Related papers: Topological invariants for interface modes

Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…

Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian…

Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation…

We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More generally we consider complete intersections of arbitrary dimension equipped with…

We propose the concept of `topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of topological Hamiltonian are significantly different from the physical energy spectra, but we show…

The interface between two materials described by spectrally gapped Hamiltonians is expected to host an in-gap interface mode, whenever a certain topological invariant changes across the interface. We provide a precise statement of this…

The main focus of this paper is a nonparametric filtering technique for the estimation of interface geometry in bulk materials obtainable from modern imaging measurements. The filtering methodology relies on an assumed hierarchy of…

We present a general recipe to describe topological phase transitions in condensed matter systems with interactions. We show that topological invariants in the presence of interactions can be efficiently calculated by means of a…

The occurrence of a topological phase transition can be demonstrated by a direct observation of a change in the topological invariant. For holographic topological semimetals, a topological Hamiltonian method needs to be employed to…

Examples of non-hermitian quantum systems admitting topological insulator phase are presented in one, two and three space dimensions. All of these non-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is maintained…

This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order…

Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a…

Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving…

We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant,…

We study the behavior of fermion spectral functions for the holographic topological Weyl and nodal line semimetals. We calculate the topological invariants from the Green functions of both holographic semimetals using the topological…

This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…

Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological…

Visualization of turbulent flows is a powerful tool to help understand the turbulence dynamics and induced transport. However, it does not provide a quantitative description of the observed structures. In this paper, an approach to…

The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…