Probing bulk crystalline topology with broken translational symmetry: Position-space markers & other techniques
Year: 2024
Type: dissertation
Abstract: This dissertation is comprised of works focused on theoretical investigations related to topological crystalline phases of matter.Within this field of study, tremendous progress has been achieved in the past several years in classifying non-interacting fermionic symmetry-protected topological phases, which are characterized by bulk topological invariants.Symmetries of the lattice can be exploited to reduce the complexity of characterizing the bulk nature of topological phases, namely translational symmetry, which is the assumption of a crystal with a perfect, periodic structure, along with internal symmetries (such as time-reversal, particle-hole, and chiral symmetries) and crystalline symmetries (such as rotations, reflections, etc.).The assumption of translational The time I spent at Urbana has served as some of the most formative years of my entire life.I feel incredibly blessed to have had the opportunity to engage in intellectual conversations, start collaborations, and listen to talks from some of the most brilliant physicists at AJL-ICMT.Although there were plenty of rough times during my PhD, some of which were more difficult to overcome than I expected, at the end of the day, I am truly honored to have completed my PhD studies at AJL-ICMT.I will certainly miss Urbana and the countless hours I have spent in the Engineering Sciences Building conversing with colleagues about physics and life, while squeezing in the time to read and write papers, work out calculations, and hastily make presentations.For the truly memorable experiences I have had here, I have many people to thank, all of whom have contributed to my growth not only as a physicist, but as a human being too.First and foremost, I am grateful to my advisor, Taylor Hughes, for allowing me into his research group and taking me on as his student.Taylor showed me how to think independently and creatively and how to recover from repeated setbacks and failures.Most importantly, he encouraged me to have confidence in my own ideas and to pursue them wholeheartedly.Even during the times when I felt that my ideas and the questions I would ask were stupid and worthless, Taylor was able to turn my negative and cynical perspective on my research progress into something positive.He was always incredibly patient with me, willing to explain things over and over again until I finally understood what he was saying.It is rare to find these qualities in an advisor, and although there were times when I felt stranded during this whole process, he always showed me that there was a path forward.If it was not for him, I would not be able to call myself a physicist at the end of this long and hard PhD journey.Second, I would like to thank my collaborators and colleagues through which the years of worth of conversations I have had with them have shaped me into the physicist I am today.I am incredibly grateful to Barry Bradlyn, who effectively co-advised me alongside Taylor during the first three years of my PhD and helped me understand the intricacies of topological quantum chemistry and helped with writing my first paper.I am grateful to Yoonseok Hwang and Giuseppe De Tomasi, two postdocs who joined AJL-ICMT rather late into my PhD but with whom I have had several intellectually stimulating conversations with that have led to plenty of new research ideas and ways of thinking about physics I had not witnessed before.I am also grateful to Penghao Zhu and Oleg Dubinkin, my brilliant group mates for years whose works have inspired me tremendously.They always had the patience and time to entertain my silly ideas and give me plenty of useful feedback on them, and provided me with plenty of help on the simple calculations I needed to get done.
Author: Velury, Saavanth
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220761820