The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows
the relation between the number of bound states and the phase shift at zero momentum for …

We present exact analytical zero-energy solutions for a class of smooth-decaying potentials,
showing that the full confinement of charge carriers in electrostatic potentials in graphene …

Searching for new states of matter and unusual quasi-particles in emerging materials and
especially low-dimensional systems is one of the major trends in contemporary condensed …

In this brief review, the problem of electrostatic confinement of massless Dirac particles is
surveyed via a number of exactly solvable one‐and two‐body models. By considering …

We consider the motion of electrons confined to a two-dimensional plane with an externally
applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb …

Using the variable phase method, we reformulate the Dirac equation governing the charge
carriers in graphene into a nonlinear first-order differential equation from which we can treat …

Simple perturbations (such as a line charge or a sheet charge) in 2D semiconducting
materials create difficult solutions to the Poisson equation due to the non-uniform out-of …

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac
equation in two dimensions is established as a relation between the total number nj of the …

We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers
in graphene, into a nonlinear first-order differential equation for scattering phase shift, using …

We study the Fermi polaron problem with dipolar fermions in a bilayer geometry, where a
single dipolar particle in one layer interacts with a Fermi sea of dipolar fermions in the other …