Related papers: Measuring Chern numbers in Hofstadter strips

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…

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound-states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an…

We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of…

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…

Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states.…

Recent experiments began to explore the topological properties of quench dynamics, i.e. the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well…

We study amorphous systems with completely random sites and find that, through constructing and exploring a concrete model Hamiltonian, such a system can host an exotic phase of topological amorphous metal in three dimensions. In contrast…

In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known…

The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…

Topological invariants are crucial for characterizing topological systems. However, experimentally measuring them presents a significant challenge, especially in non-Hermitian systems where the biorthogonal eigenvectors are often necessary.…

The topology of one-dimensional chiral systems is captured by the winding number of the Hamiltonian eigenstates. Here we show that this invariant can be read-out by measuring the mean chiral displacement of a single-particle wavefunction…

Topological materials are characterized by integer invariants that underpin their robust quantized electronic features, as famously exemplified by the Chern number in the integer quantum Hall effect. Yet, in most candidate systems, the…

In crystalline systems with a superstructure, the electron dispersion can form a nontrivial covering of the Brillouin zone. It is proved that the number of sheets in this covering and its monodromy are topological invariants under ambient…

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…

We propose a scheme for measuring topological properties in a two-photon-driven Kerr-nonlinear resonator (KNR) subjected to a single-photon modulation. The topological properties are revealed through the observation of the Berry curvature…

The appearance of fractional Chern insulators in moir\'e systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a…

Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains…

Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in non-Hermitian parity-time symmetric systems, where the topological invariant remains conserved,…

The accurate determination of non-Hermitian (NH) topological invariants plays a central role in the study of NH topological phases. In this work, we propose a general framework for directly measuring NH topological invariants in…

Topology plays a central role in nearly all disciplines of physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain…