Terahertz Tuning of Dirac Plasmons in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ Topological Insulator

Light can be strongly confined in subwavelength spatial regions through the interaction with plasmons, the collective electronic modes appearing in metals and semiconductors. This confinement, which is particularly important in the terahertz spectral region, amplifies light-matter interaction and provides a powerful mechanism for efficiently generating nonlinear optical phenomena. These effects are particularly relevant in graphene and topological insulators, where massless Dirac fermions show a naturally nonlinear optical behavior in the terahertz range. The strong interaction scenario has been considered so far from the point of view of light. In this Letter, we investigate instead the effect of strong interaction on the plasmon itself. In particular, we will show that Dirac plasmons in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator are strongly renormalized when excited by high-intensity terahertz radiation by displaying a huge red-shift down to 60% of its characteristic frequency. This opens the road towards tunable terahertz nonlinear optical devices based on topological insulators.

Figure 1

Plasmons in a topological insulator. Plasmons are collective oscillations of electrons that can be directly excited by electromagnetic radiation in the presence of an extra momentum $k_{\text{extra}}$. This is achieved in the present experiment (a),(b), through ribbon arrays (width $w$, period $2w$, and $k_{\text{extra}}=\pi /w$), fabricated onto the surface of topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films (a) with linearly dispersive electronic bands (c). Plasmons are excited after illumination with sub-ps, half-cycle THz pulses produced at the FERMI free-electron laser [8].

Figure 2

Fluence-dependent THz spectra. Panels (a)–(e) display the THz extinction coefficient $E(\nu )$ of the $w=4\mu \mathrm{m}$ ribbon array patterned film for different THz electric field values. THz light is perpendicularly polarized to the ribbons. $E(\nu )$ shows a plasmon-phonon coupled spectrum (see main text). In particular the low-frequency maxima correspond to the dressed plasmon and the high-frequency modes to the dressed $\alpha$ phonon. The full line is a fit according to Eq. (1). The same is shown in panels (f)–(i) for the $w=20\mu \mathrm{m}$ patterned film. Both the dressed plasmons (see arrows) and the bare plasmon absorption [dashed lines as calculated from Eq. (1)], show an evident softening vs the THz electric field.

Figure 3

Plasmon softening. Experimental plasmon frequency ${\nu }_p$ values for both patterned films are shown here as a function of the THz electric field $E_{\mathrm{THz}}$. According to the Boltzmann equation formalism a softening of the plasmon (dashed red line) is theoretically predicted [6]. This model fails in reproducing the experimental data. On the other hand, a thermodynamic model (black dotted line), correctly catches our experimental observations (see main text).