I have been trying to calculate the phonon dispersion of a 2d structure using Pwscf code. Dynamical matrices have been calculated with 4x4x1 mesh. Then I have used 'q2r.x' and 'matdyn.x' to get the phonon dispersion curves. The structure of the unit cell is orthorhombic and the high symmetric kpoint path is G-Y-S-X-G. Now If I look at the dispersion curve, the frequencies at Gamma(G) point ( approaching from G-Y, i.e along y-axis in reciprocal space) is different from the frequencies at Gamma(G) point (approaching from X-G, i.e along x-axis in reciprocal space). How can frequency be different at Gamma point? Though I have got positive frequency at any k-points after execution of 'matdyn.x'. What could be the reason for getting different frequency at Gamma point?
The frequency of the acoustic modes at the Gamma point is usually 0 irrespective of directions.
Even if we are talking about the optical modes, the frequencies should match irrespective of the direction.
I have attached a phonon dispersion for black phosphorene which is also a 2D orthorhombic structure for your reference.
However, since there is no additional information regarding your calculation, I am assuming that you have made a mistake in the process.
http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/Articleimage/2015/CP/c4cp04858j/c4cp04858j-f2_hi-res.gif
in polar materials the long range nature of Coulomb interaction makes the dynamical matrix non analytical in the q->0 limit. This originates the so called LO-TO splitting.
In cubic semiconductors this splitting is such that the LO frequency is direction independent but in systems of low enough symmetry the dielectric response and the effective charges tensors are not simply multiples of the identity. Hence the LO (and TO) frequencies may depend on the
direction of approach to the gamma point.
see for instance the phonon dispersion in wurtzite semiconductors
Bungaro and de Gironcoli, "Ab initio study of phonons in wurtzite AlxGa1-xN alloys", Applied Physics Letters 76, 2101-2103 (2000),DOI: 10.1063/1.126268
Well, in ansiotropic structures already the limiting frequency value of the TO mode(s) can depend on the direction along which one approaches the center of the Brillouin zone. This I know from my ab-initio phonon calculations of wurtzite GaN and AlN; there one has different values for the A1(TO) and E1(TO) mode symmetries for in-plane propagation. Have a look at my PhD thesis for the details: https://www.researchgate.net/publication/283271282_Structure_and_Lattice_Dynamics_of_GaN_and_AlN_Ab-Initio_Investigations_of_Strained_Polytypes_and_Superlattices
Thesis Structure and Lattice Dynamics of GaN and AlN: Ab-Initio Inv...
In spite the phonon wave vector tend to zeo, it is still be finite in its direction. Consequently the dielectric function depending on q and frequency will be strongly dependent on the direction of q because of the anistropic nature of the studied material.
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