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Chern numbers can be calculated within a frame of vortex fields related to phase conventions of a wave function. In a band protected by gaps the Chern number is equivalent to the total number of flux carrying vortices. In the presence of…

Mesoscale and Nanoscale Physics · Physics 2022-10-14 Axel Fünfhaus , Thilo Kopp , Elias Lettl

Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological…

Strongly Correlated Electrons · Physics 2015-11-25 Woo-Ram Lee , Kwon Park

Data from angle resolved photo-emission spectroscopy (ARPES) often serves as a smoking-gun evidence for the existence of topological materials. It provides the energy dispersion curves of the topological boundary modes which characterize…

Mesoscale and Nanoscale Physics · Physics 2015-12-08 Zohar Ringel

Scanning Kelvin probe microscopy (SKPM) is a powerful technique for investigating the electrostatic properties of material surfaces, enabling the imaging of variations in work function, topology, surface charge density, or combinations…

Applied Physics · Physics 2024-07-26 Isaac C. D. Lenton , Felix Pertl , Lubuna Shafeek , Scott R. Waitukaitis

Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…

Quantum Physics · Physics 2016-06-01 Zhihuang Luo , Chao Lei , Jun Li , Xinfang Nie , Zhaokai Li , Xinhua Peng , Jiangfeng Du

The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The…

Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials. Through the bulk-boundary correspondence, these topological phases have a one-to-one…

Disordered Systems and Neural Networks · Physics 2025-10-24 R. Moola , A. Mckenna , M. Hilke

The surface and bulk states in topological materials have shown promise in many applications. Grey or $\alpha$-Sn, the inversion symmetric analogue to HgTe, can exhibit a variety of these phases. However there is disagreement in both…

Angle-resolved photoemission spectroscopy (ARPES) is the most powerful technique to investigate the electronic band structure of crystalline solids. To completely characterize the electronic structure of topological materials, one needs to…

We formulate a bulk spectroscopic method for direct measurement of the topological invariant of nondegenerate band crossings in Weyl semimetals. We demonstrate how polarization-resolved resonant x-ray scattering captures the winding of the…

Mesoscale and Nanoscale Physics · Physics 2016-09-21 Stefanos Kourtis

The Su-Schrieffer-Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and…

Quantum Gases · Physics 2019-07-01 Dizhou Xie , Wei Gou , Teng Xiao , Bryce Gadway , Bo Yan

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…

Quantum Physics · Physics 2024-11-12 Min Yu , Xiangbei Li , Yaoming Chu , Bruno Mera , F. Nur Ünal , Pengcheng Yang , Yu Liu , Nathan Goldman , Jianming Cai

Quantum topology categorizes physical systems in integer invariants, which are robust to some deformations and certain types of disorder. A prime example is the Su-Schrieffer-Heeger (SSH) model, which has two distinct topological phases,…

Disordered Systems and Neural Networks · Physics 2026-01-01 Michael Hilke

The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization…

Mesoscale and Nanoscale Physics · Physics 2019-11-20 Tomoki Ozawa , Nathan Goldman

Angle-resolved photoemission spectroscopy (ARPES) -- with its exceptional sensitivity to both the binding energy and momentum of valence electrons in solids -- provides unparalleled insights into the electronic structure of quantum…

Strongly Correlated Electrons · Physics 2024-09-06 Fabio Boschini , Marta Zonno , Andrea Damascelli

A topological superconductor is a fully gapped superconductor that exhibits exotic zero-energy Andreev surface states at interfaces with a normal metal. In this paper we investigate the properties of a three-dimensional time reversal…

Superconductivity · Physics 2010-11-11 Andreas P. Schnyder , P. M. R. Brydon , Dirk Manske , Carsten Timm

In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices.…

Optics · Physics 2024-02-19 Stephan Wong , Terry A. Loring , Alexander Cerjan

Quantum phases provide us with important information for understanding the fundamental properties of a system. However, the observation of quantum phases, such as Berry's phase and the sign of the matrix element of the Hamiltonian between…

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…

Atomic force microscopy (AFM) is widely used to measure surface topography of solid, soft, and living matter at the nanoscale. Moreover, by mapping forces as a function of distance to the surface, AFM can provide a wealth of information…