Related papers: Second Euler number in four dimensional synthetic …
We introduce a novel gauge-invariant, quantized interband index in two-dimensional (2D) multiband systems. It provides a bulk topological classification of a submanifold of parameter space (e.g., an electron valley in a Brillouin zone), and…
Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topological transforms to be defined…
Using numerical simulations, we show that the asymptotic states of two-dimensional (2D) Euler turbulence exhibit large-scale flow structures due to nonzero energy transfers among small wavenumber modes. These asymptotic states, which depend…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly-controllable simulations of…
We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex…
2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…
A higher order topological insulator is an extended notion of the conventional topological insulator, which belongs to a special class of topological insulators where the conventional bulk-boundary correspondence is not applicable. The bulk…
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf $\mathbb{Z}$ invariant, a linking…
Chirality, a fundamental concept from biological molecules to advanced materials, is prevalent in nature. Yet, its intricate behavior in specific topological systems remains poorly understood. Here, we investigate the emergence of hidden…
Finite-dimensional state-space representations of unsteady aerodynamics implicitly assume a system with fading memory. However, the impulse response of the two-dimensional inviscid (Euler) equations is characterized by an asymptotic…
For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…
Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor, next-nearest-neighbor and…
Topology in quantum systems is typically considered in infinite crystals in one, two, or higher integer dimensions. Here, we show that one can continuously transform a system between a topological phase associated with one dimension and a…
Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eight-fold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts.…
A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…
The topological phase transition between two band insulators is mediated by a gapless state whose low-energy band structure normally contains sufficient information for describing the topology change. In this work, we show that there is a…