[Pw_forum] Convergence of imaginary modes

Stefano Baroni baroni at sissa.it
Mon Jun 27 17:09:30 CEST 2011

Dear Brad & Nicola,

I was going to reply to Brad, when I noticed that Nicola already did so, and quite appropriately. Let me just elaborate a little bit on Nicola's remarks.

The reason why Kohn anomalies require so many k-points to be properly captured on a computer is the same why they are so sensitive to temperature in nature. They are due to different portions of the Fermi surface to be quasi-parallel (i.e. connected by a same q vector, the "nesting" vector). By the way, this is why Kohn anomalies are more important on low dimensions: the lower the dimension, the easier it is to have nesting. When this occurs, perturbations with the periodicity of the nesting vector will be strongly screened, hence phonons with that periodicity will be soft or "quasi soft". When the temperature increases, the Fermi surfaces becomes "blurred", and the very concept of nesting breaks down. Computationally, in a metal the energy smearing (Gaussian or other) plays the role of an effective temperature. The smaller the smearing, the larger the number of k-points necessary to sample the Brillouin zone to an energy resolution compatible with the smearing.

An early paper studying a system where these effects show dramatically is:

Claudia Bungaro et al. PRL 77, 2491 (1996) http://link.aps.org/doi/10.1103/PhysRevLett.77.2491
You may also find Claudia's PhD thesis worth some attention: http://www.sissa.it/cm/thesis/1995/bungaro.ps.gz

Hope this may help.


On Jun 27, 2011, at 8:01 AM, Brad Malone wrote:

> Dear Nicola,
> Thanks so much for your suggestion; I was not aware of this characteristic of Kohn anomalies. I will look into some of those papers (a quick glance at them already suggests that they may be useful). My smearing is pretty "standard" for metallic systems at 0.03 Ry, and so I will look into the possible presence of a Kohn anomaly in the system.
> Best,
> Brad 
> UC Berkeley
> Dear Brad,
> if you have a Kohn anomaly it's not unusual to require that high
> of a k-point sampling - comparable numbers are needed to converge
> some of the optical modes in graphene/graphite (do check some of
> the early papers of Mauri/Lazzeri).
> I haven't heard of other cases where such high-sampling is needed
> for phonons, unless your system was a metal, and you were not using
> a smearing scheme (or way too small a smearing).
>                        nicola
> --
> ----------------------------------------------------------------------
> Prof Nicola Marzari    Department of Materials    University of Oxford
> Chair of Materials Modelling  Director, Materials Modelling Laboratory
> nicola.marzari at materials.ox.ac.uk     http://mml.materials.ox.ac.uk/NM
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Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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