Interesting reading - resonators, quantum geometry w/ phonons, and fractional quantum anomalous Hall

 Real life continues to be busy, but I wanted to point out three recent articles that I found interesting:

• Mechanical resonators are a topic with a long history, going back to the first bells and the tuning fork.  I've written about micromachined resonators before, and the quest to try to get very high quality resonators.  This recent publication is very impressive.  The authors have succeeded in fabricating suspended Si3N4 resonators that are 70 nm thick but 3 cm (!!) long.  In terms of aspect ratio, that'd be like a diving board 3 cm thick and 12.8 km long.  By varying the shape of the suspended "string" along its length, they create phononic band gaps, so that some vibrations are blocked from propagating along the resonator, leading to reduced losses.  They are able to make such resonators that work at acoustic frequencies at room temperature (in vacuum) and have quality factors as high as \(6.5 \times 10^{9}\), which is amazing.  
• Speaking of vibrations, this paper in Nature Physics is a thought-provoking piece of work.  Electrons in solids are coupled to lattice vibrations (phonons), and that's not particularly surprising.  The electronic band structure depends on how the atoms are stacked in space, and a vibration like a phonon is a particular perturbation of that atomic arrangement.  The new insight here is to look at what is being called quantum geometry and how that affects the electron-phonon coupling.  As I wrote here, electrons in crystals can be described by Bloch waves which include a function \(u_{\mathbf{k}}(\mathbf{r})\) that has the real-space periodicity of the crystal lattice.  How that function varies over \(\mathbf{k}\)-space is called quantum geometry and has all kinds of consequences (e.g., here and here).  It turns out that this piece of the band structure can have a big and sometimes dominant influence on the coupling between mobile electrons and phonons.
• Speaking of quantum geometry and all that, here is a nice article in Quanta about the observation of the fractional quantum anomalous Hall effect in different 2D material systems.  In the "ordinary" fractional quantum Hall effect, topology and interactions combine at low temperatures and (usually) high magnetic fields in clean 2D materials to give unusual electronic states with, e.g., fractionally charged low energy excitations.  Recent exciting advances have found related fractional Chern insulator states in various 2D materials at zero magnetic field.  The article does a nice job capturing the excitement of these recent works.