Tilt-induced kink in the plasmon dispersion of two-dimensional Dirac electrons

TL;DR

This paper analytically studies the effects of tilt in the Dirac cone spectrum of two-dimensional Dirac materials, revealing a tilt-induced plasmon kink and an overdamped plasmon branch, which can be experimentally used to measure the tilt.

Contribution

It provides an analytical calculation of the polarization function for tilted Dirac cones, unveiling novel plasmonic effects caused solely by the tilt parameter.

Findings

Tilt induces a linearly dispersing overdamped plasmon branch.

A kink appears in the plasmon dispersion at the inter-band continuum.

The kink's properties allow direct measurement of the tilt parameter.

Abstract

The list of two dimensional Dirac systems with a tilt in their Dirac cone spectrum is expanding, and now in addition to organic system $\alpha$(BEDT-TTF)$_2$I$_3$ includes the two dimensional $8Pmmn$-borophene sheet, which allows for controlled doping by the gate voltage. We analytically calculate the polarization function of tilted Dirac cone for arbitrary tilt parameter, $0\le \eta <1$, and arbitrary doping. This enables us to find two interesting plasmonic effects solely caused by the tilt: (i) In addition to the standard plasmon oscillations, strong enough tilt, induces an additional linearly dispersing overdamped branch of plasmons, which is strongly Landau damped due to overlap with a large density of intra-band free particle-hole (PH) excitations. (ii) There appears a kink in the plasmon dispersion for any non-zero tilt parameter. The kink appears when the plasmon branch enters the inter-band continuum of PH excitations. This kink becomes most manifest for wave vectors perpendicular to the tilt direction and fades away by approaching the tilt direction. Experimental measurement of the wave vector and energy of the plasmonic kink, when combined with our analytic formula for the kink energy scale, allows for a direct experimental measurement of the tilt parameter.