Dynamical polarization and plasmons in a two-dimensional system with merging Dirac points

TL;DR

This paper investigates how the dynamical polarization and plasmon excitations behave in a two-dimensional anisotropic system undergoing a quantum phase transition with merging Dirac points, providing analytical insights into their evolution.

Contribution

It offers analytical results for the polarization function and plasmon dispersion across the phase transition, highlighting the effects of the van Hove singularity.

Findings

Plasmon dispersion evolves smoothly at the critical merging point.

Analytical long-wavelength dispersion of the collective mode is derived.

Van Hove singularity significantly influences plasmon excitations.

Abstract

We have studied the dynamical polarization and collective excitations in an anisotropic two-dimensional system undergoing a quantum phase transition with merging of two Dirac points. Analytical results for the one-loop polarization function are obtained at the finite momentum, frequency, and chemical potential. The evolution of the plasmon dispersion across the phase transition is then analyzed within the random phase approximation. We derive analytically the long-wavelength dispersion of the undamped anisotropic collective mode and find that it evolves smoothly at the critical merging point. The effects of the van Hove singularity on the plasmon excitations are explored in detail.