Related papers: Landau levels on the 2D torus: a numerical approac…
The Schr\"odinger equation for an electron under the influence of an electromagnetic field is analyzed based on the conserved operators of the system when the magnetic field is described by Landau's gauge. It is shown that the Lorentz force…
An electron moving on plane in a uniform magnetic field orthogonal to plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schroedinger equation…
Scanning tunneling microscopy and spectroscopy in magnetic field was used to study Landau quantization in graphene and its dependence on charge carrier density. Measurements were carried out on exfoliated graphene samples deposited on a…
We present first evidence for the Landau level structure of Dirac eigenmodes in full QCD for nonzero background magnetic fields, based on first principles lattice simulations using staggered quarks. Our approach involves the identification…
When electrons are confined in a two dimensional (2D) system, typical quantum mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D…
We consider a single band approximation to the random Schroedinger operator in an external magnetic field. The spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice. In…
Magnetotransport measurements are performed in ultraclean (lithographically patterned) graphene nanoribbons down to 70 nm. At high magnetic fields, a fragmentation of the electronic spectrum into a Landau levels pattern with unusual…
An analytical approach has been developed to describe grand canonical equilibrium between a three dimensional (3D) electron system and a two dimensional (2D) one, an energy of which is determined self-consistently with an electron…
We investigate topological insulating states in both two and three dimensions with the harmonic potential and strong spin-orbit couplings breaking the inversion symmetry. Landau-level like quantizations appear with the full 2D and 3D…
Consider the quantum evolution of a charged particle subjected to a uniform magnetic field and an electric field E(t) that exists for a finite period of time. The electric field can induce intra-Landau level transitions (magnetic…
We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to…
The two-dimensional electron system (2DES) is a unique laboratory for the physics of interacting particles. Application of a large magnetic field produces massively degenerate quantum levels known as Landau levels. Within a Landau level the…
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…
This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two $2d$ Bloch eigenvalues which have a conical crossing. It turns out that in the…
It is known that in two-dimensional relativistic Dirac systems placed in orthogonal uniform magnetic and electric fields, the Landau levels collapse as the applied in-plane electric field reaches a critical value $\pm E_c$. We study this…
In this note we sharpen the lower bound from [LLP10] on the spectrum of the 2D Schroedinger operator with a delta-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D…
In elemental bismuth, emptying the low-index Landau levels is accompanied by giant Nernst quantum oscillations. The Nernst response sharply peaks each time a Landau level intersects the chemical potential. By studying the evolution of these…
Motivated by the quantum hall effect, we study N two dimensional interacting fermions in a large magnetic field limit. We work in a bounded domain, ensuring finite degeneracy of the Landau levels. In our regime, several levels are fully…
We study the Landau levels in curved graphene sheets by measuring the discrete energy spectrum in the presence of a magnetic field. We observe that in rippled graphene sheets, the Landau energy levels satisfy the same square root dependence…
Two-dimensional systems with $C_{2}\mathcal{T}$ ($P\mathcal{T}$) symmetry exhibit the Euler class topology $E\in\mathbb{Z}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying…