Tight-binding modeling and low-energy behavior of the semi-Dirac point

TL;DR

This paper models semi-Dirac spectra with anisotropic dispersion in VO2/TiO2 heterostructures, contrasting them with graphene Dirac points, and explores their low-energy physics and magnetic field responses.

Contribution

It introduces a tight-binding model for semi-Dirac points and analyzes their spectral and low-energy properties, including magnetic field effects.

Findings

Semi-Dirac points exhibit highly anisotropic dispersion.

Electronic structures are similar but low-energy physics differ.

Magnetic field influences energy levels around semi-Dirac points.

Abstract

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 VO$_2$/TiO$_2$ nano-heterostructures. 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. We find that these systems support apparently similar electronic structures but diverse low-energy physics.