Possible Ordered States in Graphene Systems

Acknowledgments I must admit that pursuing my graduate studies here at the University of Texas at Austin gave me a rare opportunity to be under the tutelage of talented professors. However, today I feel chiefly indebted to my advisor Dr. Allan MacDonald for the patience and sincerity he has shown me in regard to this dissertation. I would like to take this opportunity to express my gratitude, first and foremost, to him for successfully guiding me through my graduate studies with his encouraging advice and propitious assistance. have realized that the friendship that we were able to establish during my stay here in Austin has truly inspired me in many ways. A special thanks to Ion Garate, my all-time officemate and great friend. I would also like to extend my thanks to Becky Drake for her kindness and the immense help she provided with administrative work. I am grateful to my collaborators Bhagawan Sahu and Marco Polini for giving me their generous assistance and tireless support while we were working v on several projects together. I am likewise thankful to my committee members their beneficent feedback on this dissertation. To all the members of the UT Red Devils soccer team, I also wish to convey my overwhelming gratitude. All of you have been a great source of refreshment as I underwent through an otherwise tedious process of graduate studies. I would also like to thank all my friends whom I have failed to mention, but will be remembered. The friendship we built during my stay in Austin shall forever be etched in my heart, as I hope that it does in yours as well. My stay here could not have ended quite meaningfully as it has today, had I not encountered my friends who brightened my life with laughter and joy. Finally, I wish to thank my family for the unconditional love and unwavering support that they have shown me not only in the course of my studies, but in my life as well. They have truly been an infinite fountain of strength and hope for me. They have always stood by my side, especially in strenuous times I confronted during my studies. Even though I know that words are not enough to fully thank their unparalleled love and support, I want to offer them my immeasurable love and thanks. Graphene is a two dimensional honeycomb lattice of carbon atoms …