Institute of
Solid State Physics
TU Wien

Group of Karsten Held


woptic: optical conductivity with Wannier functions and adaptive k-mesh refinement

E. Assmann, P. Wissgott, J. Kuneš, A. Toschi, P. Blaha, and K. Held, arXiv:1507.04881 (to appear in Computer Physics Communications)

WOPTIC calculates the optical conductivity of interacting systems in a maximally-localized Wannier basis from the expression

σαβ(Ω)=e2ℏ/(2π)2∫d3k∫dω w(ω;Ω)tr[A(k,ω)Vα(k)A(k,ω+Ω)Vβ(k)]

where σαβ(Ω) is the (α,β) element of the optical conductivity tensor (α,β∈{x,y,z} at external frequency Ω, w(ω;Ω)=[f(ω)−f(ω+Ω)]/Ω is a weight in terms of the Fermi functions f, A=i(G−G)/(2π) the generalized spectral function, and Vα the group velocity in direction α. The numerical bottleneck in evaluating σαβ is the k-summation, since usually many k-points are required to obtain converged results.

WOPTIC is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License. In addition, we ask that you cite

Comp. Phys. Commun. (2015, in print) [also available at arXiv:1507.04881]

in any publication arising from the use of WOPTIC.

WOPTIC is built on top of WIEN2kWIEN2WANNIER, and Wannier90. It consists of two main programs: woptic_main, which calculates the optical conductivity, and refine_tetra, where the k-mesh is refined; as well as several smaller support programs. The individual programs are normally called by means of the driver script woptic. WOPTIC was written by P. Wissgott and E. Assmann, who is also the current maintainer.


WOPTIC can be downloaded at GitHub. The user guide and E. Assmann's Ph.D. thesis contain further information.


  • Many-body calculations: WOPTIC can incorporate a many-body self-energy Σ(ω), e.g. from DMFT. "Uncorrelated" bands not treated in DMFT can be included as an outer window.
  • Adaptive integration: The contributions to σαβ are often sharply peaked in k-space. WOPTIC employs an adaptive tetrahedral grid for efficient Brillouin-zone integration.
  • Full dipole matrix elements: Often, the band velocities Vα are approximated by k-derivatives of the bandstructure. WOPTIC uses the full matrix elements as calculated by WIEN2k's optic module.