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A topologically ordered material is characterized by a rare quantumorganization of electrons that evades the conventional spontaneously brokensymmetry based classification of condensed matter. Exotic spin transportphenomena such as the dissipationless quantum spin Hall effect have beenspeculated to originate from a novel topological order whose identificationrequires a spin sensitive measurement. Using Spin-resolved-ARPES, we probe thespin degrees of freedom and demonstrate that topological quantum numbers areuniquely determined from spin-texture Berry Phase imaging measurements.Applying this method to pure antimony (Sb) and Bi-Sb, we identify the origin ofits novel Topological Order and the negative value of the mirror Chern number.These results taken together constitute the first observation of surfaceelectrons collectively carrying a topological Berry's phase and definite mirrorChern chirality in pure Antimony (Sb) which are the key electronic propertiesfor realizing topological quantum computing via the interface Majorana fermionframework. This paper contains the details of the above mentioned previouslyreported (Science \textbf{323}, 919 (2009)) results.

Observation of topologically protected Dirac spin-textures and \pi Berry's phase in pure Antimony (Sb) and topological insulator BiSb