[gpaw-users] Intraband contributions in dielectric function calculations

[Thomas Olsen]

Dear Sharmila



The intraband contributions to the response are included by the "standard" response code at any finite q. The code does not really distinguish between intraband and interband, but simply adds contributions from pairs of occupied and unoccupied states. However, q=0 is a limiting case where special care must be taken and an extra term appears, which is essentially a Fermi surface integral of the band velocities.



BR

Thomas



________________________________
Fra: gpaw-users-bounces at listserv.fysik.dtu.dk [gpaw-users-bounces at listserv.fysik.dtu.dk] på vegne af Sharmila Shirodkar [sharmila.shirodkar86 at gmail.com]
Sendt: 23. marts 2016 19:50
Til: gpaw-users at listserv.fysik.dtu.dk
Emne: [gpaw-users] Intraband contributions in dielectric function calculations

Dear All

I have looked through the pair.py and chi0.py files in gpaw/response folders.
The condition for adding intraband contributions to the dielectric or response matrix
is given by

optical_limit = not self.no_optical_limit and np.allclose(q_c, 0.0) ------ (1)

Implying that the intraband contributions are added only when q_c = (0,0,0).
Hence the dielectric matrix only contains the interband transitions.
However, the paper "Plasmons in metallic monolayer and bilayer transition metal dichalcogenides",
Andersen et al, PHYSICAL REVIEW B 88, 155128 (2013) does report plasmon dispersion with intraband contributions at non-zero q_c.

I also changed the condition (1) to

optical_limit = not self.no_optical_limit and self.intraband ----- (2)

And made appropriate changes to chi0.py and pair.py files to accommodate condition (2), as given below.

A) In chi0.py
    Line 139
    replace  if np.allclose(q_c, 0.0):
    with   if self.intraband:

    Line 167
    replace optical_limit = not self.no_optical_limit and np.allclose(q_c, 0.0)
    with   optical_limit = not self.no_optical_limit and self.intraband

B) In pair.py
    Line 757
    replace optical_limit = not disable_optical_limit and np.allclose(q_c, 0.0)
    with      optical_limit = not disable_optical_limit and intraband #SHARMILA

    Line 916
    replace assert np.allclose(pd.kd.bzk_kc[0], 0.0)
    with assert np.allclose(0.0, 0.0)

However, I was unable to reproduce the results of the above mentioned paper.
I observe that potential of the eigenmodes have a curvature (implying that charge is not conserved, rho is non-zero (0.005) in vacuum).
Please find the plots of potential and charge density (rho) of the plasmon eigenmodes attached to this email.

Any advice will be appreciated.

Best Regards
Sharmila Shirodkar

Postdoctoral Research Fellow
SEAS, Harvard University
Cambridge, MA 02138
USA






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