Landau levels for graphene layers in noncommutative plane

Starting from the zero modes of the single and bilayer graphene Hamiltonians we develop a mechanism to construct the eigenstates and eigenenergies for Landau levels in noncommutative plane. General formulas for the spectrum of energies are deduced, for both cases, single and bilayer graphene. In both cases we find that the effect to introduce noncommutative coordinates is a shift in the energy spectrum with respect to result obtained in commutative space.

Dimension of noncommutative plane curves

In this paper, we prove that an algebra of the form [Formula: see text] is never right (or left) artinian in case [Formula: see text] is a proper ideal and [Formula: see text] is an uncountable, algebraically closed field of characteristic [Formula: see text].

Noncommutative massive unquenched ABJM

In this paper, we study noncommutative massive unquenched Chern–Simons matter theory using its gravity dual. We construct this novel background by applying a TsT-transformation on the known parent commutative solution. We discuss several aspects of this solution to the Type IIA supergravity equations of motion and, amongst others, check that it preserves [Formula: see text] supersymmetry. We then turn our attention to applications and investigate how dynamical flavor degrees of freedom affect numerous observables of interest. Our framework can be regarded as a key step toward the construction of holographic quantum Hall states on a noncommutative plane.