# Schools

## GW quasiparticle calculations in condensed matter physics and nanoscience

### Organisers

- Paolo Umari
*(University of Padova, Italy)* - Andrea Marini
*(National Research Council, Rome, Italy)* - Angel Rubio
*(University of the Basque Country, San Sebastian, Spain)* - Feliciano Giustino
*(University of Oxford, United Kingdom)*

### Supports

### Description

Therefore we will address several non-standard applications of the GW method like the calculation of the electronic lifetimes or total-energies. In addition the numerical procedures that define the basis of a successful GW calculation will be extensively discusses. We will dedicate specific lectures to choice of an accurate sampling of the Brillouin Zone, especially in low-dimensional systems like nano-structures that represent an important class of systems studied in the scientific community. We will also discuss the impact of the used basis (plane-waves versus localized basis) and the impact of pseudo-potentials versus all-electrons calculations.

More specific lectures will be developed to the problem of self-consistency, vertex corrections and total-energies evaluation in the GW method. These theoretical aspects will provide the students a more general view on the formal justifications, as well on the most up-to-date developments of the GW theory.

Besides theoretical and technical lectures (preferably in the morning) the tutorial will characterized by long hands-on sessions (in the afternoon) where the students will perform calculations on realistic materials following pre-organized tutorials[14]. During and after these hands-on sessions the students will have the possibility of discussing with the teachers about any aspect of the tutorial. These interactions will be particularly meaningful as the teachers of the hands-on sessions will be the main developers of the code used. We also plan to encourage the students, after the completion of the proposed hands-on exercises, to initiate small projects from their own.

Indeed a particularly valuable aspect of this tutorial is that two out of the four organizers (A. Marini and P. Umari) are the developers of two of the code used: Yambo7 and GWL6. These codes adopt a starting formalism based on plane-waves and pseudopotentials, used to describe the core and valence electrons. Moreover, both codes can perform MBPT calculations starting from DFT calculations performed using the Quantum-Espresso package [4] that we will use to to calculate the ground-state wave-functions using Density-functional Theory.

Yambo is a widely used GW code. Based on a plane-have expansion for wave-functions and operators, it offers a large range of capabilities. It is freely available through the GNU license. GWL is a more recent code which is based on optimized basis sets for representing operators in order to accelerate calculations in particular for isolated and non-crystalline systems. Within 2011 it will be fully available through the GNU license.

In addition to Yambo and GWL we will also use the FHI-aims[11] code.

### References

[1] Electronic excitations: density-functional versus many-body Green's-function approaches

G. Onida, L. Reining and A. Rubio, Rev. Mod. Phys. 74, 601 (2002).

[2] F. Giustino, M. L. Cohen, S. G. Louie, Phys. Rev. B 81, 115105 (2010).

[3] P. Umari, G. Stenuit, S. Baroni, Phys. Rev. B. 79, 201104R (2009); P. Umari,

G. Stenuit, S. Baroni, Phys. Rev. B. 81, 115104 (2010)

[4] J. Berger et al, Phys. Rev. B. 041103, 82 (2010).

[5] F. Bruneval and X. Gonze, Phys. Rev. B. 085125, 78 (2008)

[6] The GWL code, gww.qe-forge.org

[7] QUANTUM ESPRESSO: a modular and open-source software project for

quantum simulations of materials P. Giannozzi et al.

J. Phys. Condens. Matter 21, 395502 (2009). www.quantum-espresso.org

[8] ABINIT : First-principles approach of materials and nanosystem properties.

X. Gonze et al.,, Computer Phys. Commun. 180, 2582 (2009). www.abinit.org

[9] Efficient iterative schemes for ab initio total-energy calculations using a

plane-wave basis set, G. Kresse, J. Furthmüller,

Computational Materials Science 6, 15 (1996). http://cms.mpi.univie.ac.at/marsweb/

[10] Yambo: an ab initio tool for excited state calculations Andrea Marini, Conor Hogan,

Myrta Grüning, Daniele Varsano Comp. Phys. Comm. 180, 1392 (2009).

www.yambo-code.org

[11] Ab initio molecular simulations with numeric atom-centered orbitals,

Volker Blum, Ralf Gehrke, Felix Hanke, Paula Havu, Ville Havu, Xinguo Ren,

Karsten Reuter, and Matthias Scheffler,

Computer Physics Communications 180, 2175 (2009). https://aimsclub.fhi-berlin.mpg.de/

[12] The GW method, F Aryasetiawan and O Gunnarsson,

Reports on Progress in Physics 61, 237 (1998).

[13] B.-C- Shih, Y. Xue, P. Zhang, M.L. Cohen, S. Louie, Phys. Rev. Lett.105, 146401 (2010).

[14] See, for example, the Yambo tutorials available at http://www.yambo-code.org/tutorials/