John Carlos Baez on Nostr: In blue bronze the Peierls instability kicks in below about 180 K. The octahedra in ...

In blue bronze the Peierls instability kicks in below about 180 K. The octahedra in the chains bunch into pairs, the crystal abruptly stops conducting, and a charge density wave forms along each chain of octahedra.

Once the charge density wave has formed, it has two natural ways to wiggle:

• its amplitude (how strongly bunched the ripple is) can pulse;
• its phase (where exactly the peaks of the ripple sit along the chain) can shift.

Pulsing the amplitude costs real energy. But sliding the phase - pushing the entire density wave bodily along the chains - costs essentially nothing. Why? Because nothing in the crystal cares where the peaks of the ripple happen to land. This is a strange gift of the fact that the charge density waves have a wavelength that's an irrational multiple of the spacing between atom pairs. No position is preferred over any other, so the wave can slip freely!

The resulting slow, almost-free sliding excitation is called a phason, and very gentle, long-stretching versions of it cost vanishingly little energy to excite. There's a deep principle at work here, known as Goldstone's theorem, that says whenever a system spontaneously settles into one of infinitely many equivalent configurations, it must come with a corresponding gentle shimmer mode that explores the alternatives.

So the Peierls instability in blue bronze doesn't just give a static charge density wave: we get phasons too!

(6/n)