Abstract We consider the level-crossing problem in a three-level system with non-linearly time-varying Hamiltonian (time-dependence t). We study the validity of the so-called independent crossing approximation in the Landau-Zener model by making comparison with results obtained numerically in density matrix approach. We also demonstrate the failure of the so-called ”nearest zero” approximation ...

The N → ∞ limit of the edges of finite planar electron densities is discussed for higher Landau levels. For full filling, the particle number is correlated with the magnetic flux, and hence with the boundary location, making the N → ∞ limit more subtle at the edges than in the bulk. In the nth Landau level, the density exhibits n distinct steps at the edge, in both circular and rectangular samp...

In previous papers we solved the Landau problems, indexed by 2M , for a particle on the “superflag” SU(2|1)/[U(1) × U(1)], the M = 0 case being equivalent to the Landau problem for a particle on the “supersphere” SU(2|1)/[U(1|1)]. Here we solve these models in the planar limit. For M = 0 we have a particle on the complex superplane C; its Hilbert space is the tensor product of that of the Landa...

The Landau problem is discussed in two similar but still different non-commutative frameworks. The “standard” one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The “exotic” approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states as advocated by Peierls, and widely us...

Interaction driven integer quantum-Hall effects are anticipated in graphene bilayers because of the near degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate k3/2 dispers...

In the strong magnetic field fractional quantum Hall regime, electrons in a twodimensional electron system are confined to their lowest Landau level. Because of the macroscopic Landau level degeneracy nearly all physical properties at low energies and temperatures are then entirely determined by electron-electron interactions. The properties of these non-Fermi-liquid electronic systems continue...

We present magneto-Raman scattering studies of electronic inter-Landau level excitations in quasineutral graphene samples with different strengths of Coulomb interaction. The band velocity associated with these excitations is found to depend on the dielectric environment, on the index of Landau level involved, and to vary as a function of the magnetic field. This contradicts the single-particle...

The charge carriers in graphene are massless Dirac fermions and exhibit a relativistic Landau-level quantization in a magnetic field. Recently, it has been reported that, without any external magnetic field, quantized energy levels have been also observed from strained graphene nanobubbles on a platinum surface, which were attributed to the Landau levels of massless Dirac fermions in graphene f...

Using scanning tunneling spectroscopy, we study a 3D topological insulator Bi(2)Te(3) with a periodic structural deformation (buckling). The buckled surface allows us to measure the response of Dirac electrons in a magnetic field to the presence of a well-defined potential variation. We find that while the n=0 Landau level exhibits a 12 meV energy shift across the buckled structure at 7 T, the ...

A variational method of calculating the spin 1 excitation energies of the n51 quantum Hall liquid is presented in detail. We are able to include Landau-level mixing and finite-thickness effects. The many-body wave functions of the states near n51 filling are taken to be a product of a lowest-Landau-level Laughlin-type wave function and a Jastrow factor. A significant reduction in the calculated...