Implementing a model of polyacetylene

An impressive paper was just published in Nature, in which atomically precisely fabricated structures in Si were used as an analog model of a very famous problem in physics, the topological transition in trans-polyacetylene. 

Actual trans-polyacetylene is an aromatic organic chain molecule, consisting of sp2 hybridized carbons, as shown.  This is an interesting system, because you could imagine swapping the C-C and C=C bonds, and having domains where the (bottom-left to top-right) links are double bonds, and other domains where the (top-left to bottom-right) links are double bonds.  The boundaries between domains are topological defects ("solitons").  As was shown by Su, Schrieffer, and Heeger, these defects are spread out over a few bonds, are energetically cheap to form, and are mobile.  

(Adapted from Fig 1 here)

The Su-Schrieffer-Heeger model is a famous example of a model that shows a topological transition.  Label site-to-site hopping along those two bond directions as \(v\) and \(w\).  If you have a finite chain, as shown here, and \(v > w\), there are no special states at the ends of the chain.  However, \(v < w\) for the system as shown, it is favorable to nucleate two "surface states" at the chain ends, with the topological transition happening at \(v = w\).  

The new paper that's just been published takes advantage of the technical capabilities developed over the last two decades by the team of Michelle Simmons at UNSW.  I have written about this approach here.  They have developed and refined the ability to place individual phosphorus dopant atoms on Si with near-atomic precision, leading them to be able to fabricate "dots" (doped islands) and gate electrodes, and then wire these up and characterize them electrically.  The authors made two devices, each  a chain of islands analogous to the C atoms, and most importantly were able to use gate electrodes to tune the charge population on the islands.  One device was designed to be in the topologically trivial limit, and the other (when population-tuned) in the limit with topological end states.  Using electronic transport, they could perform spectroscopy and confirm that the energy level structure agrees with expectations for these two cases.

(Adapted from Fig 2 here)

This is quite a technical accomplishment.  Sure, we "knew" what should happen, but the level of control demonstrated in the fabrication and measurement are very impressive.  These bode well for the future of using these tools to implement analog quantum simulators for more complicated, much harder to solve many-body systems.