What fixes periodicity seen in ARPES?

[sam_bell]

Hi. I know ARPES is supposed to show the k-space resolved density of states within the BZ. But sometimes the correct BZ is not so obvious. Take for instance La₂Mn₂O₆. If you ignore the magnetism, then you would choose one BZ and get one set of bands. If you now turn the magnetism on, and continue to use the same zone, k would no longer be a good quantum number and the bands would show some disperson. This is apparently what is seen in the ARPES experiment. However, I might have chosen the double my unit cell to incorporate the lower periodicity due to the anti-ferromagnetic ordering. Then my BZ would shrink, k would again become a good quantum number, and there would be many more bands than in the original picture.

What determines which one ARPES sees?

 

[OhYoungLions]

I don't know much about ARPES, but I think you have a misconception about what is a good or bad quantum number. When you choose a different cell, it only rescales or rotates the k-vectors, so their goodness or badness has nothing really to do with the particular choice of BZ.

In other words, I'd claim that a redefinition of the BZ cannot affect any of the properties of the band (like the effective quasiparticle weight or sharpness of the ARPES features). It's really simply a labeling scheme.

Can you say more about the experiment, or give a reference?

 

[sam_bell]

I agree with you, but I didn't explain myself clearly. The example I gave is in this short paper by W. Ku et al: http://arxiv.org/pdf/1002.4218v1.pdf, figure on last page. The periodicity of La₂Mn₂O₆ in the nonmagnetic and the antiferromagnetic phase differ. In the AFM case, the size of the primitive cell is double, so it's really La₄Mn₄O₁₂. k is a good quantum number (for either phase) in the BZ of the doubled cell. The "normal" BZ (from the nonmagnetic phase) is twice as large, and k is a good quantum number for THAT phase. Now, you can still adopt the BZ of the nonmagnet to describe the antiferromagnet. In that case you define the Bloch spectral function A(k,E). It's the density of states resolved in E and k, and then folded back in the BZ: A(k,E) = sum( recip. vector K, n(E, k + K) ) = sum(K, -1/pi Imag G(k+K,k+K,E). They look like the original nonmagnetic bands, but with dispersion in k. If you look at the 1st page of that paper, they mention that a supercell can result in "bands that no longer resemble the original band structure or the experimental ARPES".

ah, ok. well ... What decides what the ARPES sees in the 1st place?

 

[ZapperZ]

I'm not sure if I've understood you correctly.

In case of ARPES, I'm not sure what the problem is. It doesn't care if "k" is a good quantum number or not, because you get what you're supposed to get, i.e. the momentum of the emitted electrons.

Now, if you are asking how to interpret what you see, then that's a different issue that will require that you know what's going on. Note that if the BZ or the Fermi level changes, you will see the different in the ARPES signal, especially if you are collecting a 2D E vs. k spectroscopy, i.e. you will see the change in the dispersion.

Zz.

 

[sam_bell]

Ok, I think I have some idea now. The raw data coming out of ARPES (for a given material) never changes. However, there is freedom in the way you reorganize and plot the data. You might choose a lower periodicity than that of the material (supercell with many sharp bands), or higher periodicity (large BZ with a few dispersed bands). I still don't know how they do that (so I'm not REALLY sure of what I'm saying), but this would clear up my confusion.

Thanks Zz and OhYoungLion