Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction

Details Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction

2008-02-06

arxiv.org/abs/0802.0795v2

J. Stat. Mech. (2008) P06008

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

25 pages, 15 figures, 12 tables. Various kinds of minor improvements

Scientific paper

10.1088/1742-5468/2008/06/P06008

This is the second of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. We investigate the problem of an electron subject to a spin-orbit interaction generated by the radial electric field of a static point charge sitting at the center of the sphere. The tight-binding Hamiltonian considered is a discretization on polyhedral graphs of the familiar form ${\bm L}\cdot{\bm S}$ of the spin-orbit Hamiltonian. It involves SU(2) hopping matrices of the form $\exp({\rm i}\mu{\bm n}\cdot{\bm\sigma})$ living on the oriented links of the graph. For a given structure, the dimensionless coupling constant $\mu$ is the only parameter of the model. An analysis of the energy spectrum is carried out for the five Platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron) and the C$_{60}$ fullerene. Except for the latter, the $\mu$-dependence of all the energy levels is obtained analytically in closed form. Rather unexpectedly, the spectra are symmetric under the exchange $\mu\leftrightarrow\Theta-\mu$, where $\Theta$ is the common arc length of the links. For the symmetric point $\mu=\Theta/2$, the problem can be exactly mapped onto a tight-binding model in the presence of the magnetic field generated by a Dirac monopole, studied recently. The dependence of the total energy at half filling on $\mu$ is investigated in all examples.

Affiliated with

Also associated with

No associations

Rating

Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tight-binding electronic spectra on graphs with spherical topology. II. The effect of spin-orbit interaction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-559786