Renormalization group analysis of multi-Dirac-node materials

TL;DR

This paper uses renormalization group analysis to study electromagnetic interactions in multi-Dirac-node materials, revealing how the speed of light and electron velocity scale differently, with implications for topological phase transitions and Weyl semimetals.

Contribution

It provides an analytic solution for the large N limit and an approximate solution for generic N, showing how the renormalization affects key physical parameters in multi-Dirac-node systems.

Findings

For large N, the speed of light c decreases while electron velocity v remains unchanged.

The product c^2 v^N remains nearly unrenormalized across different N.

Temperature-dependent properties like dielectric constant and conductivity are discussed based on the renormalization results.

Abstract

We theoretically study the electromagnetic interaction in Dirac systems with $N$ nodes by using the renormalization group, which is relevant to the quantum critical phenomena of topological phase transition ($N=1$) and Weyl semimetals ($N=4$ or $N=12$). Compared with the previous work for $N=1$ [H. Isobe and N. Nagaosa, Phys. Rev. B 86, 165127 (2012); arXiv:1205.2427], we obtained the analytic solution for the large $N$ limit, which differs qualitatively for the scaling of the speed of light $c$ and that of electron $v$, i.e., $v$ does notchange while $c$ is reduced to $v$. We also found a reasonably accurate approximate analytic solution for generic $N$, which well interpolates between $N=1$ and large $N$ limit, and it concludes that $c^2 v^N$ is almost unrenormalized. The temperature dependence of the physical properties, the dielectric constant, magnetic susceptibility, spectral function, DC conductivity, and mass gap are discussed based on these results.