Related papers: Preparing and probing Chern bands with cold atoms

Topological invariants, including the Chern numbers, can topologically classify parameterized Hamiltonians. We find that topological invariants can be properly defined and calculated even if the parameter space is discrete, which is done by…

Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index.…

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states.…

Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We…

The emerging possibilities to steer and control electronic motion on subcycle time scales with strong electric fields enable studying the nonperturbative optical response and Bloch bands' topological properties, originated from Berry's…

We construct an artificial U(1) gauge field in the cold atom system to form a monopole along with vortices. It is supposed that the cold atoms are confined on a spherical surface, and two sets of identical laser beams in the opposite…

This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different…

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However,…

Thouless pumping with nontrivial topological phases provides a powerful means for the manipulation of matter waves in one-dimensional lattice systems. The band topology is revealed by the quantization of pumped charge. In the context of…

We introduce and study the Chern filtration on the cohomology of the moduli of bundles on curves. This can be viewed as a natural cohomological invariant defined via tautological classes that interpolates between additive Betti numbers and…

Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band…

We analyze the energy spectrum and eigenstates of cold atoms in a tilted brick-wall optical lattice. When the tilt is applied, the system exhibits a sequence of topological phase transitions reflected in an abrupt change of the eigenstates.…

We propose and analyze a general scheme to create chiral topological edge modes within the bulk of two-dimensional engineered quantum systems. Our method is based on the implementation of topological interfaces, designed within the bulk of…

Topological quantum phase transitions in superconductivity are discussed on two dimensional lattices. The main focus is on the Chern number for superconducting states. Each superconductivity is characterized by the Chern number, and the…

Topological behavior has been observed in quantum systems including ultracold atoms. However, background harmonic traps for cold-atoms hinder direct detection of topological edge states arising at the boundary because the distortion fuses…

Here we study the systematic evolution of the topological properties of a Chern insulator in presence of an electronic dispersion that can be tuned smoothly from being Dirac-like till a semi-Dirac one and beyond. The band structure under…

We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical…

The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…

We investigate the Bloch bands and develop a linear response theory for nonlinear systems, where the interplay between topological parameters and nonlinearity leads to new band structures. The nonlinear system under consideration is…