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Help me critique and pin pint my SoP


Can someone help me out to critique my SoP. It is very urgent


Symmetry breaking in quantum mechanics is an important concept used to characterize the phases of matter. Crystals break translational symmetry, magnets breaking time-reversal and rotational symmetry, and superconductors breaking gauge symmetry are all different states of matter. The symmetry of crystal structure leads to various electronic Bloch states in a material on which the entire band theory of non-interacting fermions is established. Going through the recent advances in the band theory, I was intrigued by a different phase of material characterized by the topology of band structure without breaking any symmetry, having dissipation less spin-polarized conducting edge states protected from disorder by time-reversal symmetry. Experimental study of these novel phases of matter with an emphasis on the possible applications in spintronics and quantum computing is my motivation to pursue a Ph.D. at the Department of X at UCSB.

Topological insulators are insulating in bulk and have a conducting state at the edge with opposite spin electrons traveling in opposite directions (spin momentum locking). A recent proposal by Samarth et al. combining the topological insulator phase with magnetic ordering has given a unique way to generate spin currents for spintronic applications. Another ambitious proposal relies on solving the decoherence problem of qubits, which is a major source of error in a quantum computer. Topologically protected non-trivial states in proximity to superconductors give rise to emergent anyons (Majorana quasiparticles) with non-abelian braiding statistics when exchanged among each other. Fermions or Bosons do not carry any information when exchanged and are abelian but these quasiparticles carry the information of braid with a phase term in their wavefunction. As proposed by Kitaev et al. If researchers could create several of these anyons next to each other and shuffle them around, their quantum states would remember how they had been rearranged and thus encode information. As a part of my study, I would like to develop the materials which can host these Majorana modes with the robustness against the environment provided by topology. TMDCs with their 1T’ phase and more recently discovered T’’ phase in WTe2, MoS2 can be a possible host to these quasiparticle excitations. These theoretical proposals require careful material design and innovative methodologies for their observation and analysis. According to me, prediction, fabrication, observation, and potential applications are four important steps for the life cycle of any new concept in physics and topological insulators are currently in their infancy, with theories significantly advancing at a rapid pace while leaving experimentalists behind. I would like to shorten this gap between theory and experiments through my Ph.D. thesis.

Most of my research experience as an undergraduate was carried out in the chemical and structural analysis lab of Prof. Bratindranath Mukherjee, trying to develop an efficient catalyst for hydrogen evolution reaction in fuel cell applications. In my sophomore year, I was involved in an exploratory project trying to synthesize nanocomposite of Au and MoS2 for photo electrocatalytic applications. Shi et al. have already demonstrated this proposal of utilizing metallic nanoparticles to inject hot electrons to semiconductors upon irradiation with photons. Mie scattering theory applied to gold nanoparticles by Jain et al. demonstrated a much higher intensity resonance peak of nanorods as compared to spheres or flowers in the required wavelength due to localized surface plasmon property. Combining both the effects we developed the nanocomposite of 1T phase of MoS2 formed by lithium intercalation of 2H MoS2 with Au nanorods, developed by the seed growth methods. Optimizing the aspect ratio of nanorods, we were able to enhance the turnover frequency, reduce the overpotential and increase the current density of the electrolysis reaction. As a sophomore with the course structure involving three-dimensional bravais lattices, two-dimensional materials were interesting to study.


To further my quest and fulfill my excitement for the 2-dimensional material phases, I was granted an opportunity at the Defence Research and Development labs in Pune, India, under Dr. Balasubramanian to work on the rockstar and seminal 2-dimensional material, Graphene. With electronic structure characterized by Dirac cone-like linear dispersion of electrons, graphene shows excellent conductivity, flexibility, and tunability in the electronic structure. We developed a hydrogen storage solid-state material by the growth of Ni- based Metal-organic framework on graphene. Graphene provided excellent stability to the structure and a controllable adsorption and desorption cycle of hydrogen molecule by an applied external electric field. The results obtained are in the process of being published in an international journal with a good impact factor. Although the project was more experimental but during the two months, I began realizing that I was more interested in understanding the physics of the problem by the analysis of electronic structure and density of states.  I met people performing theoretical calculations by DFT trying to understand adsorption, desorption energies on the material surface. With my significant base of undergraduate level quantum mechanics and a curious mind, I modeled a small system of our composite to understand the energies of adsorption and desorption states using VdW corrected DFT simulations.

Back to Varanasi advancing my research in Mukherjee sir lab in chalcogenide materials, I took an independent project performing temporal study of different phases of Nickel selenide and reduced graphene oxide heterojunction by XRD and TEM performing parallel electrochemical measurements to analyze the most efficient and active phase for electrocatalysis. We presented the two parallel studies in the form of an oral presentation at the national conference on energy materials, one of them winning the best oral presentation award as well. Alongside working through the book on solid-state physics by Kittel as a junior, I got interested in understanding the electronic band structure, its tunability by material design perspective and how it can help us in achieving the desired properties and performance. I realized that the chemical synthesis route is not sufficient enough to get highly phase pure material and a defect-free lattice is required to probe and study the actual band structure and fundamental properties of materials.

I wrote to Prof. Stefano Agnoli and Gaetano Granozzi at the University of Padova in Italy and got an opportunity to work on two-dimensional chalcogenide materials and understand their growth by molecular beam epitaxy. Hands-on experience with XPS, ARUPS and STM helped me in understanding the spin-orbit coupling, its influence on the electronic structure, the atomic structure of material and surface states. We observed the indirect to direct bandgap transition in the electronic structure  on a reduction in the thickness of the layered structure to monolayer which and attributed it to the orbital hybridization effects in thicker layers. Concludingly, the effect of these properties on the HER activity was analyzed by performing the ex-situ electrochemistry and in-situ electrochemical scanning tunneling microscopy. Different from Ultra High Vacuum-STMs, our home-built EC-STM used tunneling through electrolytes to dynamically analyze the surface in the hydrogen evolution active region. As illustrated and demonstrated in the paper by Mitterreiter et al. we observed the additional noise in the EC-STM signal at the dopant site which is attributed to the local catalytic activity and thus concluded that Co sites are more active for HER. Contrary to the earlier proposed results we did not observe any activation of the basal plane upon doping with transition metals. The results were presented in the form of a poster at the Annual Technical Meeting organized by the Indian Institute of Metals.   

Being an undergraduate in metallurgy, I have had a strong knowledge in the understanding and observation of crystal structure and their importance for efficient material design. The freedom given by the parent university in the form of electives has allowed me to take several advanced courses in electronic properties of materials, quantum mechanics and condensed matter physics. Recognizing my interest in physics, I have been involved in several reading projects under physics faculty, Dr. Rajeev Singh and Prof. Sandip Chatterjee and self pedagoging myself to understand the complex ideas of topological condensed matter. Discussions with them outside classroom hours has refined my understanding of several concepts and improved my scientific temperament. A paper titled “A short course on topological materials” by Asboth et al. has helped me to understand the concept of Berry phase, Chern number and several proposed models (SSH model, Kane-Mele model, Zhang model) to develop a solid understanding of the theory. Together with my varied interdisciplinary experiences as an experimentalist with a good understanding of theory, I believe I would be able to contribute towards the high level of research carried out at UCSB. I have a solid understanding of the point group and space group symmetries important for topological state engineering in 2D and 3-dimensional materials.

UCSB is my top choice because it is home to highly experienced and famed experimentalists working in topological insulators and spintronics. It provides me with world-class facilities and a highly stimulating and natural environment for research to flourish. Especially the work performed in the laboratory of Susanne Steemer is particularly interesting to me, as she is trying to design quantum materials and engineer the electronic states with the help of strain-induced effects and external electric field. A recent paper by Qian et al. demonstrated that strain engineering can help in the transition from a trivial topological state to a non-trivial state in the 1T’ phase of WTe2 important for switching characteristics for device applications. Utilization of STEM (scanning transmission electron microscope) in Susanne's lab can further help in the study of atomic-level defects (like antisite defects) which can deteriorate topological insulator properties. Chris Palmtrom’s lab, who is a pioneer in spintronics, at UCSB is equipped with world-class facilities for the growth of high-quality materials and heterostructure of low dimensional materials and semiconductors. A recent paper from the Palmstrom group on the realization of quantized Majorana conductance in InSb nanowires in proximity to Al has paved the way for quasiparticle braiding for the realization of TQC. Hence, UCSB, with its excellent facilities and faculties would be a perfect assortment of my previous experience and prospects as a researcher.

Not only in academia, but I have also tried to incorporate my knowledge of materials to bring a change in the lives of people who are deprived of amenities like electricity. While participating in one of the Social Entrepreneurship events organized by the HULT International Business school, we presented our ideas for the utilization of piezoelectric sensors to harness energy from the motion and movement. We incorporated these piezoelectric in footwears, walking panels and analyzed the amount of energy we can generate by this simple modification. Although not highly efficient, these can be used as an alternative source of energy in highly deprived and hilly areas. During this project, I realized that materials can bring a change in the world and innovative ways to optimize their properties can bring a positive impact to the major pressing problems of society.

My entire journey as an undergraduate, I have been guided by great lecturers and professors who have incorporated in me a love for the subject, always helping me in overcoming different obstacles with due guidance and mentoring. Following them, I want to remain in academia and transfer the wisdom and knowledge which I have gained from these amazing personalities for the growth of the next generation individuals. I enjoy the art of teaching myself and have been an active member of the physics and astronomy club of the college, where we try to teach and develop the interest of young undergraduates towards the subject and mentor them to pursue their interests. I have been organizing Saturday sessions for the past one year teaching young undergraduates the importance of studying economics and continuously writing for the business blog. I am a firm believer that knowledge grows with sharing and I have learned countless new things interacting with the students trying to develop in them a desire to understand nature. I believe that It is my duty to pass this information to the unknowing, which I am trying to achieve through articles and blogs and will continue to do by remaining in academia. I have been an active writer for our science magazine “Corona” where I have written articles breaking the myths about quantum mechanics, black holes and other areas which have been falsely represented by some popular science. In my free time, you would find me practicing music or playing a synthesizer. I have been trained in classical Indian music right from my childhood which grew as my most important hobby. Music gives me inspiration, energy and, most importantly happiness to others.

Edited by Vats
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