Energy quantization at the "three-quarter Dirac point" in a magnetic field

Abstract

The quantization of the energy in a magnetic field (Landau quantization) at a three-quarter Dirac point is studied theoretically. The three-quarter Dirac point is realized in the system of massless Dirac fermions with the critically tilted Dirac cone in one direction, where a linear term disappears and a quadratic term ${\alpha }_2{q}_x^2$ with aconstant ${\alpha }_2$ plays an important role. The energy is obtained as $E_n\propto {\alpha }_2^{\frac{3}{5}}(nB{)}^{\frac{4}{5}}$, where $n=1,2,3,\dots$, by means of numerically and analytically solving the differential equation, as well as by the semiclassical quantization rule. The existence of the $n=0$ state is studied by introducing the energy gap due to the inversion-symmetry-breaking term, and it is obtained that the $n=0$ state exists in one of a pair of three-quarter Dirac points, depending on the direction of the magnetic field when the energy gap is finite.

9 pages

References in corpus (6)

• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• A new magnetic field dependence of Landau levels on a graphene like structure
• Zero modes of tight binding electrons on the honeycomb lattice
• A semi-Dirac point in the Hofstadter spectrum
• Three-quarter Dirac points, Landau levels and magnetization in $\alpha$-(BEDT-TTF)${}_2$I${}_3$

Cited by in corpus (3)

• De Haas-van Alphen oscillations near the Lifshitz transition from two electron pockets to one electron pocket in the two-dimensional Dirac fermion systems
• Enhancements of the 3/2 and 5/2 frequencies of de Haas-van Alphen oscillations near the Lifshitz transition in the two-dimensional compensated metal with overtilted Dirac cones
• Designer gapped and tilted Dirac cones in lateral graphene superlattices