Related papers: Geometrical Responses of Generalized Landau Levels…
Quantum geometry is a fundamental concept to characterize the local properties of quantum states. It is recently demonstrated that saturating certain quantum geometric bounds allows a topological Chern band to share many essential features…
A single Landau level (LL) dressed with periodic electrostatic potentials can realize a plethora of interacting topological phases where the Hall conductivity generally does not equal to the LL filling factor. Their physics can be captured…
The rise of moir\'{e} materials has led to experimental realizations of integer and fractional Chern insulators in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee a Abelian…
According to the Onsager's semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this…
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.…
We introduce a universal formulation of the generalized real space interactions with translational invariance, when projected into a single Landau level, can be equivalent to density-density interaction projected into any Chern bands (e.g.…
Flatbands appear in many condensed matter systems, such as in high magnetic fields, correlated materials and moire heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study…
The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a…
Landau levels (LLs) are the massively-degenerate discrete energy spectrum of a charged particle in a transverse magnetic field and lie at the heart of many intriguing phenomena such as the integer and fractional quantum Hall effects as well…
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…
Physics of two-dimensional electron gases under perpendicular magnetic field often displays three distinct stages when increasing the field amplitude: a low field regime with classical magnetotransport, followed at intermediate field by a…
Analytical calculations based on a Landau Level (LL) picture are reported for an interface (with a finite-width Quantum Well (QW)) and for a fully three-dimensional charged quantum electronic system in an external magnetic field. They lead…
We discuss the Berry curvature calculations of the Hall viscosity for the unprojected to the lowest Landau level wave function of the Fermi-liquid-like state. We conclude, within assumptions made, that in the linear response, with small…
We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point…
Analytical calculations based on a Landau Level (LL) picture are reported for an interface (with a finite-width Quantum Well (QW)) and for a fully three-dimensional charged quantum electronic system in an external magnetic field. They lead…
We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband…
We show that Hall viscosity in lattice bands is governed by a band-projected electric quadrupole encoded within the quantum geometry: Berry curvature sets the projected-coordinate algebra, while the quantum metric determines the quadrupolar…
We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with…
In this Letter, we study topological flat bands with distinct features that deviate from conventional Landau level behavior. We show that even in the ideal quantum geometry limit, moire flat band systems can exhibit physical phenomena…
We propose a geometric mechanism for fractional quantum Hall states based on impurity-induced correlations within a Landau level. A correlated distribution of ionized impurities partially modifies the Landau-level degeneracy through…