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

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.