalline symmetries. Here, we show that this classification is incomplete even in the elementary case of spinless systems possessing both P and T symmetries. We obtain the complete classification through a first-principles analysis of the topological classes of P- and T-symmetric bands, namely, by classifying the corresponding symmetric clutching data. We identify a topological invariant that is invisible from the K-theoretic perspective when the occupied states at each inversion-invariant momentum have uniformly positive or uniformly negative parity. In special cases, such as when all inversion-invariant momenta have uniformly positive parity, this invariant can be interpreted as the second Stiefel--Whitney class or the Euler number defined over an inversion fundamental domain, namely, half of the Brillouin zone. Our work not only reveals a new topological invariant that cannot be determined from the parity spectra at inversion-invariant momenta under P and T symmetries, but also demonstrates the existence of crystalline topological phases that are absent from the K-theoretic classification.

cond-mat.mes-hall↗

arXiv2026

Realization of Arbitrary Gauge Fields via Symmetry-Protected Zero Modes

Gauge fields are fundamental to modern physics, but prescribed gauge configurations are often difficult to implement in artificial systems. Here, we present a general scheme for realizing arbitrary static $\mathrm{O}(N)$ lattice gauge configurations using symmetry-protected zero modes of sublattice-imbalanced bipartite units. The target $\mathrm{O}(N)$ link on each bond is encoded in the connectivity and strengths of positive microscopic couplings. By decoupling the zero-mode manifold from the remaining modes, the target gauge Hamiltonian forms an exact spectral block of the microscopic tight-binding model rather than a perturbative approximation. We experimentally demonstrate this framework in acoustic crystals through a $\mathbb{Z}_2$ quadrupole topological insulator, an $\mathrm{SO}(2)$ Hofstadter model, and an $\mathrm{SO}(3)$ non-Abelian topological insulator. Our results provide a general and accessible route to gauge-field physics in artificial systems.

cond-mat.mes-hall↗

arXiv2026

A New Low $Q^2$ Measurement of the Proton's $g_1$ Spin Structure Function from Longitudinal & Transverse Polarized Data

The proton's spin structure has proven to be far more complicated than was originally believed, and has been the subject of a number of experimental investigations. %Early measurements of the proton's spin structure function $g_1$ showed that the proton does not solely derive its spin from the spins of its quarks, starting the `proton spin crisis'. Of particular interest are the spin structure functions $g_1$ and $g_2$, which can be used to generate moments to directly compare experimental results to Chiral Perturbation Theory and other theories of Quantum Chromodynamics (QCD). The proton's $g_1$ structure function has been the subject of two other recent low momentum transfer experiments, but there are currently no published low momentum transfer measurements which collected data on the proton structure functions using both a longitudinally-polarized and a transversely-polarized target at the same kinematics. In this paper, we present the longitudinally polarized results of the Jefferson Lab E08-027 experiment, along with linked moments which combine this new result with the previously published transversely-polarized data from the same experiment. These results provide a proton $g_1$ extraction measured with very high precision across the resonance region, and provide new information on the value of $g_1$ dependent sum rules and moments.

nucl-ex↗

arXiv2026

Flux-Mediated Correspondence Between Real- and Momentum-Space Nonsymmorphicity

Momentum-space nonsymmorphic symmetries have recently attracted significant interest in both artificial and condensed-matter crystals, whereas real-space nonsymmorphic symmetries have long played an important role in the study of crystalline topological phases. Here, we establish a general theory of momentum-space crystallographic groups that emerge from projective representations of real-space crystallographic groups in the presence of gauge flux, applicable in particular to real-space nonsymmorphic groups. A central result is a flux-mediated ``bi-nonsymmorphicity'' relation that reveals a structural correspondence between real-space and momentum-space nonsymmorphicity mediated by gauge flux. This relation implies that, under a symmetric gauge flux, real-space nonsymmorphicity can enforce momentum-space nonsymmorphicity, and that in some cases a symmetric gauge flux requires nonsymmorphicity in both real and momentum space. Our work not only identifies a fundamental structure in projective crystal symmetries, but also provides guiding principles for designing artificial crystals and condensed-matter platforms that exhibit both real-space and momentum-space nonsymmorphic symmetries.

cond-mat.mes-hall↗

arXiv2026

$PT$ Symmetry's Real Topology

Symmetry-protected topological phases have been a central theme in condensed matter physics and beyond over the past two decades. Most efforts have focused on topological classifications of physical systems under given symmetries, while the intrinsic topology of the symmetries themselves has received much less attention. Here, we show that, in generic non-interacting spinless crystals, the spacetime inversion symmetry $PT$ naturally carries a real vector-bundle structure whose topology is characterized by Stiefel--Whitney (SW) classes. In contrast to previous work, where SW classes were used to describe the topology of real valence bundles protected by $PT$, we identify SW classes associated to the $PT$ symmetry itself. These symmetry SW classes can endow the \emph{total} real bundle of a $PT$-symmetric band structure with nontrivial topology, overturning the common assumption that the total bundle is always trivial. As a consequence, valence and conduction bands can exhibit asymmetric SW classes, in sharp contrast to the usual symmetric scenario. We further demonstrate that the symmetry SW classes provide a refined distinction between atomic insulator phases. Our results underscore the importance of treating crystal symmetries as topological objects in their own right, rather than focusing solely on the topology of energy bands.

cond-mat.mes-hall↗

arXiv2025

A Cohomological Framework for Topological Phases from Momentum-Space Crystallographic Groups

Crystallographic groups are conventionally studied in real space to characterize crystal symmetries. Recent work has recognized that when these symmetries are realized projectively, momentum space inherently accommodates nonsymmorphic symmetries, thereby evoking the concept of \textit{momentum-space crystallographic groups} (MCGs). Here, we reveal that the cohomology of MCGs encodes fundamental data of crystalline topological band structures. Specifically, the collection of second cohomology groups, $H^2(\Gamma_F,\mathbb{Z})$, for all MCGs $\Gamma_F$, provides an exhaustive classification of Abelian crystalline topological insulators, serving as an effective approximation to the full crystalline topological classification. Meanwhile, the third cohomology groups $H^3(\Gamma_F,\mathbb{Z})$ across all MCGs exhaustively classify all possible twistings of point-group actions on the Brillouin torus, essential data for twisted equivariant K-theory. Furthermore, we establish the isomorphism $H^{n+1}(\Gamma_F,\mathbb{Z})\cong H^n\big(\Gamma_F,\operatorname{\mathcal{F}}(\mathbb{R}^d_F,U(1))\big)$ for $ n\ge 1$, where $\operatorname{\mathcal{F}}(\mathbb{R}^d_F,U(1))$ denotes the space of continuous $U(1)$-valued functions on the $d$D momentum space $\mathbb{R}^d_F$. The case $n=1$ yields a complete set of topological invariants formulated in purely algebraic terms, which differs fundamentally from the conventional formulation in terms of differential forms. The case $n=2$, analogously, provides a fully algebraic description for all such twistings. Thus, the cohomological theory of MCGs serves as a key technical framework for analyzing crystalline topological phases within the general setting of projective symmetry.

cond-mat.mes-hall↗

arXiv2025

Switchable half-quantum flux states in a ring of the kagome superconductor CsV$_3$Sb$_5$

Magnetic flux quantization in units of $\Phi_0 = h/2e$ is a defining feature of superconductivity, rooted in the charge-2e nature of Cooper pairs. In a ring geometry, the flux quantization leads to oscillations in the critical temperature with magnetic flux, known as the Little-Parks effect. While the maximal critical temperature is conventionally at zero flux, departures from this rule, for instance shifts by a half-quantum flux $\Phi_0/2$, clearly signal unconventional superconducting states and require sign-changing order parameters. Historically, such $\pi$-phase shifts in Little-Parks oscillations have been found in tricrystals or engineered ring structures that intentionally incorporate a $\pi$-phase shift. Here we report the discovery of switchable half-quantum flux states in rings made from single crystals of the kagome superconductor CsV$_3$Sb$_5$. We observe Little-Parks oscillations with a $\pi$-phase shift at zero bias current, which can be reversibly tuned to conventional Little-Parks oscillations upon applying a bias current. Between the $\pi$-phase and 0-phase regimes, $h/4e$ periodic oscillations appear. Our observations suggest unconventional pairing, potentially in the form of a multicomponent order parameter in the kagome superconductor CsV$_3$Sb$_5$, and reveal an electrically tunable landscape of competing superconducting condensates and fractional flux states.

cond-mat.supr-con↗

arXiv2025

Universal valley filtering via uniform dissipation and velocity contrast

Valley, as a ubiquitous degree of freedom in lattices, has found wide applications in both electronic and classical-wave devices in recent years. However, achieving valley-polarized states, a prerequisite for valley-based operations, still remains challenging. Here, we propose and experimentally demonstrate a universal non-Hermitian mechanism for valley filtering using only uniform background dissipation, which creates a propagation length contrast between valleys through their intrinsic group velocity differences. We implement this concept in an acoustic crystal, observing switchable and robust valley polarization of sound through large-scale field mapping. Remarkably, our approach is solely based on uniform loss, without the need for any special lattice structures, tailored excitations, or external fields. We further provide designs of our non-Hermitian valley filter on photonic and electronic platforms. Our results offer a simple and effective solution to valley-polarized state generation and may advance the development of novel valley-based devices in both classical and quantum regimes.

cond-mat.mes-hall↗

arXiv2025

Projective crystal symmetry and topological phases

Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and experimental studies have now brought this to light, demonstrating that projective representations of crystal symmetries lead to remarkable consequences in condensed matter physics and various artificial crystals, particularly in their connection to topological phenomena. In this article, we explain the basic ideas and notions underpinning these recent developments and share our perspective on this emerging research area. We specifically highlight that the appearance of momentum-space nonsymmorphic symmetry is a unique feature of projective crystal symmetry representations. This, in turn, has the profound consequence of reducing the fundamental domain of momentum space to all possible flat compact manifolds, which include torus and Klein bottle in 2D and the ten platycosms in 3D, presenting a significantly richer landscape for topological structures than conventional settings. Finally, the ongoing efforts and promising future research directions are discussed.

cond-mat.mes-hall↗

arXiv2025

Observation of returning Thouless pumping

Introduced by David Thouless in 1983, Thouless pumping exemplifies topological properties in topological systems, where the transported charge is quantized by the Chern number. Recently, returning Thouless pumping was theoretically proposed, in which quantized charge is pumped during the first half of the cycle but returns to zero in the second half. This mechanism leads to crystalline symmetry-protected delicate topological insulators. Unlike conventional topological bands, a delicate topological band is Wannierizable but not atomically obstructed, which features multicellular Wannier functions extending beyond a single unit cell. Here, by replacing the second dimension with a synthetic dimension, we realize a two-dimensional delicate topological insulator via a set of one-dimensional acoustic crystals with fine-tuned geometric parameters. Through acoustic bands and wavefunction measurements, we directly observe returning Thouless pumping and symmetric multicellular Wannier functions, followed by establishing the bulk-boundary correspondence between sub-Brillouin zone Chern numbers and gapless boundary modes. As enriched by crystalline symmetries, our experimental demonstration of returning Thouless pumping expands the current understanding of topological phases of matter.

cond-mat.mes-hall↗

arXiv2025

Topological $\pi/2$ modes in photonic waveguide arrays

Periodic driving is a powerful tool to generate exotic topological phases without static counterparts, such as the anomalous chiral edge modes from bulk bands with zero Chern number and topological $\pi$ modes exhibiting period-doubled dynamics. Recently, a new class of Floquet topological mode, namely the $\pi/2$ mode, which carries four-period periodicity and has potential applications in quantum computing, was proposed based on a square-root method and realized in an acoustic system. Here we propose a laser-written waveguide array lattice to realize topological $\pi/2$ modes in photonics. Our photonic model simulates a square-root periodically driven Su-Schrieffer-Heeger model and has a rich phase diagram allowing for the co-existence of conventional zero, $\pi$ modes, and the new $\pi/2$ modes. Through numerical simulations of the wave equation, we uncover the unique four-period evolution feature of the $\pi/2$ modes. Our model, which only contains four waveguides per unit cell and two driving steps, is easy to implement with current fabrication techniques and may find applications in quantum optics.

physics.optics↗

arXiv2025

Asymmetric real topology of conduction and valence bands

Previously, it was believed that conduction and valence bands exhibit a symmetry: They possess opposite topological invariants (e.g., the Chern numbers of conduction and valence bands for the Chern insulator are $\pm C$). However, we present a counterexample: The second Stiefel-Whitney numbers for conduction and valence bands over the Klein bottle may be asymmetric, with one being nontrivial while the other trivial. Here, the Stiefel-Whitney classes are the characteristic classes for real Bloch functions under $PT$ symmetry with $(PT)^2=1$, and the Klein bottle is the momentum-space unit under the projective anticommutation relation of the mirror reflection reversing $x$ and the translation along the $y$ direction. The asymmetry originates from the algebraic difference of real cohomology classes over the Klein bottle and torus. This discovery is rooted in the foundation of topological band theory, and has the potential to fundamentally refresh our current understanding of topological phases.

cond-mat.mes-hall↗

arXiv2025

Brillouin Platycosms and Topological Phases

There exist ten distinct closed flat $3$D manifolds, known as platycosms, which hold significance in mathematics and have been postulated as potential geometric models for our universe. In this work, we demonstrate their manifestation as universes of Bloch particles, namely as momentum-space units referred to as Brillouin platycosms, which are natural extensions of the Brillouin torus within a broader framework of projective crystallographic symmetries. Moreover, we provide exact K-theoretical classifications of topological insulators over these platycosms by the Atiyah-Hirzebruch spectral sequence, and formulate a complete set of topological invariants for their identification. Topological phase transitions are generically characterized by Weyl semimetals, adhering to the generalized Nielsen-Ninomiya theorem: the total chirality number over a Brillouin platycosm is even (zero) if the platycosm is non-orientable (orientable). Our work generalizes the notion of Brillouin torus to ten Brillouin platycosms and therefore fundamentally diversifies the stages on which Block wavefunctions can perform their topological dance.

cond-mat.mes-hall↗

arXiv2024

Instanton-Induced Supersymmetry Breaking in Topological Semimetals

Supersymmetry (SUSY) proposed as an elementary symmetry for physics beyond the Standard Model has found important applications in various areas outside high-energy physics. Here, we systematically implement supersymmetric quantum mechanics -- exhibiting fundamental SUSY properties in the simple setting of quantum mechanics -- into a wide range of topological semimetals, where the broken translational symmetry, e.g., by a magnetic field, is effectively captured by a SUSY potential. We show that the dynamical SUSY breaking via the instanton effect over the SUSY potential valleys works as the underlying mechanism for the gap opening of the topological semimetallic phases, and the magnitude of the instanton effect is proportional to the energy gap. This instanton mechanism provides a simple criterion for determining whether the energy gap has been opened, without resorting to detailed calculations, i.e., a finite energy gap is opened if and only if the SUSY potential has an even number of zeros. Our theory leads to previously unexpected results: even an infinitesimal magnetic field can open a gap in topologically robust Dirac, Weyl, and nodal-line semimetallic phases due to the dynamical SUSY breaking. Overall, the revealed connection between SUSY quantum mechanics and non-uniform topological semimetals can elucidate previously ambiguous phenomena, provide guidance for future investigations, and open a new avenue for exploring topological semimetals.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian Dirac cones with valley-dependent lifetimes

Relativistic quasiparticles emerging from band degeneracies in crystals play crucial roles in the transport and topological properties of materials and metamaterials. Quasiparticles are commonly described by Hermitian Hamiltonians, with non-Hermiticity usually considered detrimental. In this work, we show that such an assumption of Hermiticity can be lifted to bring quasiparticles into non-Hermitian regime. We propose a concrete lattice model containing two Dirac cones with valley-dependent lifetimes. The lifetime contrast enables an ultra-strong valley selection rule: only one valley can survive in the long-time limit regardless of the excitation, lattice shape and other details. This property leads to an effective parity anomaly with a single Dirac cone and offers a simple way to generate vortex states. Additionally, extending non-Hermitian features to boundaries generates valley kink states with valley-locked lifetimes, making them effectively unidirectional and more resistant against inter-valley scattering. All these phenomena are experimentally demonstrated in a non-Hermitian electric circuit lattice.

cond-mat.mes-hall↗

arXiv2024

Balancing chemical equations: form the perspective of Hilbert basis

The balancing of chemical equations is a basic problem in chemistry. A commonly employed method is to convert the task to a linear algebra problem, and then solve the null space of the constructed formula matrix. However, in this method, the directly obtained solution may be invalid, and there is no canonical choice of independent basis reactions. Here, we show that these drawbacks originate from the fact that the fundamental structure of solutions here is not a linear space but a positive affine monoid. This new understanding enables a systematic approach and a complete description of all possible reactions by a unique set of independent elementary reactions, called Hilbert-basis reactions. By clarifying its underlying mathematical structure, our work offers a new perspective on this old problem of balancing chemical equations.

physics.chem-ph↗

arXiv2024

Hilbert band complexes and their applications

The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of band complexes. By translating the symmetry conditions into a set of band balance equations, we show that all possible band structure solutions can be described by a positive affine monoid structure, which has a unique minimal set of generators, called Hilbert basis. We show that Hilbert basis completely determine whether a band complex is reducible and how it can be decomposed. The band complexes corresponding to Hilbert basis vectors, termed as Hilbert band complexes (HBCs), can be regarded as elementary building blocks of band structures. We develop algorithms to construct HBCs, analyze their graph features, and merge them into large complexes. We find some interesting examples, such as HBCs corresponding to complete bipartite graphs, and complexes which can grow without bound by successively merging a HBC.

cond-mat.mes-hall↗

arXiv2024

Topological classification for chiral symmetry with non-equal sublattices

Chiral symmetry on bipartite lattices with different numbers of $A$-sites and $B$-sites is exceptional in condensed matter, as it gives rise to zero-energy flat bands. Crystalline systems featuring chiral symmetry with non-equal sublattices include Lieb lattices, dice lattices, and particularly Moir\'e systems, where interaction converts the flat bands into fascinating many-body phases. In this work, we present a comprehensive classification theory for chiral symmetry with non-equal sublattices. First, we identify the classifying spaces as Stiefel manifolds and derive the topological classification table. Then, we extend the symmetry by taking $\mathcal{PT}$ symmetry into account, and ultimately obtain three symmetry classes corresponding to complex, real, and quaternionic Stiefel manifolds, respectively. Finally, we apply our theory to clarify the topological invariant for $\mathcal{PT}$-invariant Moir\'e systems and construct physical models with Lieb and dice lattice structures to demonstrate our theory. Our work establishes the theoretical foundation of topological phases protected by chiral symmetries with non-equal sublattices.

cond-mat.mes-hall↗