#### Year

2014

#### Degree Name

Doctor of Philosophy

#### Department

School of Physics

#### Recommended Citation

Chen, Qinjun, Electrical and optical properties of the bulk states in HgTe/CdTe quantum wells topological insulator, Doctor of Philosophy thesis, School of Physics, University of Wollongong, 2014. https://ro.uow.edu.au/theses/4360

#### Abstract

HgTe/CdTe quantum wells (QWs) are the first known topological insulator material, which requires strong intrinsic spin orbit coupling (SOC). In HgTe/CdTe QW, a phase transition happens when the thickness of the HgTe “well” exceeds the critical value (6.3 nm), which results in band inversion. The band inverted HgTe/CdTe QWs form topological edge states that support currents with opposite spins transporting in opposite directions, while the bulk state remains insulating. On the edge, the gap closed with linear energy dispersion at the low energy regime, creating a pair of Dirac cones. Such edge states have attracted great attention and have been extensively studied. However, the bulk insulating state should not be forgotten, especially, when the Fermi energy is out of the bulk gap.

We first study the dielectric function of *n*-type HgTe/CdTe QWs. We present the dielectric response contributed from intraband and interband excitations, respectively. The thermal effects have significant effect on the intraband contributed polarization function, of which the peaks shift toward high frequency with increasing temperature. The plasmons in the two-dimensional (2D) electron gas (2DEG) in the HgTe “well” decays rapidly.

We then investigated the energy loss rate (ELR) of a charged particle in an ntype HgTe/CdTe QW. It is found that the ELR characteristics due to the intraband excitation have linear energy dependence while those due to interband excitation depends on the energy exponentially. An interesting quantitative result is that for a large range of the incident energy, the mean inelastic scattering rate is around a few terahertzs.

We also studied the frequency-dependent current response of the bulk state of topological insulator HgTe/CdTe QW. Our formalism is based on the quantum transport equation, considering the second order electron-impurity scattering under a weak external field. The optical conductivity is attributed to the intra-band process under a weak excitation. We found out that the conductivity decreases with temperature at low temperature and increases with temperature at high temperature. The transport scattering rate has an opposite frequency dependence in the low temperature regime and in the high temperature regime. The different frequency dependence is due to the interplay of (i) impurity scattering probability of a single electron decreases frequency at any temperature and (ii) number of electrons satisfying scattering condition at high temperature increases with the frequency.

We reveal that the *n*-type HgTe/CdTe quantum well have a strong nonlinear optical property in the three-photon mixing. While the gapless surface state in TI can exhibit strong nonlinear effect due to the linear energy dispersion, the nonparabolic energy dispersion of the bulk state is responsible for the photo mixing effect reported here. To produce response at terahertz frequency regime from femtosecond electrical field, the mixing efficiency is around 10^{-4} comparable to that of nonlinear semiconductor crystals. The optimal temperature for this nonlinear effect is around 50-100K. The results suggest a potential application of TI in terahertz photonics.

We present strong nonlinear optical responses in terahertz regime in the bulk state of an *n*-type HgTe/CdTe QW. The third-order nonlinear optical conductance can be observed under a moderate electric field. There are sign changes of third order conductance happen in the low chemical potential μ for two types of band structures at low energy regime. The thermal influences on nonlinear optical responses of HgTe/CdTe QWs are also studied, especially when μ lies between 6 meV and 10 meV. The sign changes are observed when temperature increases up to 300 K. These results suggest that HgTe/CdTe QWs are promising candidates for nonlinear photonics and optoelectronics devices applications.

We finally investigated the nonlinear response of 2D surface states of a 3D strong topological insulator (e.g. Bi_{2}Se_{3}). We report that for such surface states on Bi_{2}Se_{3}, there exist strong nonlinear optical responses in terahertz regime. The thirdorder nonlinear optical conductance can be observed under a moderate electric field. The thermal influence on nonlinear optical responses of the surface states of Bi_{2}Se_{3} are also studied in different temperature and frequency ranges. The results suggest that the 3D TIs such as Bi_{2}Se_{3} are promising candidates for nonlinear photonics and optoelectronics devices.