1 / 5

Bulk Magnetization of graphene

Bulk Magnetization of graphene. Tight binding approximation : the mobile electrons are always located in the proximity of an atom , and then are conveniently described by the p z atomic orbital of the atoms it touches. : normalized wavefunction for an isolated atom.

aidan-ford
Download Presentation

Bulk Magnetization of graphene

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bulk Magnetization of graphene Tight bindingapproximation: the mobile electrons are alwayslocated in the proximity of an atom, and then are convenientlydescribed by the pzatomicorbital of the atomsittouches. : normalized wavefunction for an isolatedatom. 1 conduction electron for each C atom in the state. Unit cell (WXYZ) contains 2 atoms ( and ). (foundamental lattice displacement). The base functions are periodicalfunctions with the sameperiodicityas the (2D) lattice. kis a wavevector. Itdefines a reciprocal lattice and actsas a kind of quantum number. Extended wavefunction A. Barbon, Corso di Magnetochimica. A.A. 2013-14. Graphene

  2. The band theory of graphene Variationalprincipleto obtain the best value of substituting the wavefunction in the Schroedingerequation: By pre-multiplicationby or and integrationwehave: Number of unitcells We obtain: /N A. Barbon, Corso di Magnetochimica. A.A. 2013-14. Graphene

  3. : interactionbetween an or atom with itself : interactionbetween first neighbors of the sametype ( or ) : interaction between first neighbors of opposite type ( and ) Energy levelsasfunction of ky (kx=0) Zero band-gap Calculation of the density of states: A. Barbon, Corso di Magnetochimica. A.A. 2013-14. Graphene

  4. N° of free electrons plus positive holes per atom: : Fermi distribution At room temperature () the effectivenumber of free electrons (), per atom, is Itispossible to show that the number of electronicenergystates per atom: : number of atoms in the lattice N(E) E Ec A. Barbon, Corso di Magnetochimica. A.A. 2013-14. Graphene

  5. Magnetic susceptivity: G. Wagoner, Phys. Rev., 118, 647 (1960). A. Barbon, Corso di Magnetochimica. A.A. 2013-14. Graphene

More Related