相关论文: Topological Triviality of Flat Hamiltonians

We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple…

The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…

Two-dimensional systems in magnetic fields host rich physics, most notably the quantum Hall effect arising from Landau level quantization. In a broad class of two-dimensional models, flat bands with topologically nontrivial band…

The Landau level spectra and the quantum Hall effect of ABA-stacked multilayer graphenes are studied in the effective mass approximation. The low-energy effective mass Hamiltonian may be partially diagonalized into an approximate…

On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact…

When electrons moving in two-dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels, which are the basis for the quantum Hall effect. Landau levels can also arise from pseudomagnetic…

Landau levels have represented a very rich field of research, which has gained widespread attention after their application to quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of…

We show that the Landau quantum systems (or integer quantum Hall effect systems) in a plane, sphere or a hyperboloid, can be explained in a complete meaningful way from group-theoretical considerations concerning the symmetry group of the…

Landau levels are the eigenstates of a charged particle in two dimensions under a magnetic field, and are at the heart of the integer and fractional quantum Hall effects, which are two prototypical phenomena showing topological features.…

In this paper we study the Landau levels in the non-relativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved spacetime background with the…

In the presence of a periodic potential Landau levels (LLs) are broadened, forming a barrier for accurate simulation of fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of…

Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1$^\circ$. This is now strongly supported by experiment, which furthermore…

The quest for universal signatures of topological phases is fundamentally important since these properties are robust to variations in system-specific details. Here we present general results for the response of quantum Hall states to…

The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light (and with the jargon) of theory of topological insulators. In particular it is shown that the Landau…

Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures…

Flat bands correspond to the spatial localization of a quantum particle moving in a field with discrete or continuous translational invariance. The canonical example is the flat Landau levels in a homogeneous magnetic field. Several…

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the…

We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of…

Flat bands underlie a diverse range of quantum phenomena, from strongly correlated phases to superconductivity. We theoretically establish that a two-dimensional electron gas under a linear magnetic-field gradient and a transverse electric…

It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…