# Signatures of merging Dirac points in optics and transport

## TL;DR

This paper investigates the optical and transport signatures of merging Dirac points in a 2D model, revealing universal behaviors and deviations that signal the transition from Dirac to semi-Dirac dispersion as the energy gap varies.

## Contribution

It provides analytic formulas and identifies signatures in optical and transport properties for the Dirac to semi-Dirac transition in a 2D system.

## Key findings

- Universal functions describe optical transitions in Dirac and semi-Dirac regimes.
- Deviations from asymptotic behaviors indicate the transition between regimes.
- Signatures in conductivity and thermal properties reveal the merging of Dirac points.

## Abstract

We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter $\Delta$, there are two distinct Dirac points with linear dispersion, these are connected by a saddle point at higher energy. As $\Delta$ goes to zero, the two Dirac points merge and the resulting dispersion exhibits semi-Dirac behaviour which is quadratic in the $x$-direction ("nonrelativistic") and linear the $y$-direction ("relativistic").In the clean limit for each direction ($x,y$) the contribution of the intraband and interband optical transitions are both given by universal functions of photon energy $\Omega$ and chemical potential $\mu$ normalized to the energy gap. We provide analytic formulas for both small and large $\Omega/2\Delta$ and $\mu/\Delta$ limits. These define, respectively, Dirac and semi-Dirac-like regions. For $\Omega/2\Delta$ and $\mu/\Delta$ of order one, there are deviations from these asymptotic behaviors. Considering optics and also transport, such as dc conductivity, thermal conductivity and the Lorenz number, such deviations provide signatures of the evolution from the Dirac to the semi-Dirac regime as the gap $\Delta$ is varied.