Optical and Collective Properties of Excitons in 2D Semiconductors by Matthew N. Brunetti A dissertation submitted to the Graduate Faculty in Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2019 ii © 2019 Matthew N. Brunetti All Rights Reserved iii This manuscript has been read and accepted by the Graduate Faculty in Physics in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy. Professor Oleg L. Berman Date Chair of Examining Committee Professor Igor L. Kuskovsky Date Executive Officer Professor Roman Ya. Kezerashvili Distinguished Professor Godfrey Gumbs Professor Antonios Balassis Professor Paula Fekete Supervisory Committee The City University of New York iv Abstract Optical and Collective Properties of Excitons in 2D Semiconductors by Matthew N. Brunetti Advisers: Professor Oleg L. Berman & Professor Roman Ya. Kezerashvili We study the properties of excitons in 2D semiconductors (2DSC) by numerically solv- ing the Schrödinger equation for an interacting electron and hole in the effective mass ap- proximation, then calculating optical properties such as the transition energies, oscillator strengths, and absorption coefficients. Our theoretical approach allows us to consider both direct excitons in monolayer (ML) 2DSC and spatially indirect excitons in heterostructures (HS) consisting of two 2DSC MLs separated by few-layer insulating hexagonal boron nitride (h-BN). In particular, we study indirect excitons in TMDC HS, namely MoS2, MoSe2, WS2, and WSe2; both direct and indirect excitons in the buckled 2D allotropes of silicon, germa- nium, and tin, known as silicene, germanene, and stanene respectively, or collectively as the Xenes; and both direct and indirect excitons in the anisotropic 2DSC phosphorene, the 2D allotrope of black phosphorus. Our study of indirect excitons in TMDC/h-BN HS was one of the first to study the dependence of the properties of spatially indirect excitons in 2DSC HS with respect to the interlayer separation. When considering excitons in the Xenes, we focused on the dependence of the excitonic properties on the magnitude of an external electric field oriented perpendic- ular to the Xene monolayer(s), which can be used to tune the band gap of the Xenes in-situ, thereby changing the charge carrier effective mass and thus the properties of the excitons themselves. Interestingly, our results for excitons in the Xenes indicate that freestanding ML Xenes may in fact be excitonic insulators in their ground states, that is, when there is zero v external electric field. Furthermore, we predict, based on our results, that the freestanding ML Xenes should undergo a phase transition from the excitonic insulator state to a semicon- ducting state as the external electric field is increased beyond some critical value which is unique to each material. Lastly, our results show that the anisotropic exciton reduced mass, inherited from the anisotropic effective masses of electrons and holes in phosphorene, causes significant deviations in the eigenstates compared to the isotropic 2D model used for TMDCs and Xenes, and that furthermore, this anisotropy leads to enhanced (suppressed) optical ab- sorption compared to the isotropic exciton, under linearly polarized excitations along the in-plane crystal axes with relatively smaller (larger) charge carrier effective masses. In addition, we were able to extend our theoretical framework to consider both exciton- photon and exciton-exciton interactions in a weakly interacting Bose gas of excitons, thereby allowing for the study of exciton-polaritons in an optical microcavity. Using this extended framework, we calculate the Rabi splitting between upper and lower polaritons in a model microcavity, as well as the critical temperature for the Berezinskii-Kosterlitz-Thouless (BKT) phase transition of a weakly interacting Bose gas of lower polaritons. In particular, we applied these methods to study polaritons in the ML Xenes, once again focusing on the dependence of these quantities on the magnitude of the external electric field. Based on our calculations, we predict that, assuming a particular type of open microcavity which maximizes the exciton- photon interaction strength, both freestanding ML silicene and ML silicene encapsulated by h-BN should support polaritons with relatively large Rabi splittings whose BKT critical temperature is greater than room temperature, such that it should be possible to achieve room-temperature superfluidity of polaritons in these materials for a particular range of values of the external electric field. Acknowledgments I would like to express my sincere gratitude to my family and friends for their emotional support during this long, challenging, wonderful, and weird journey. I am grateful to my advisors, Oleg Berman and Roman Kezerashvili, for the uncountable ways in which their ad- vice, guidance, leadership, and patience influenced my personal, professional, and academic growth over the past four years. Oleg, your genuine enthusiasm for scientific research was one of the first things I noticed when we first met back in the Spring of 2015. It has been a constant source of inspiration and motivation, especially during those times when a setback in my calculations or an unexpected theoretical roadblock challenged my resolve and perseverance. Now, looking back at the end of my Ph.D. journey, I can honestly say, thanks to the example set by your own enthusiastic approach to scientific research, that every new topic I learned and challenge I overcame brought with it a sense of wonder and fascination, as if I was rediscovering physics for the first time. Thank you for showing me that it is possible to maintain that sense of wonder, that appreciation for the natural beauty of physics and mathematics, no matter the topic or my level of prior understanding. Dr. Roman, your relentless work ethic was a huge inspiration to me, and it motivated me to push myself to work harder than I ever thought I was capable of. Indeed, it was often the case that you and I were literally or figuratively working side-by-side during those times of intense work, and in those moments, I was deeply appreciative of, and was reassured by, vi vii your obvious and unwavering dedication to the personal and professional success of everyone around you. Whether it was receiving a heavily annotated manuscript draft only a few hours after first sending it to you, spending an entire day or more on the phone with me to polish, refine, and improve my writing, spending 3+ hours in your office after a full day of classes to finalize a manuscript, or meeting you in your office on the weekend, I will never forget how you would put aside your numerous other responsibilities without a second thought in order to help me when I needed it. I am simply left in awe by your unstoppable determination to make the most out of every day and every opportunity, and by your unyielding committment to the success of everyone around you. Thank you for showing me the true meaning of words like determination, dedication, preseverance, and professionalism. I am grateful for the enlightening scientific discussions with Dr. Yurii E. Lozovik, whose extensive scientific knowledge and experience provided invaluable insight into our results, particularly regarding my studies of the excitonic insulator phase in the Xenes. I am also grateful to Distinguished Professor Godfrey Gumbs, who first suggested that I consider Oleg as my Ph.D. advisor. Dr. Gumbs also introduced me to the AFRL summer scholars program, from which I have two summers filled with memories of fascinating and awe-inspiring science performed by hundreds of extremely talented, friendly, and welcoming people. Without Dr. Gumbs’ sound advice and helpful guidance in the earliest days of my graduate career, I may very well have followed a different path entirely. I am also extremely grateful to the user Jens from the Mathematica Stack Exchange message boards, whose extremely detailed response to a basic coding question was immensely helpful to me in the earliest days of my research, when I was inundated with new academic subjects to learn and master, from condensed matter physics to quantum optics, as well as a new, wholly unfamiliar coding language. I am also grateful to my colleagues in the Physics Department at City Tech, who immedi- ately made me feel comfortable and welcome as I adjusted to my new role in the department; viii I am happy to thank Professors Allyson Sheffield and John Toland for giving me to oppor- tunity to teach at Laguardia Community College in the Fall of 2015; I am grateful for the opportunity to have spent two summers in the AFRL summer scholars program, which not only stands as the most completely satisfying and thoroughly enjoyable work experience I’ve ever had, but from which I made many friends and fond memories in between our time in the lab; I am also grateful to have been surrounded by a cohort of talented and wonderful classmates during my first year in the program; I am similarly grateful for the friends that I made, and the moments that we shared, during my year with the Physics graduate program at the University of Delaware; finally, I’d like to thank Daniel Moy and Ebony Holloway in particular for all of the myriad ways they helped keep me organized amidst the chaos of graduate school. I consider myself fortunate to have been positively influenced by many great teachers throughout my life, and I am especially grateful for the following people, by whom my own teaching style has been heavily influenced, and from whom I gained a deep appreciation for their class: Mr. Van Soest, Miss Pearsall, Mrs. Meneghin, Mr. William J. Oliver, Mr. John Nihen, and Ms. Farah Farhadian from Fair Lawn High School; and Dr. Jane L. Pinchin, Dr. Jonathan Levine, and Dr.