Two Electrons in a Quantum Dot: A Unified Approach

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.Comment: 14 page

Variational calculations on the energy levels of graphene quantum antidots

Within the Dirac-Weyl description of the graphene, the ground and low-lying excited state energies of a graphene quantum antidot subjected to a uniform static magnetic field is calculated by employing a variational scheme. The procedure is based on the choice of exact solutions of the Dirac-Weyl equation corresponding to massless fermions under the homogeneous magnetic field as basis sets for the trial wave functions. It is found that, for parabolic graphene antidots, the valley splitting occurs due to the introduction of spatial confinement, and it increases as the confinement strength increases. Furthermore, it is also investigated that, in such dot structures, switching an antidot potential on enhances this splitting. Therefore, we investigated that it is possible to control valley splitting by geometrical parameters of a graphene quantum antidot and/or by the strength of external magnetic field

Chiral symmetry breaking by a magnetic field in graphene

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Spin-dependent polaron formation in pristine graphene

We investigate the effects of spin-orbit couplings on the electron (hole)-E2g phonon interaction in graphene. We examine the effects of spin-orbit couplings on electron and hole polaron formation as well as DC conductivity, and spin polarizations of charge carriers. We use Fröhlich type Hamiltonian to describe the electron-phonon system within the continuum limit. Our theoretical analysis shows that, the polaronic effect is decreased due to the spin-orbit couplings, for both spin and pseudospin states, but it is enhanced beyond some critical values of wavevector for spin-up states of both sublattices in the presence of spin-orbit couplings. The Rashba spin-orbit coupling in the graphene single layer splits up- and down- states, and produces perfect spin polarized conductivity. Also the phonon-restricted and phonon-assisted conduction are reported for positive and negative Fermi energies

Magnetotransport properties of corrugated stanene in the presence of electric modulation and tilted magnetic field

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