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, opens an external URL in a new window (to appear in Computer Physics Communications)

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

\(\sigma_{\alpha\beta}\left(\Omega\right)=\frac{e^2\hbar}{\left(2\pi\right)^2}\int d^3k\int \omega\; w(\omega;\Omega)\text{tr}\left[A\left(k,\omega\right)v^\alpha\left(k\right)A\left(k,\omega+\Omega\right)v^\beta\left(k\right)\right]\;,\)

where \(\sigma_{\alpha\beta}\left(\Omega\right)\) is the \(\left(\alpha,\beta\right)\) element of the optical conductivity tensor \(\alpha,\beta \in \{x,y,z\}\) at external frequency \(\Omega\), \(w\left(\omega;\Omega\right)=\left[f(\omega)-f(\omega+\Omega)\right]/\Omega\) is a weight in terms of the Fermi functions \(f\), \(A = I \left(G-G^\dagger\right)/\left(2\pi\right)\) the generalized spectral function, and \(v^\alpha\) the group velocity in direction \(\alpha\). The numerical bottleneck in evaluating \(\sigma_{\alpha\beta}\) 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, opens an external URL in a new window. In addition, we ask that you cite Comp. Phys. Commun. (2015, in print) [also available at arXiv:1507.04881, opens an external URL in a new window] in any publication arising from the use of WOPTIC.

WOPTIC is built on top of WIEN2k, opens an external URL in a new window, WIEN2WANNIER, opens in new window, and Wannier90, opens an external URL in a new window. 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, opens an external URL in a new window.

Download

WOPTIC can be downloaded at GitHub, opens an external URL in a new window. The user guide, opens an external URL in a new window and E. Assmann's Ph.D. thesis, opens an external URL in a new window contain further information.

Features

• Many-body calculations: WOPTIC can incorporate a many-body self-energy \(\Sigma(\omega)\), e.g. from DMFT. "Uncorrelated" bands not treated in DMFT can be included as an outer window.

• Adaptive integration: The contributions to \(\sigma_{\alpha\beta}\) 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 \(v^\alpha\) are approximated by k-derivatives of the bandstructure. WOPTIC uses the full matrix elements as calculated by WIEN2k's optic module.