Abstract
Low symmetries of a crystal structure could allow the energy dispersion to exhibit Weyl fermions with several different velocities. The quasi-two-dimensional organic semiconductor \(\alpha \)-(BEDT-TTF)\(_2\)I\(_3\) has an anisotropic linear dispersion with a zero energy gap near its Fermi level. Since the density of states vanishes at the Fermi level, the Coulomb interaction is unscreened and long-ranged. We study the effect of the long-range Coulomb interaction and the low-energy behavior of the two-dimensional Weyl/Dirac fermions with tilted energy dispersion. The renormalization group analysis within nonrelativistic scheme reveals that the nearly logarithmic enhancement of the velocity parameters reshapes the tilted Dirac cones and changes the low-energy behavior. The suppression of the spin susceptibility at low temperatures is calculated theoretically, which well explains an NMR experiment. By taking into account of the relativistic effect, we observe the recovery of the isotropic Dirac cone and the Lorentz invariance in the low-energy limit, accompanying the Cherenkov radiation. This result applies even when the Dirac cone is strongly tilted and the velocity is negative in one direction.
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Notes
- 1.
The regularization by the cutoff \(\Lambda \) violates the gauge invariance in the intermediate stage; the self-energy explicitly depends on the cutoff. But the resultant RG equations do not include the cutoff \(\Lambda \) and seem to be in gauge-invariant form. Actually the same RG equations can also be derived by dimensional regularization, which preserves the gauge invariance.
- 2.
Actually, Eq. (3.19) gives the spin susceptibility in the noninteracting case. When we treat an interaction U by RPA approximation, the spin susceptibility \(\chi \) without the lattice site dependence becomes
$$\begin{aligned} \chi = \frac{\chi _0}{1-U\chi _0}, \end{aligned}$$where \(\chi _0\) is the spin susceptibility for the corresponding noninteracting system. We use the representation for the noninteracting system in the following analysis, by assuming \(\chi _0\) is small. This approximation \(\chi = \chi _0\) becomes accurate in the low-temperature region, where the effect of the RG analysis is stronger, because \(\chi _0\) is suppressed in low temperature as we will see later.
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Isobe, H. (2017). Tilted Dirac Cones in Two Dimensions. In: Theoretical Study on Correlation Effects in Topological Matter. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-3743-6_3
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DOI: https://doi.org/10.1007/978-981-10-3743-6_3
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