Terahertz tuning of Dirac plasmons in Bi₂Se₃ Topological Insulator

Plasmons are the collective electronic excitations appearing in metals and semiconductors which can strongly confine light in subwavelength spatial regions. This confinement amplifies light-matter interaction and provides a powerful mechanism for efficiently generating nonlinear optical phenomena. In the terahertz range these effects are particularly relevant in Dirac materials, like graphene and topological insulators, where Dirac massless electrons show a naturally nonlinear optical behavior. The strong interaction scenario has been considered so far from the point of view of light. Here, we investigate instead the effect of strong interaction on the plasmon itself.
In particular we want to assess whether THz light can be used to continuously tune the plasmon resonance in Bi₂Se₃ topological insulator, by taking advantage of its THz nonlinear properties.
Two films of Bi₂Se₃ patterned in the form of parallel ribbons with width of 4 and 20 μm (filling factor ½) have been prepared. The patterning provides to THz light the necessary momentum to match, in the absorption process, the plasmon’s dispersion relation. It has been already shown that the THz plasmon in Bi₂Se₃ is due mainly to the Dirac carriers (see Di Pietro et al. Nature Nanotechnology 6, 630 (2011)). The THz extinction coefficient (see Figure 1) is investigated for different electric fields associated to THz light ranging from ~0.1 kV/cm (corresponding to the linear regime as measured at the SISSI beamline) to >MV/cm (which are made available at the TeraFERMI source).  
In the linear regime one identifies a two hump structure, which can be attributed to the THz plasmon resonance coupled via a Fano interaction with the a phonon at nearly 2 THz. As the THz electric field increases, entering the nonlinear regime, the plasmon softens (see the arrows in Figure 1). In order to map the softening of the bare plasmon, decoupled from the Fano interaction, we fit the extinction coefficient through a model which takes into account the coupling. After fitting we can establish the THz electric field dependence of the plasmon frequency, as reported in Figure 2. With increasing field the plasmon frequency of the 4 μm ribbon array film shifts 85% of its linear value, while it shifts 60% of its linear value for the 20 μm ribbon array film.

Figure 1.    THz fluence-dependent extinction coefficient of the 4 μm (a-e) and 20 μm (f-i) patterned films. The full line is a fit (see text). The dashed line is the bare plasmon calculated from the fitting parameters. Reprinted from Phys. Rev. Lett. 124, 226403 (2020).

From a theoretical point of view the nonlinear properties induced by high THz electric field can be modelled by the Boltzmann equation of transport in a nonperturbative way. This model predicts a very significant plasmon softening at relatively low fields, which is however not found in our experiment (Figure 2, red dashed line). A probable explanation for this disagreement is related to the low heat capacity associated to the massless Dirac electrons. Indeed, the temperature of the electron bath undergoes a strong enhancement upon intense THz excitation, which is not considered in the Boltzmann equation. In order to take into account the local variation of temperature due to the absorption of the THz energy, we adopt a standard two-temperature model. As a consequence of the THz pulse absorption, the electronic temperature of Bi₂Se₃ reaches up to 1500 K at about 1 MV/cm, following the pump profile within few 10s of fs, and relaxing back to the lattice temperature within few ps. The increase of the electronic temperature due to THz illumination can be traced in a strong modification of the electronic chemical potential and, finally, in the softening of the plasmon frequency (see black dotted line in Figure 2). The plasmon frequencies, predicted within the thermodynamic model are in remarkable agreement with the experimental data. 
The strong renormalization of plasmon excitation, observed here, is extremely promising for the exploitation of topological insulators as a platform for the realization of ultrafast nanospintronics and active plasmonic devices.
 

Figure 2.    Experimental plasmon frequencies for both patterned films are shown as a function of the THz electric field, together with a thermodynamic model (black dotted line) and the Boltzmann equation result (dashed red line). Reprinted from Phys. Rev. Lett. 124, 226403 (2020).

This research was conducted by the following research team:

¹  Elettra – Sincrotrone Trieste, Italy
²  CNR-IOM Trieste, Italy
³  NEST, CNRNANO and Scuola Normale Superiore, Pisa, Italy
⁴ Department of Physics and Astronomy Rutgers, USA
⁵ CNR-IOM and Dipartimento di Fisica, Sapienza Università di Roma, Italy
 

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