Arijit Bhattacharyay is an Assistant Professor in Physics and Biology at IISER Pune. His research interests are in the area of statistical physics and his work involves complex systems that have multiple degrees of freedom and generally not in equilibrium. Resistive regime of a superconductor represents one such complex system that he is working on. He describes here a recent publication from his laboratory along with undergraduate student Darshan Joshi in Journal of Physics: Condensed Matter (23:342203).
In the paper titled “Revisiting the Langer–Ambegaokar–McCumber–Halperin theory of resistive transitions in one-dimensional superconductors with exact solutions” we have discussed about an almost 40 years old accepted theory for the mixed phase of a one-dimensional superconductor where the superconducting and the normal phase (phase with a nonzero resistance) co-exist. Generally, there exists a temperature called the critical temperature for a superconducting material below which the material becomes superconducting i.e., the resistance to electrical conduction goes to zero and above the critical temperature the material remains normal i.e., it has nonzero resistance to electrical currents through it.
Now, for a very thin wire of superconducting material it has been seen that if one applies a voltage across the length of the wire at a temperature below and close to the critical temperature, there exists a mixed phase, called resistive regime, in which superconductivity and normal behavior co-exist. For this to happen, the superconducting order parameter (a measure of superconductivity) has to vanish at least at some points along the length of the wire and that is where the so far standard Langer–Ambegaokar–McCumber–Halperin theory had some inconsistencies. The Langer–Ambegaokar description of the free energy of the system diverges at the vanishing amplitude of the superconducting order parameter and we have corrected this part of the theory in our present paper to account for the local vanishing of the order parameter amplitude without diverging free energy.
– By Arijit Bhattacharyay
A Chat with Darshan Joshi
Darshan Joshi is an Integrated M.S. student at IISER-Pune and is presently doing his fifth year project at the Tata Institute of Fundamental Research (TIFR) in Mumbai. In this interview Darshan talks about his research on superconductors and what initiated him to this field.
SK: Hi Darshan! Congratulations on your recent publication with Arijit Bhattacharyay. Before we talk about this work, could you tell us when you did this project and what made you choose Dr. Bhattacharyay’s lab?
DJ: Thanks! We have a course at IISER-Pune called theory project/lab project as a 3 credit elective for 3/4th year students. I started my project with Arijit Bhattacharyay in my 6th semester, around January, 2010. There were two reasons why I chose his laboratory. One, I wanted to do some theoretical work and I admired his logic and perspective irrespective of the field. And two, there was a Physics Day at IISER-Pune in which Dr. Bhattacharyay had presented his work related to superconductors at that time. That topic fascinated me a lot… and I wished to know more about it… so at the end of 5th semester I approached him for a theory project and he agreed instantly!
SK: Was this a semester-long project?
DJ: More than that actually. My 6th semester was primarily devoted to getting acquainted to basics of superconductors and related theories. It was in the 7th semester that majority of the work got done….8th semester was mostly refining what was done and adding few important pieces to complete the work.
SK: Can you describe this work—what were the questions you asked and what were your main findings?
DJ: Sure! I had persuaded Dr. Bhattacharyay to allow me to work on something related to his research on superconductors. The first aim was to calculate the drop in ‘critical temperature’ due to resistive transition by a different and simpler method than that originally proposed in a theory by Langer–Ambegaokar–McCumber–Halperin (LAMH) in 1968.
But during this investigation, when we went through the original LAMH theory, we kept finding some inconsistencies and were uncomfortable about their approach. So we went to the root cause, identified the inconsistency and then calculated the ‘energy barrier’, which is of prime importance, from our point of view……and to our surprise it matched exactly with that given by LAMH (within a given limit)!
SK: Can you describe this a bit more? If you have found and corrected an inconsistency in the LAMH theory, how can your energy barrier calculation provide you the same result as the LAMH theory?
DJ: Yes, this is very important! It was rather puzzling… but then a detailed look at the derivation of earlier work suggested that they had stuck to ‘energy conservation’ (although their idea of the way the barrier is overcome was incorrect!) However, the energy barrier calculations match only within the limit of q=0 (q is wave number).
Frankly speaking, we cannot comment on which theory fits best to the experiments in the non-zero q limit…but since our theory is very consistent, adhering to all the requirements, we believe it to work better.
SK: Fair enough!
DJ: The “different approach” that we used was based on a very simple idea (Dr. Bhattacharyay’s previous work) that the dynamics of amplitude and phase of the superconducting order parameter can be considered independent.
SK: And the prevailing view suggested otherwise…
DJ: Yes, initially not many believed that amplitude and phase dynamics could be independent… in fact as a ‘by product’ of our work, we actually got the same relation which was arrived at by Dr. Bhattacharyay previously by a completely different approach.
SK: Sounds like a nice validation, I can see the excitement! Which lab are you in and what are you currently working on?
DJ: I’m right now working with Prof. Unnikrishnan (TIFR) and the project is about investigating the ‘radiation reaction force’. It is in a preliminary stage now but, broadly, it is to do with electrodynamics of charged particles in some special situations.
SK: So, you will be graduating in 2012? Have you thought of what after that, or is it too early to ask?
DJ: Yes…! As of now, I’m aiming for a Ph.D.
SK: In Physics? Any favorite areas?
DJ: Well, actually I like Physics. It’s difficult for me to narrow down my likes to a particular sub-field, although eventually I have to decide upon it during Ph.D. But I think I still have time for it!
-Interviewed by Shanti Kalipatnapu