I have calculated phonon frequencies of 2D sheet by analytical, classical solution as what we learned from basic solid state texts.
But I have complex values for frequencies out of Gama point.
Have these values any meaning or it may be a calculation mistake?
Dear Narges,
The complex values of the phonon frequeny is wrong, perhaps you have forgotten to calculate the modulus of the last harmonic oscillator lattice frequency.
In general, an image part of the frequency signifies a decay., some sort of friction. However, if there is no energy exchange between various subsystems (for example, between phonons and electrons), then a complex value simply marks an error. I guess, this is indeed the case if I understand correctly the meaning of "classical solution".
I mean classical solution as what we learned in solid state physic books as Gupta or Ashcroft ....
I represented my sheet as "masses and springs" and have find the frequency from energy equation.
In fact the result is square of frequency and out of Gamma point I have complex values.
Dear Narges,
Imagine one-phonon model: a spring fixed at the top, and mass connected at the spring bottom. One friquency; and you may include friction in the model by damping element (Newtonian dampfer: Force~Viscosity x Deformation time derivative) in-parallel to the spring. For small viscosity you may find complex frequency. Try to play with more than two phonons' model: two masses connected with a spring, and two springs fixing this pair to the top and to the bottom. Dampfer (s) may be connected in parallel to each spring. If in series, it will be Voigt-Maxwell model. So much fun mechanics! Even nonlinear effects in relaxation for 5-10 element chain. A lot of in the 2D and 3D networks! May be you will find smth in
Data BookKobelevEnglish
Best wishes,
A Kobelev
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