We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as magnetic field is varied. These ``zero level'' (ZQOs) appear limit where zero-field volume vanishes and have distinctive periodicity temperature dependence. link spectrum two-dimensional (2D) semimetal to Rabi model, show e...

Via measurements of commensurability features near the Landau filling factor ν=1/2, we probe the shape of the Fermi contour for hole-flux composite fermions confined to a wide GaAs quantum well. The data reveal that the composite fermions are strongly influenced by the characteristics of the Landau level in which they are formed. In particular, their Fermi contour is warped when their Landau le...

Graphene nanoribbons can be folded into a double layer system keeping the two layers decoupled. In the quantum Hall regime folds behave as a new type of Hall bar edge. We show that the symmetry properties of the zero Landau level in metallic nanoribbons dictate that the zero energy edge states traversing a fold are perfectly transmitted onto the opposite layer. This result is valid irrespective...

While a large number of fractional quantized Hall states have been discovered in the lowest Landau level, such states become increasingly rare in higher Landau levels. Few quantized Hall states have been observed in the first Landau level (Landau level filling factor 2 ≤ ν < 4) and no such states have so far been found for filling factors ν ≥ 4. Correspondingly, the role of electron-electron in...

We report on the experimental results of interlayer magnetoresistance in the multilayer massless Dirac fermion system alpha-(BEDT-TTF)2I3 under hydrostatic pressure and its interpretation. We succeeded in detecting the zero-mode Landau level (n=0 Landau level) that is expected to appear at the contact points of Dirac cones in the magnetic field normal to the two-dimensional plane. The character...

We present exact solution of an electrostatic problem in terms of the potential distribution and density profile of an incompletely depleted two-dimensional electron gas in a heterostructure covered by a half-infinite gate. Using this solution, we calculate configurations of compressible and incompressible (insulating) strips that are formed in the presence of a quantizing magnetic field. We di...

A recent theory of a compressible Fermi-liquid like state at Landau level filling factors ν = 1/q or 1 − 1/q, q even, is reviewed, with emphasis on the basic physical concepts.

Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the proper...