We study edge states in the integral quantum Hall effect on a square lattice in a rational
magnetic field φ= p/q. The system is periodic in the y direction but has two edges in the x …

We investigate the properties of the Lieb lattice, that is, a face-centered square lattice,
subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar …

We study the energy spectrum and the Hall effect of electrons on the square lattice with next-
nearest-neighbor (NNN) hop** as well as nearest-neighbor hop**. This lattice includes …

Recent experiments have demonstrated that neutral graphene sheets have an insulating
ground state in the presence of an external magnetic field. We report on a π-band tight …

We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $
H={{\rm {e}}}^{x}+{{\rm {e}}}^{-x}+{{\rm {e}}}^{p}+{{\rm {e}}}^{-p} $ in terms of the refined …

Recently, an unusual integer quantum Hall effect was observed in graphene in which the
Hall conductivity is quantized as σ xy=(±2,±6,±10,…)× e 2∕ h, where e is the electron …

We present transport measurements of bilayer graphene with a 1.38∘ interlayer twist. As
with other devices with twist angles substantially larger than the magic angle of 1.1∘, we do …

The trans-series completion of perturbative series of a wide class of quantum mechanical
systems can be determined by combining the resurgence program and extra input coming …

Electrons on three dimensional lattice in external magnetic field are investigated. If the field
is applied in the (1, 1, 1) direction with the flux per plaquette in each plane φ= p/q, the …

Intricate interplay between the periodicity of the lattice structure and that of the cyclotron
motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue …