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The engineering of topological non-trivial states of matter, using cold atoms, has made great progress in the last decade. Driven by experimental successes, it has become of major interest in the cold atom community. In this work we…
Local topological markers are used to characterize Chern insulators in the presence of spatial inhomogeneities, such as boundaries and disorder. In this paper, we study the local Chern marker in systems with partial translational symmetry.…
Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…
A system having macroscopic patches in different topological phases have no well-defined global topological invariant. To treat such a case, the quantities labeling different areas of the sample according to their topological state are…
Local topological markers are effective tools for determining the topological properties of both homogeneous and inhomogeneous systems. The Chern marker is an established topological marker that has previously been shown to effectively…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
Robust zero modes supported by defects is one of the key features of topological matter. Its presence renders a system topologically inhomegeneuous, thus having no well-defined global topological invariant. The quantities labeling different…
A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…
We propose a simple scheme for tomography of band-insulating states in one- and two-dimensional optical lattices with two sublattice states. In particular, the scheme maps out the Berry curvature in the entire Brillouin zone and extracts…
Local topological markers, topological invariants evaluated by local expectation values, are valuable for characterizing topological phases in materials lacking translation invariance. The Chern marker -- the Chern number expressed in terms…
We introduce a scheme by which flat bands with higher Chern number $\vert C\vert>1$ can be designed in ultracold gases through a coherent manipulation of Bloch bands. Inspired by quantum-optics methods, our approach consists in creating a…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
The low-energy excitations of a spin system can display Bloch bands with non-trivial topological properties. While topological magnons can be identified through the detection of chiral propagating modes at the sample's edge, an intriguing…
A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for…
Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems…
Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…
Cold-atom experiments in optical lattices offer a versatile platform to realize various topological quantum phases. A key challenge in those experiments is to unambiguously probe the topological order. We propose a method to directly…
We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the…