Athaesos02: Scientific background



CECAM PSI-k WORKSHOP

Ab initio Theoretical Approaches to the Electronic Structure and Optical Spectra of Materials

SCIENTIFIC BACKGROUND

The recent development of new methods for the calculation of excited states constitutes a breakthrough that allows to tackle complex problems with novel, powerful tools. In the past five years, many difficulties of the theoretical foundations have been solved. As an example, the ingredients necessary to calculate form first-principles the optical spectrum of materials as "simple" as bulk silicon, have been identified and implemented in sophisticated codes only recently [1,2].

The existence of user-friendly codes and the accessibility of high performance computing capacities has allowed density-functional theory [3] to be used as a standard tool in research and development for systems of high technological and industrial interest. The fact that electronic excitations are not accessible in this scheme --- for instance, the nonlocal and dynamic self-energy must be calculated to evaluate quasiparticle energies instead of using Kohn-Sham eigenvalues --- has stimulated the search for alternative theoretical approaches.

Green-function approaches for the self-energy and the electron-hole two-particle propagator have been developed in the solid-state community. The evaluation of the self-energy is based on Hedin's GW approximation [4], which has been highly successful in predicting single-particle spectra [5]. The quasiparticle energies alone are not sufficient to obtain a correct description of the photoabsorption spectrum, however, because the electron-hole interaction leads to the appearance of bound or resonant excitons. A realistic many-body descriptions of two-particle excitations is achieved through higher Green functions, and excitonic effects can be evaluated [1,2].

Time-dependent density-functional theory (TDDFT) [1,6], originating from the chemistry and nuclear physics communities, is a promising, computationally efficient alternative for the calculation of optical spectra with neutral excitations, because the exchange-correlation potential and kernel depend only on the density. Significant advances [7] have recently been made regarding their exact properties.

The systems of interest have evolved from simple atoms or the homogeneous electron gas to complex systems like nanostructures and surfaces. As a consequence, in both approaches fundamental questions have appeared that still remain unanswered. In particular, the high precision of modern implementations shows an increasing need for conceptual advances beyond the established GW approximation. This, in turn, requires a detailed assessment of the interplay of self-consistency and vertex corrections in the self-energy [8], which to date remains only partially understood.

Another point is the application of many-body techniques in ground-state calculations, which also has a direct bearing on the construction of realistic and truly ab initio exchange-correlation kernels for TDDFT. Furthermore, the apparent success of simple TDDFT schemes for the optical spectra of finite systems contrasts with the need for infinite systems to take the full electron-hole interaction into account and deserves further clarification.

Finally, it is now possible to make reliable interpretations of experiments such as photoemission (single and two-photon, inverse and femtosecond time-resolved), photoabsorption [9] , electron-energy-loss spectroscopy [10] , X-ray absorption [11] or scanning-tunneling microscopy [12]. Inclusion of new physical effects, such as the excitation of the phonons in core photoemission spectra [13], need to be investigated.


Activities in the field of ab initio theoretical approaches to the electronic structure and optical spectra of materials have much benefited from the previous workshops on
Excited Electrons in Molecules, Solids and Atoms (CECAM, 1997),
Spectroscopy of Electronic Excitations in Materials (Valladolid, 1998),
Calculation of Electronic Excitations in Finite and Infinite Systems (CECAM, 1999) and
Excited States and Electronic Spectra (CECAM, 2000),
organised by Giovanni Onida, Angel Rubio, and Lucia Reining.
After an intermission in 2001, the present workshop continues this series with a new team of organisers. We expect that the relatively informal atmosphere of a CECAM workshop will lead to an intense and stimulating exchange of ideas.

Our motivation for organising this workshop is threefold :

The solution of the open questions described above, demands further discussions between people with different experience and points of view. This workshop brings together a majority of scientists using either Green's functions methods or TDDFT for the calculation of electronic excitations.
The invited scientists are encouraged to disseminate their experience on applications that could be handled with our methods in the future, like excitonic effects in nanostructures [14] or the excitation energies in correlated oxydes [15].
The workshop is essential for maintaining links among researchers with traditionally different backgrounds. The latter point has contributed significantly to the formation of a strong community and has been invaluable for the development of this field during the last years.

REFERENCES

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

[2] S. Albrecht et al., Phys. Rev. Lett. 80, 4510 (1998); L. X. Benedict et al., Phys. Rev. Lett. 80, 4514 (1998); M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 81, 2312 (1998)

[3] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

[4] L. Hedin, Phys. Rev. 139, 796 (1965).

[5] M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. 55, 1418 (1985); Phys. Rev. B 34, 5390 (1986); R. W. Godby et al., Phys. Rev. Lett. 56, 2415 (1986); Phys. Rev. B 37, 10159 (1988).

[6] E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); M. Petersilka et al., Phys. Rev. Lett. 74, 872 (1995); Phys. Rev. Lett. 76, 1212 (1996).

[7] G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996); K. Capelle and E. K. U. Gross, Phys. Rev. Lett. 78, 1872 (1997); R. van Leeuwen, Phys. Rev. Lett. 76, 3610 (1996); Phys. Rev. Lett. 82, 3863 (1999); X. Gonze and M. Scheffler, Phys. Rev. Lett. 82, 4416 (1999); I. V. Tokatly and O. Pankratov, Phys. Rev. Lett. 86, 2078 (2001).

[8] F. Aryasetiawan et al., Phys. Rev. Lett. 77, 2268 (1996); M. Springer et al., Phys. Rev. Lett. 80, 2389 (1998); W.-D. Schöne and A. G. Eguiluz, Phys. Rev. Lett. 81, 5374 (1998).

[9] I. Campillo et al., Phys. Rev. Lett. 83, 2230 (1999); A. G. Borisov et al., Phys. Rev. Lett. 86, 488 (2001).

[10] A. Franceschetti et al., Phys. Rev. B 60, 1819 (1999); T. Miyake et al., Phys. Rev. B 61, 16941 (2000).

[11] W. Ku and A. G. Eguiluz, Phys. Rev. Lett. 82, 1995 (1999); S. Waidmann et al., Phys. Rev. B 61, 10149 (2000).

[12] E. L. Shirley, Phys. Rev. Lett. 80, 794 (1998).

[13] J. N. Andersen, T. Balasubramanian, C.-O. Almbladh, L. I. Johansson, and R. Nyholm, Phys. Rev. Lett. 86, 4398 (2001); S. de Gironcoli et al., in preparation.

[14] J. Shumway, A. Franceschetti, and A. Zunger, Phys. Rev. B 63, 155316 (2001).

[15] N. Suaud and M.B. Lepetit, Phys. Rev. B 62, 402 (2000).

Main page Information for participants Workshop programme Scientific Background Practical information