Effect of finite temperature and uniaxial anisotropy on the Casimir
  effect with three-dimensional topological insulators

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Abstract

In this work we study the Casimir effect with three-dimensional topological insulators including the effects of temperature and uniaxial anisotropy. Although precise experimental values for the optical properties of these materials are yet to be established, qualitative analysis is still possible. We find qualitatively that the reported repulsive behavior and the equilibrium point are robust features of the system, and are favored by low temperatures and the enhancement of the optical response parallel to the optical axis. The dependence of the equilibrium point with temperature and with the topological magnetoelectric polarizability characteristic of three-dimensional topological insulators is also discussed.

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A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator

R. Cava, D Hsieh, M. Hasan … (2009)

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect \cite{Klitzing,Tsui} dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the extreme quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic field. Bulk Bi\(_{1-x}\)Sb\(_x\) single crystals are expected to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher dimensional analogues of the edge states that characterize a spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi\(_{1-x}\)Sb\(_x\) is predicted to exhibit three-dimensional Dirac particles, another topic of heightened current interest. Here, using incident-photon-energy-modulated (IPEM-ARPES), we report the first direct observation of massive Dirac particles in the bulk of Bi\(_{0.9}\)Sb\(_{0.1}\), locate the Kramers' points at the sample's boundary and provide a comprehensive mapping of the topological Dirac insulator's gapless surface modes. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the much sought exotic "topological metal". They also suggest that this material has potential application in developing next-generation quantum computing devices.

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Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface

H. LIN, Y. Hor, M. Hasan … (2009)

Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement effects. Such systems feature two-dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe strongly interacting particles. It has been proposed that a topological insulator with a single spin-textured Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study and first-principle theoretical calculation-predictions that reveal the first observation of such a topological state of matter featuring a single-surface-Dirac-cone realized in the naturally occurring Bi\(_2\)Se\(_3\) class of materials. Our results, supported by our theoretical predictions and calculations, demonstrate that undoped compound of this class of materials can serve as the parent matrix compound for the long-sought topological device where in-plane surface carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.

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First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase

Y. Hor, J. H. Dil, C. L. Kane … (2009)

A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry based classification of condensed matter. Exotic spin transport phenomena such as the dissipationless quantum spin Hall effect have been speculated to originate from a novel topological order whose identification requires a spin sensitive measurement, which does not exist to this date in any system (neither in Hg(Cd)Te quantum wells nor in the topological insulator BiSb). Using Mott polarimetry, we probe the spin degrees of freedom of these quantum spin Hall states and demonstrate that topological quantum numbers are uniquely determined from spin texture imaging measurements. Applying this method to the Bi{1-x}Sb{x} series, we identify the origin of its novel order and unusual chiral properties. These results taken together constitute the first observation of surface electrons collectively carrying a geometrical quantum (Berry's) phase and definite chirality (mirror Chern number, n_M =-1), which are the key electronic properties for realizing topological computing bits with intrinsic spin Hall-like topological phenomena. Our spin-resolved results not only provides the first clear proof of a topological insulating state in nature but also demonstrate the utility of spin-resolved ARPES technique in measuring the quantum spin Hall phases of matter.