**4. Temperature-dependent charge and phonon dynamics in Bi2Se3, Sb2Te3, and Bi2Te3**

## **4.1 Bi2Se3**

TRUS is used to investigate the exotic topological quantum characteristics of Bi2Se3, Sb2Te3, and Bi2Te3. This particular regime probing aids in comprehending the TI's enigmatic behavior. Considering the bismuth selenide, the PL emission indicates a significant 2 eV optical transition [56] caused by the state bunching effect [53]. The inert nature of these transitions is explained using density functional theory (DFT) calculations on the band structure and Kramer's Kroning method on reflectance data from crystal flake. Additionally, TRUS measurements are performed with a variety of pump excitation energies (3.02, 2.61, 1.91, and 1.4 eV) to obtain a spectrum in the VIS–NIR region (2.58–0.77 eV) [53]. These wide regime experiments on carrier dynamics demonstrate that the Moss–Burstein and shielding effects exist in bismuth selenide. Additionally, these studies demonstrate a variety of relaxation mechanisms, including thermalization of hot carriers, COP and CAP relaxation, and recombination.

All of the phenomena mentioned above are observed at room temperature, and there is a strong need to explore the TIs at low temperatures to assess surface stateinduced transitions. Essentially, there are two distinct ways for probing surface states or surface-related transitions. We already know that TIs are conducted at the surface while insulating bulk. Thus, the surface states of TIs are located on the uppermost layer. Therefore, in order to explore these surface states, the sample thickness should

### *Temperature-Dependent Evaluation of Charge Carriers and Terahertz Generation in Bismuth… DOI: http://dx.doi.org/10.5772/intechopen.102887*

be reduced to the ultrathin regime [17, 18, 55]. The sole disadvantage of this strategy is the complexity of the systems, required to develop this kind of ultrathin film. Alternatively, the low-temperature technique is used to investigate the temperaturedependent dynamics of charge carriers and phonons between 5 and 300 K. The perceptions of observing the surface states or surface states associated with transitions at low temperatures may be explained by performing a magneto-resistance analysis using the HLN equation. The literature demonstrates that at extremely low temperatures and magnetic fields, the surface states of TIs prevail over the bulk states [57–60]. Thus, it may be interesting to examine the charge and phonon dynamics of TIs at low temperatures in order to see surface states or surface state-related transitions.

The TRUS is carried out at low temperatures on micro flakes of single-crystalline bismuth selenide to observe the associated transitions in the temperature range of 5–300 K [53]. **Figure 3a** illustrates the DR spectra of crystalline flake across a wide range of NIR wavelengths at various temperatures. The wide DR signal demonstrates TI's ability to exhibit a broad range of optically allowed transitions, distinguished as 0.7, 1.1, and 1.4 eV. DFT band structure calculations anticipated that these specific transitions are permissible in bismuth selenide [53]. As seen in **Figure 3a**, a DR signal is denoted by a B peak that is only present above 200 K. At low temperatures, this specific transition is suppressed, indicating that it is associated with certain phononassigned carriers. Essentially, these carriers have initial energy of below 200 K, caused by thermalization at high temperatures.

Additionally, when the temperature decreases below 200 K, a tiny DR signal of 1.2 eV is formed at 100 K. The level of these DR signals increases when the temperature is lowered and becomes more noticeable below 5 K. These DR signals correspond to the same as the second strategy of exploring surface states associated transitions mentioned above. There are two possible explanations for this transition: defectinduced peak and surface state-related transition. If we consider the first option of

#### **Figure 3.**

*(a) illustrates the differential reflectance at 750 fs of a single crystal throughout the whole NIR range (800–1600 nm) at temperatures ranging from 5–300 K. It demonstrates the presence of a blue shift with the temperature that happened as a result of thermal fluctuations being suppressed. A decrease in DR at 1000 nm at low temperature coincides with the surface state transition, confirming the shift to the second surface state. (b)Theoretical transition model in which BCBs and BVBs are drawn to resemble bands in the same way as DFT calculations are performed on an ideal system. It is a DFT-based model, and TRUS predicted a variety of OBTs. These OBTs have a threshold voltage of 0.7, 1.0, 1.3, and 2.0 eV and stimulated emission of 0.8 eV. Additionally, using lowtemperature TRUS verifies the occurrence of a second surface condition.Reprinted from ref. [53], with permission of Elsevier.* 

a defect-induced peak, then this kind of transition has a common property, i.e., the carrier relaxation lifetime must be very short. However, the lifetimes in this situation are in the picosecond range, which eliminates the likelihood of a defect-induced peak [61]. Additionally, the kinetic profile of the same does not alter with temperature, corroborating the preceding explanation. Thus, one thing is evident that this specific DR signal is not the result of a defect.

After establishing that the DR signal at 1.2 eV is not attributable to defects, it is not incorrect to assert that the signal is predicted to be due to a surface state-related transition. DFT calculations are used to determine the band structure using the effective SOC inclusion to resolve this particular uncertainty. After learning about the band structure, it was relatively simple to formulate the 1.2 eV transition. This transition occurs when the carrier is excited from its ground state to its second surface state. Additionally, the kinetic profile during this transition is fitted using three lifetimes, and the fitting of this kinetic profile indicates that carriers relax in the picosecond time domain when they migrate from this energy level to a lower energy level. In the case of noble metals, when the relaxation time is in the picosecond range, it is widely known that the surface states reveal metallic nature. However, in our case, too, the surface states exhibit metallic properties. As a result, the relaxation lifetime suggests the occurrence of a surface state-related transition in TI [53].

Band structure calculations utilizing DFT in conjunction with actual pump-probe spectroscopy may be used to predict various optically allowed transitions in bismuth selenide. First surface state below Fermi level (SS1), second surface state above second valence band (SS2), first bulk valence band (BVB1), second bulk valence band (BVB2), first bulk conduction band (BCB1), and second bulk conduction band (BCB2) of TI are shown in **Figure 3b**. The temperature-dependent TRUS response is shown in **Figure 3a**. The most prominent optical transitions in TRUS are ~0.7, ~1.0, ~1.4, and ~ 2.0 eV. Charge carriers are stimulated to the second bulk valance band, exhibiting ~0.7 and ~ 1.0 eV DR signal peaks, whereas the ~2.0 eV transition occurs in the second bulk conduction band. Additionally, the low-temperature investigation reveals the existence of a DR peak of about 1.2 eV, which corresponds to the transition to the second surface state. Thus, the temperature-dependent study of charge carrier dynamics enables the investigation of various bands and surface-related transitions.

#### **Figure 4.**

*The temperature-dependent differential reflectance (DR) at 500 fs is analyzed using micro-flakes stimulated at 3.02 eV and probed in the 1.55–0.77 eV region of (a) Bi2Te3 and (b) Sb2Te3, respectively. The peaks highlighted in the TSS region of both TIs exhibit a blue shift when the temperature decreases, which is attributable to a reduction in the thermalization process. Reprinted from ref. [62], with permission of Elsevier.*

*Temperature-Dependent Evaluation of Charge Carriers and Terahertz Generation in Bismuth… DOI: http://dx.doi.org/10.5772/intechopen.102887*
