vrajan Posted November 22, 2019 Share Posted November 22, 2019 Hello everyone, Here is my SOP for Physics PhD. programs. Please take a look and give me some feedback. Also, recommendations and suggestions for my target grad schools would be really helpful. Some details about me: GRE general: 153 V, 157 Q, AWA: 4; TOEFL: 98/120; GPA : 3.7/4; GRE physics: results yet to be declared. I plan to specialize in Theoretical Condensed Matter Physics, particularly in Topological Insulators. I would like to appreciate for your help, in advance. Thank you very much !! I had an influencing fascination towards science right from my school days. Honestly put, those are the days, when I was not able to distinguish between scientific accomplishments and technological inventions, yet the curiosity I had all along, had driven me to constantly search for the scientific inquiries and to inculcate scientific temperament from the sources that were available in and out of classrooms. My Bachelor’s Program (B.Sc 2014-17): I got admitted in a Bachelors course (B.Sc) with a triple major in Physics, Electronics, and Mathematics in the prestigious [University___X]. Apart from the curriculum done in the classrooms, I had a great enthusiasm for taking part in various science fests and competitions both at inter and intra-college level. It was during one such fest, I along with two of my batch-mates devised a “Voice - commanded wheelchair for disabled people”. In this project, I wrote a JAVA code to accept voice commands using audio sensors which were then processed by Arduino UNO microprocessor. This was the first time I was able to realize the immensity of computation in everyday life. By staying in [location] which is a hub of basic sciences with research institutes like [institute names] around, I had an excellent opportunity to participate in and attend many inspiring lectures and seminars by luminary physicists from all over the world. The lecture in a state-level seminar on “Science from Space-new Findings and Challenges Ahead” sponsored by [institute name], has drawn me towards the beautiful world viz., the field of plasma physics. I was particularly captivated by this unique state of matter because of its wide-ranging applications in various fields like solar physics, nuclear fusion and so on. This led me to do a term paper entitled [title] under [Dr.A]. In this term paper, I studied the basic equations (M.H.D equations) of plasma physics in the context of astrophysical plasmas using the fluid description of plasmas. To widen my understanding of plasma, I did a research project at the [Institute name] under the guidance of Prof. [Dr.B] and Prof.[Dr.C]' during the summer of 2016. In this project, we studied the acoustic waves in a classic fluid model. By taking a linear perturbation, we solved the fluid equations analytically to get the dispersion relation. Further, by using LCPFCT (Flux corrected transport) code, - an algorithm to simulate generalized continuity type equations - we solved the equations computationally and plotted the velocity and density profiles at different time steps. Secondly, We modified fluid equations to simulate plasma oscillations and followed the same steps as above to understand how plasma oscillations propagate. During this tenure of two months, I was able to acquire some knowledge on the different computational techniques which are being used in physics. This exposure helped me to get motivated towards having an in-depth understanding of the field of condensed matter physics. My Master’s Program (M.Sc 2017-19): After having completed my B.Sc, I proceeded to do my Masters majoring in physics at [University___Y]. I have undergone many important courses both basic(core) and advanced courses(electives) - to name a few - like advanced condensed matter physics and soft condensed matter physics to explore different sub-fields of Condensed Matter Physics on one hand and Quantum Field theory on the other hand. It was during this time that I came across a more exotic phase of materials in solid-state systems called Topological Insulators by Prof. [D]. This prompted me to do my Master’s thesis, under him entitled “Study of Topological Insulators in 1-D and 2-D”. We studied the basic models for topological insulators in 1-D, the SSH(Su-Schrieffer–Heeger) model and 2-D, the Haldane model. We considered tight-binding Hamiltonian of these models and solved them both analytically and numerically by applying periodic boundary conditions to get the band structure. Also, we computed the Berry phase and the Chern number analytically to specify the distinction between a topological insulator and a normal insulator. Another unique characteristic property of topological insulators is the Bulk-edge correspondence (i.e insulating in the bulk and conducting at the edges). To see this edge peculiarity, we applied Open boundary conditions and analyzed the characteristics of these edge states by plotting their wave functions. This thesis turned out to be a major factor in shaping my current interests towards Topological Insulators. After my masters, I have been reading about the 3-D Kane-Mele model and also attempting to understand a new situation wherein we keep the complex (arbitrary phase instead of the spin-orbit coupling term where the phase can only be either maximum or minimum) second nearest hopping Haldane's term and the Rashba coupling term in the Kane-Mele Hamiltonian and compare their competing effects upon the topological phase. The way forward: Having gone through these varied experiences of computational and theoretical studies, I want to pursue my P.h.D in Theoretical Condensed matter physics. It is true that Topological Insulators are quite captivating due to their intimate association with the concepts of topology, solid-state physics, and symmetry. But I am equally fascinated to explore new vistas in physics if opportunities are available. With topology having wide applications ranging from topological insulators to quantum computation, I believe that there are many unexplored areas for me to pursue my career in this emerging field. Therefore, I consider P.h.D as a platform for fulfilling my immediate goal of extending my understanding of Topology in Physics and also a necessary condition for a good research career in the future. To sum up, with the aforementioned knowledge I hitherto acquired and with my realistic understanding of the challenges of contemporary research I am fairly confident that if I am qualified to get an opportunity to pursue research in the Department of Physics of this highly esteemed institute, it will certainly shape my career in my quest to understand nature through physics. My love for listening, learning, conceptualizing and discussing science and its pursuits with my teachers and classmates and the experience I gathered in giving informal lectures to my juniors, impacted to a greater extent to develop a strong penchant for teaching. I am equally confident that I will create a niche for myself in the world of teaching. Thanks for reading !! Link to comment Share on other sites More sharing options...

## Recommended Posts

## Create an account or sign in to comment

You need to be a member in order to leave a comment

## Create an account

Sign up for a new account in our community. It's easy!

Register a new account## Sign in

Already have an account? Sign in here.

Sign In Now