arXiv subjects

J. X. Dai

Publications and source records attributed to J. X. Dai.

5 recordsLinked to original sources

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

$PT$ 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

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↗

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 Moiré 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 Moiré 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↗

arXiv2023

Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence: while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results establish the Stiefel-Whitney topological charges as intrinsic topological invariants for topological materials, with their unique bulk-boundary correspondence beyond the conventional framework of topological band theory.

cond-mat.mes-hall↗