AcknowledgmentsAll praises for almighty ALLAH who gave me the opportunity and strength to accomplish this job. I am deeply indebted to my supervisor, Professor Gennady Gusev, for his insightful guidance and for introducing me to the fast growing field of topological insulators. I greatly appreciate him for his ideas, extensive discussions, valuable comments and encouragement throughout the course of my studies at USP. This work would not have been possible without his support and interest and I am so grateful for all the time that Prof. Gusev devoted to work on this project.I am also very grateful to Prof. Alexander Levine, for introducing me to programming and the code written for simulation of transport properties of 2d topological insulators. I appreciate helpful discussions with him and how to edit the code for our device geometries. I would express my sincere appreciation to Prof. Felix Hernandez, Prof. Luis Dias and Prof. Alain Quivy for helpful discussions on research and other topics of condensed matter Physics. I gratefully acknowledge our collaborators at the Institute of Semiconductor Physics, Novosibirsk, for providing HgTe samples studied in this work. I would like to express my gratitude to Prof. Lucy Assali and Prof. Carmen Prado, for their help in bureaucracy and official matters. I would like to thank the professors of the Institute of Physics, particularly those with whom I studied my postgraduate courses.I am also very thankful to the jury of my qualification exam: Prof. Valmir Chitta, Prof. Felix Hernandez and Prof. Luiz Nagamine for their valuable suggestions and comments that helped improving this manuscript.I would like to thank all my friends and colleagues from University of São Paulo for their various form of support, during my PhD, especially, Jorge Leon, Bruno Anghinoni, Zahra Sadre Momtaz, Julio Cesar, Pablo Badilla, Fernando Aliaga, Diana Torres, Dennis Brennes, Anastasia Burimova, Natalia Ballaminut, Thiago Melo, Luiz Eleno, Ricardo Igarashi, Fernando Massa, Luiz Gomes, Victor Manotas, Gerson Pessoto, Giovanni Galgano, Flavio Moraes, Juan Enrique, Antonio Pasquale, Carlos Mera, David Tamayo, Niko Mamani, Claudio Padilha and Fabricio Marques. I would like to acknowledge peoples in CPG (Claudia, Eber, Andrea and Paula) and the secretaries of DFMT (Rosana, Sandra, Cecilia and Tatiana) for their help in all official documentations and correspondences. I would also like to acknowledge peoples in cryogenics and the lab technicians Paulinho, Geraldo, Eron, Renato and Olimpio for their help in cryo and other lab related stuff and Luiz Carlos for network and computer related work.A special thanks go to all my Pakistani friends in São Paulo: Saeed Ullah, Hanif ur Rehman, Irfan Ullah, Taj Ali Khan, Asif Iqbal, Huma Asif, Ishtiaq Ahmed, Anees Ahmad, Anwar Shamim, Faiz Ahmed, Haq Nawaz, Ali Paracha, M Khalid, Latif Ullah, M Nawaz, Liaqat Ali, Niaz Marwat, Ajmir khan and Bakhat Ali for their moral support and also Ishtiaq Ahmed for help in correction of thesis.I would express my gratitude to my ...