Reading the right papers

Students often find it particularly hard to tell which papers are worth an in-depth reading, which can be skimmed, and which are not essential to the current research project. Since this is something that is usually only learned through experience, examples can be helpful for building intuition.

Consider the first paper from my PhD research, Pseudospin and nonlinear conical diffraction in Lieb lattices, published in Physical Review A. With the benefit of hindsight, this turned out to be a Good Paper, with multiple experimental groups exploring some of the ideas in the following years. Why did it have an impact?

The research project didn't start by reading a bunch of papers and getting a new idea. The idea arose from talking to people - experimental collaborators, and one of the eventual co-authors (Omri), who had recently finished his PhD on the theory of wave propagation in graphene-like honeycomb photonic lattices. 

I was asked to see whether any of the ideas in his thesis could be feasibly investigated by our experimental collaborators. Honeycomb lattices being hard to do in their setup at the time, they wanted to know whether similar phenomena might be observable in a square lattice. Similar to how one can remove a period-doubled lattice from the triangular lattice to create a honeycomb lattice, removing sites from an ordinary square lattice yields a face-centred square lattice with intersecting bands. Great!

As is so often the case in research, we were not the first to have this idea, and actually in the preceding few years several groups had been exploring the properties of this lattice, motivated by huge interest in the electronic properties of graphene (Refs. [7,8,10,11,12,13] in the paper). These works were all published in the Physical Review, not "high impact" venues such as Nature / PRL, probably because referees thought it would be difficult to reproduce this model in an experiment. Being background material, an in-depth reading of all these papers was not required - we just needed to know roughly what they did and how they did it to understand how novel our results were.

In these papers we not only found the now commonly-used name for this lattice (the Lieb lattice), but also learned about how its properties were of interest in the context of cold atoms / BECs and electronic properties of materials. Lucky for us, we could not find any papers studying this lattice from the point of view of photonics, meaning that we had something novel! But on the other hand, we clearly couldn't just take these existing results (based on tight binding models) and do exactly the same using a "photonic" tight binding model without our work ending up being merely incremental and forgettable. Therefore we considered a few photonics-specific extensions:

(1) Wave propagation dynamics in the nonlinear regime, translating the analysis in one of Omri's recent papers (Ref. [11]) to the Lieb lattice setting. This one I had to read and re-read in detail to fully understand the analytical and numerical simulation tools used.

(2) Understanding the coupling between the different angular momentum degrees of freedom in our system. This similarly involved an extension of previous results by others for the honeycomb lattice (Ref. [18]) to the Lieb lattice setting. We also had to carefully read and understand this paper.

(3) Photonics-specific simulations not limited to a tight binding approximation and using experimentally-feasible parameters similar to those used in our collaborators' recent work (Ref. [26]).

In summary:

• Talk to experts early on to find out what the real important problems are and whether they have any that you are in a position to solve.
• Once you have an approximate solution or plan of attack, you need to check the literature to understand its importance and relevance to other work. At this stage you will often encounter papers with ideas very similar to yours.
• Identify your niche and expand on the novel points of your work, usually building on a few specific related papers that need to be carefully read and understood.
• It is usually easier to first solve a specific problem a single expert is having, and then figure out how your solution generalizes. The reverse approach - solving a problem in generality before considering specific examples - should only be attempted with extreme caution.