Ultra-high modulation depth exceeding 2,400% in optically controlled topological surface plasmons

Modulating light via coherent charge oscillations in solids is the subject of intense research topics in opto-plasmonics. Although a variety of methods are proposed to increase such modulation efficiency, one central challenge is to achieve a high modulation depth (defined by a ratio of extinction with/without light) under small photon-flux injection, which becomes a fundamental trade-off issue both in metals and semiconductors. Here, by fabricating simple micro-ribbon arrays of topological insulator Bi2Se3, we report an unprecedentedly large modulation depth of 2,400% at 1.5 THz with very low optical fluence of 45 μJ cm−2. This was possible, first because the extinction spectrum is nearly zero due to the Fano-like plasmon–phonon-destructive interference, thereby contributing an extremely small denominator to the extinction ratio. Second, the numerator of the extinction ratio is markedly increased due to the photoinduced formation of massive two-dimensional electron gas below the topological surface states, which is another contributor to the ultra-high modulation depth.


Supplementary Note 1. THz extinction spectra without optical pump injection
In this section, we discuss the extinction responses of both patterned and unpatterned Bi 2 Se 3 thin film samples without optical pump injection. As displayed in the Fig. 2 of the main text, the patterned sample exhibits the Dirac plasmon response with THz polarization perpendicular to the ribbon axis.
The measured lineshape can be understood by the plasmon-phonon interaction model analysis.
Corresponding fitting parameters in Supplementary Table 1 are well in accordance with the prior investigation 1 . The unpatterned sample, unlike the plasmonic response, shows a simple Drude response of Dirac electrons, whose featureless shape overlaps with the narrow ~1.9 THz phonon Lorentz oscillator (see Supplementary Figure 1a). It reveals that the THz irradiation cannot be coupled to the collective charge oscillations due to their momentum mismatch. For the same reason, the patterned micro-ribbon sample also exhibits the Drude-Lorentz response when the THz polarization is parallel to the ribbon axis, as shown in Supplementary Figure 1b

Supplementary Note 4. Details of plasmon dynamics
In this section, we discuss details of time-resolved plasmon dynamics in Fig. 3b of the main text. The plasmon-phonon interaction model has several coupling parameters as well as bare phonon and plasmon response (see Method for the detailed description of this model). Supplementary Figure 3a illustrates the light-induced coupling between each states and the corresponding parameters; w and g indicates the coupling of ground state to phonon and plasmon, respectively, and parameter v describes the strength of interaction between these two states 1,6 . To understand the plasmon dynamics, we discuss the change in these couplings under optical injection.
In Supplementary Figure 3b, we plot the time-resolved transients of parameters for the plasmonphonon interaction model. Here, we plot again the dynamics of bare plasmon frequency ( plasmon , red circles) and linewidth ( plasmon , black circles) in the main text for clear comparison. First, while the transition from ground to phonon mode (w, blue squares) does not show significant changes upon photoexcitation, the transient coupling between the ground and the plasmon (g, green triangles) exhibits meaningful dynamics, which essentially follow the temporal evolution of the plasmon resonance  plasmon . Both g and  plasmon show their maximum at t = 5 ps, which can be understood by the pump-induced increase of the surface carriers contributing to the collective charge oscillation.
Second, the coupling between phonon and plasmon is largely decreased upon photoexcitation (v, gray squares). Notable is that it reaches its minimum at t = 5 ps, at which  plasmon has a peak value. This coincidence may be explained by the origin of plasmon shift. As discussed in the main text, without optical injection, the main species responsible for the plasmon excitation is the TSS electrons, which exhibit a strong coupling with the 1.9 THz phonon. In contrast, 2DEG dominates the plasmon excitation under optical injection, which may account for the observed decrease in the plasmonphonon interaction (v) because the reported 2DEG-phonon coupling constant 7 is much smaller than that for the TSS electrons 8 . However, more theoretical studies are needed for complete understanding.

Supplementary Note 6. Dissipation pathways of excess energy injected by the optical control pulse
In the main text, we have shown that the large modulation of topological surface plasmon response can be achieved by injecting optical control pulse. Since the photon energy of the optical control pulse (1.55 eV) is much larger than the bulk band-gap of Bi 2 Se 3 (~250 meV), it is instructive to discuss the dissipation pathways of the excess energy injected by the control pulse. In this section, we briefly discuss the dynamic pathways of the excess energy.
After the photoexcitation, the injected photons are initially absorbed by electrons, producing nonthermal electrons and holes with high energies in a conduction and valence band, respectively. Then, a fast carrier-carrier scattering takes place within 200 fs, leading to the increased effective carrier temperature, which can be described by the so called "hot quasi-Fermi distributions" 11 . Consequently, the carrier scattering rate strongly increases 2 , which gives rise to the broadening of the plasmon response because the plasmon damping rate directly depends on the carrier scattering rate. This scenario can explain the initial, fast rise of the plasmon linewidth (Fig. 3d in the main text). Next, the excess carrier energies are transferred to the lattice via the carrier-phonon scattering, whose timescales are typically on the order of 1-10 picoseconds 2,12-15 . As a result of this process, the lattice temperature is increased, and consequently the optical phonon mode near 2 THz slightly stiffens 14,15 .
In our measurements, we have observed that the phonon frequency increases upon photoexcitation, which reaches its maximum near t = 5-10 ps (see the change in the position of gray vertical lines in transferred to the substrate. In addition to this carrier-phonon scattering, the system recovers its thermodynamic equilibrium via various relaxation pathways, such as hot carrier diffusion 16,17 , radiative and non-radiative recombination 18,19 and defect scattering 18 . These processes are possibly related to the observed recovery dynamics of the plasmon response.