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arXiv · 1809.02276

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

Yasumasa Hasegawa·Keita Kishigi
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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 $α_2 q_x^2$ with aconstant $α_2$ plays an important role. The energy is obtained as $E_n \propto α_2^{\frac{3}{5}} (n B)^{\frac{4}{5}}$, 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.

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Yasumasa Hasegawa, Keita Kishigi. 2019-01-25. Energy quantization at the "three-quarter Dirac point" in a magnetic field. https://doi.org/10.1103/physrevb.99.045409

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