Topological insulators represent a unique class of materials characterized by an insulating bulk and conducting surface states protected by time-reversal symmetry. Among these, bismuth selenide (Bi₂Se₃) has emerged as a prototypical example due to its relatively large bandgap and well-defined topological surface states. The interaction of light with Bi₂Se₃ reveals intricate phenomena, particularly in optical conductivity and terahertz (THz) response, which are critical for understanding its electronic and plasmonic behavior.

The optical conductivity of Bi₂Se₃ is a key parameter that captures its light-matter interactions. In the low-frequency regime, the optical conductivity is dominated by the surface states, while the bulk contributes at higher energies. Experimental studies have shown that the real part of the optical conductivity (σ₁) exhibits a Drude-like response at THz frequencies, indicative of free-carrier contributions from the topological surface states. The Drude weight, proportional to the carrier density and inversely proportional to the effective mass, provides insights into the dynamics of these surface carriers. For Bi₂Se₃, the Drude response is typically observed below 2 THz, with a scattering rate on the order of 1–10 meV, reflecting the high mobility of surface electrons.

At mid-infrared frequencies, interband transitions between the surface Dirac cones become significant. The optical conductivity in this regime shows a nearly linear dependence on frequency, a hallmark of Dirac fermions. This linearity arises from the constant density of states near the Dirac point, distinguishing topological insulators from conventional semiconductors. The interband conductivity peaks around 0.3 eV, corresponding to transitions across the bulk bandgap, which for Bi₂Se₃ is approximately 0.35 eV.

The THz response of Bi₂Se₃ is particularly noteworthy for its potential applications in high-speed optoelectronics. When exposed to THz radiation, the material exhibits a pronounced photoconductive effect, where incident photons excite electron-hole pairs in the surface states. Time-resolved THz spectroscopy measurements have revealed ultrafast carrier dynamics, with relaxation times on the order of picoseconds. The THz photoconductivity is highly sensitive to surface conditions, making it a valuable probe for studying defects and adsorbates.

Plasmonic excitations in Bi₂Se₃ are another critical aspect of its light-matter interactions. Unlike conventional plasmonic semiconductors, where plasmons are primarily bulk phenomena, topological insulators support surface plasmon polaritons (SPPs) due to their metallic surface states. These SPPs are confined to the interface between the topological insulator and the surrounding medium, with dispersion relations that differ markedly from those in ordinary metals. The plasmon frequency in Bi₂Se₃ typically falls in the THz to mid-infrared range, depending on the carrier density. For a doping level of 10¹² cm⁻², the plasmon energy is approximately 10 meV, corresponding to a frequency of 2.4 THz.

The unique plasmonic properties of Bi₂Se₃ stem from the Dirac nature of its surface states. The plasmon dispersion follows a √q dependence (where q is the wavevector) at long wavelengths, deviating from the linear dispersion of conventional 2D electron gases. This behavior is a direct consequence of the absence of backscattering in topological surface states, which also leads to reduced plasmon damping compared to ordinary materials. Experimental observations using near-field optical microscopy have confirmed the existence of these Dirac plasmons, highlighting their potential for subwavelength light manipulation.

The interaction of THz radiation with Bi₂Se₃ also reveals nonlinear optical effects. At high field strengths, the material exhibits harmonic generation and saturable absorption, attributed to the Pauli blocking of interband transitions. These nonlinearities are enhanced by the large Berry curvature of the surface states, which influences the optical selection rules. For instance, second-harmonic generation (SHG) measurements have shown a strong dependence on the polarization of the incident light, reflecting the spin-momentum locking of the surface electrons.

Temperature plays a significant role in modulating the optical and THz properties of Bi₂Se₃. At low temperatures, carrier freeze-out reduces the bulk conductivity, making the surface states more dominant. The optical conductivity thus becomes more sensitive to surface perturbations, such as magnetic doping or proximity effects. Conversely, at room temperature, thermal excitation of bulk carriers can obscure the surface response, necessitating careful experimental design to isolate the topological contributions.

The interplay between light and Bi₂Se₃ also extends to magneto-optical effects. Under an external magnetic field, the surface states exhibit quantized Landau levels, which modify the optical conductivity. Cyclotron resonance measurements have revealed Landau level spacings consistent with Dirac fermions, further confirming the topological nature of the material. These magneto-optical studies provide a powerful tool for probing the Fermi velocity and carrier density of the surface states.

In summary, the light-matter interactions in Bi₂Se₃ are governed by its unique electronic structure, with distinct signatures in optical conductivity, THz response, and plasmonic excitations. The material’s Dirac-like surface states give rise to linear optical conductivity, unconventional plasmon dispersion, and robust nonlinear effects, setting it apart from conventional semiconductors. These properties not only deepen our understanding of topological insulators but also open avenues for novel optoelectronic and plasmonic applications. Future research may explore engineered heterostructures to further enhance these effects or integrate them into functional devices.