In this article, we present a summary of the current status of the study of the transport of electrons confined to one dimension in very low disorder GaAs-AlGaAs heterostructures. By means of suitably located gates and application of a voltage to 'electrostatically squeeze' the electronic wave functions, it is possible to produce a controllable size quantization and a transition from two-dimens...

We report benchmark results for one-dimensional (1D) atomic and molecular systems interacting via the Coulomb operator |x|(-1). Using various wavefunction-type approaches, such as Hartree-Fock theory, second- and third-order Møller-Plesset perturbation theory and explicitly correlated calculations, we study the ground state of atoms with up to ten electrons as well as small diatomic and triatom...

The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body potentials which can be solved algebraically. Analytic expressions for the eigenspectrum and the eigenfunctions are given with and without confinement.

Among graphene-like family, phosphorene is a typical semiconducting layered material, which can also be a superconductor in low temperature. Applying pressure or tension on phosphorene lattice results in changing the hopping terms, which change the energy bands of the material. In this research we use the tight-binding Hamiltonian, including relevant hopping terms, to calculate energy bands of ...

With modern microelectronics moving towards smaller and smaller length scales on the (sub-) nm scale, quantum effects (apart from band structure and band gaps) have begun to play an increasingly important role. This especially concerns dimensional confinement to 2D (high electron mobility transistors and integer/fractional quantum Hall effect physics, graphene and topological insulators) and 1D...

Due to progress in nanotechnology high-quality quantum wires can nowadays be fabricated. The behavior of particles in one dimension differs significantly from that in three-dimensional (3D) systems, yet the physics of such lowdimensional systems is generally not very well represented in standard undergraduate or graduate curricula. For instance, the Fermi liquid paradigm, working well for elect...

Magnetic impurities coupled antiferromagnetically to a one-dimensional Heisenberg model are studied by numerical diagonalization of chains of finite clusters. By calculating the binding energy and the correlation function, it is shown that a local singlet develops around each impurity. This holds true for systems with a single impurity, with two impurities, and for impurities forming a lattice....