One of the major challenges for the semiconductor industry is to continue with the miniaturization of the device features, increasing the integration densities with higher operation frequency. Silicon the material of choice so far, has been arriving at its physical limits which has led the condensed matter researchers to look for alternative new material which can set the foundation for the next generation computing paradigms or lead to applications in spintronics. There has been a rising interest in so-called Dirac materials, characterized by a linear dispersion relation, giving rise to exotic physical phenomena such as high carrier velocities ~ 106 m/s and dissipationless charge transport. In this thesis, we have studied two classes of Dirac materials - graphene and topological insulators (TIs) namely, bismuth selenide (Bi2Se3) and antimony telluride (Sb2Te3). Specifically, we investigate the optical behavior of Dirac materials using terahertz time domain spectroscopy (THz-TDS) contact-free optical technique, used to probe the low-energy excitations in strongly correlated electron gases. Chapter 1 provides a broad introduction to the field of topological insulators and graphene the various optical and electronic methods, which have been employed to explore their response. In particular the focus in on detecting and isolating the response from the topological surface state (TSS) in TIs, which are “robust”, as it is protected against backscattering by spin− momentum locking and time reversal symmetry. Various literature reports describing the current understanding of the TI field are then discussed. This sets the context for understanding the approach undertaken in the rest of the thesis, towards investigating these materials. In Chapter 2 we discuss the intrinsic plasmonic response in chemical vapour deposited (CVD) graphene and its relation to the domain size of graphene. A novel ion gel based top gate is implemented with the possibility of tuning the plasmonic resonances by ~ 70 GHz. We further employ THz-TDS to map the conductivity of graphene film on different substrates such as germanium and sapphire. In chapter 3, we investigate Bi2Se3, a representative TI using THz spectroscopy and magnetotransport measurements. The temperature-dependent optical behavior of a 23-quintuple-thick film of Bi2Se3, is used to deconvolve the surface state response from the bulk resulting in an optical mobility exceeding 2000 cm^2/V·s at 4 K, indicative of a surface-dominated response. Further, a scattering lifetime of ∼0.18 ps and a carrier density of 6 × 10^12 cm^−2 at 4 K is obtained using the THz measurements. The electrical transport measurements reveal weak antilocalization behavior in the Bi2Se3 sample, consistent with the presence of a topological surface state. Chapter 4, discusses the phase transition in a rather less considered TI, Sb2Te3, using THz-TDS. We track through a series of topological phase transitions from 3D-TI to 2D hybrid topological insulator and then a 2D trivial insulator, as function of Sb2Te3 film thickness. Reducing the film thickness further resulted in a reduced mobility suggesting that the formation of a spin-conserving scattering channel characteristic of hybridized topological insulator phase. Finally, the Chapter 5, concludes with a summary of the thesis and presents future opportunities for further research arising from this work.

The purpose of this paper is to examine the important topological properties of the function spaces BC(X,Y) and C(X,Y). Emphasis is given to the relationship between the metrizability of X and the separability of these function spaces. The paper is divided into three major parts: the preliminary definitions and theorems; the relationship between the topological properties of X and BC (X ,Y), for compact X; and the extension of the results of Part II for X not compact and for the case when we have C(X, Y).

acase@tulane.edu / 1 / Jinyu Liu

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In this thesis, I show my effort in growing atomically flat Bi₂Se₃ thin films using molecular beam epitaxy (MBE) method. Bi₂Se₃ is a kind of topological insulator, whose exotic surface states have been found in the samples that I grew. / text

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