We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of ${\mathrm{VO}}_2\mathrm{\text{−}}{\mathrm{TiO}}_2$ nanoheterostructures. We contrast their spectral properties with the well-known Dirac points on the honeycomb lattice relevant to graphene layers and the spectra of bands touching each other in zero-gap semiconductors. We also consider the lowest order dispersion around one of the semi-Dirac points and calculate the resulting electronic energy levels in an external magnetic field. In spite of apparently similar electronic structures, Dirac and semi-Dirac systems support diverse low-energy physics.

• Received 9 April 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.016402