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Comment by gus_massa | Hacker News Reader

No. I had a similar idea, and the article is confusing, but it's explained near the end

> "Now, at certain points the tracks intersect, so our particle train is moving along its fast track, at light speed, but then it hits an intersection and needs to switch to a perpendicular track.

It's about a different effective mass for the particle in the x, y and z direction. The idea is that inside a crystal you have quasiparticles like the "holes" or the "electrons", but the "electrons" inside a crystal have a different mass that an electron movin in vacuum https://en.wikipedia.org/wiki/Effective_mass_(solid-state_ph...

If the crystal is not symetrical in the x, y and z directions, it's not so weird that the "electron" (or whatever this is) has a different mass in each direction. For example crystals that are differen in the x, y and z directions may have different speed of light in each direction.

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crystal... ofc.. :(

IIRC, inside iron, the magnetic field makes "electrons" with spin up and down have different band that have different curcature and then diferent effective mass. So perhaps it's possible to have a similae effect in one direction, but we should ask an expert...

Retracted: IIUC the particle with spin in one direction will have a different effective mass than the particle in with dpin in the opposite direction. But they will not change mass when they change direction. (What about crystals with an asymmetric cell???)

> What about crystals with an asymmetric cell???

Asymmetric unit cells can also cause spin-orbit coupling (e.g. Rashba effect) or altermagnetism (recently discovered effect), so it depends on the asymmetry type.

The effective mass of an electron is related to d^2E(k)/dk^2 where E(k) is the electron band structure. If E(k) is linear in k_x but parabolic in k_y, the effective mass is zero in the x direction but finite in the y direction. But as far as I know, it is not possible to make the mass finite in the +x direction but zero in the -x direction.

What happens in a half filled asymmetric band? Like https://imgur.com/a/half-filled-asymetric-band-P7NQ7zU

A new electron will fall in places with different curvature if you choose one direction or the other.

Or the mass is calculated as the average because an electric field must remove an electron form one side and put it in the oher?

(I took my solid physics class too many years ago, I don't remember the details and I never understood all of them anyway.)

I’m actually not sure. Do you know of such a material, with that kind of asymmetric band structure in equilibrium?

I would expect such a material as you linked to have a momentum imbalance in the x direction, which leads to mass transport in the x direction, until a new equilibrium is achieved.

> I would expect such a material as you linked to have a momentum imbalance in the x direction, which leads to mass transport in the x direction, until a new equilibrium is achieved.

That makes sense. So it electrons will flow in one direction until there is a static electric field that create a slope in the fermi level. Perohaps https://en.wikipedia.org/wiki/Electret

It says that quartz is an electret, but I can't find the band structrure.

directional dependence of mass isn't as strange as it might first appear, since we already see similar effects in solid-state physics. But you're drawing a good parallel here.

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